Heat Transfer. Introduction. Heat Transfer

Size: px
Start display at page:

Download "Heat Transfer. Introduction. Heat Transfer"

Transcription

1 Heat Transfer Heat Transfer Introduction Practical occurrences, applications, factors affecting heat transfer Categories and modes of heat transfer Conduction In a slab and across a pipe Convection Free (natural) and forced (in a pipe and over a solid object) Determination of convective heat transfer coefficient (h and h fp ) Radiation Thermal resistances to heat transfer Overall heat transfer coefficient (U) Steady state heat transfer In a tubular heat exchanger (without and with insulation) Dimensionless numbers in heat transfer Steady: Reynolds #, Prandtl #, Nusselt #, Grashof #; Unsteady: Fourier #, Biot # Unsteady state heat transfer For conduction/convection driven heat transfer; Heisler chart 2 Introduction 3 1

2 Practical Occurrences Is a metallic park bench colder than a wooden park bench? What is wind-chill factor? What is heat index? Why dress in layers during winter? How does a fan provide cooling effect? Does it blow cold air? What is the insulation used in houses? Is it for winter or summer? Why does our skin dry-up in a heated room? What time of the day and why do we get sea-breeze? Why are higher altitude places colder? Does hot water freeze faster than cold water? In winter, do hot or cold water pipes burst first? What is greenhouse effect? What is the principle behind it? Can you lose weight by drinking cold water? Why are fins present on the outside of the radiator of a car? Bridge freezes before road -- Why? Why is salt used to melt ice on the road? When is sand used? How does an igloo keep an Eskimo warm? Why do you see cars breakdown or pull over to the shoulder of a highway during traffic jams? Do traffic jams cause breakdowns or do breakdowns cause traffic jams? 4 Heat Transfer in Various Industries Automobile: Radiator and engine coolant Electronics: Cooling of motherboard/cpu by fan Pharmaceutical: Freeze drying of vaccines Metallurgical: Heating/cooling during steel manufacture Chemical: Condensation, boiling, distillation of chemicals Home: Refrigerator, AC, heater, dryer, stove, microwave 5 Heat Transfer in the Food Industry Melting: Thawing of a frozen food (turkey) Freezing: Freezing of ice-cream mix Drying: Drying of fruits Evaporation: Spray drying of coffee or concentration of juices Sublimation: Freeze drying of coffee Heating/cooling of milk Baking of bread Processing of canned soups (inactivate microorganisms & maximize nutrient content, color/flavor/texture) 6 2

3 What Factors Affect Rate of Heat Transfer? Thermal Specific heat (c p in J/kg K) Measured using Differential scanning calorimeter (DSC) Thermal conductivity (k in W/m K) Measured using Fitch apparatus or thermal conductivity probe (Lab #5) Physical Density ( in kg/m 3 ) Measured using pycnometer Rheological (measured using rheometer/viscometer) Viscosity ( in Pa s) for Newtonian fluids OR Consistency coefficient (K in Pa s n ) and flow behavior index (n) for power-law fluids Note: Thermal diffusivity ( = k/ c p in m 2 /s) combines the effect of several factors 7 Specific Heat, Thermal Conductivity, and Thermal Diffusivity Specific heat (c p ) A measure of how much energy is required to raise the temperature of an object Thermal conductivity (k) A measure of how quickly heat gets conducted from one part of an object to another Thermal diffusivity ( ) It combines the effects of specific heat, thermal conductivity, and density of a material. Thus, this one quantity can be used to determine how temperature changes at various points within an object. 8 Specific Heat (DSC Method) Heat flux held constant & temperature diff. measured Q = m 1 c p(1) ( T 1 ) = m 2 c p(2) ( T 2 ) c p(2) = {m 1 /m 2 } {( T 1 )/ ( T 2 )} c p(1) Differential Scanning Calorimeter (DSC) Manufacturer: Perkin-Elmer 9 3

4 Thermal Conductivity (Fitch Apparatus) Sample (cheese slice) Heat Sink (copper block) Heat Source (ice-water mix) Q Insulation This can be rewritten as: t: time m, c p, A, T: For heat sink (mass, sp. ht., area, temp.) T i : Initial temp. of heat sink T : Temp. of heat source L: Thickness of sample Y Slope Intercept X Plot on y-axis versus t on x-axis & set intercept = 0 Slope = -ka/(m c p L); Solve for k: k = - (Slope) (m c p L)/A Note: k is always a positive number 10 Thermal Conductivity Probe KD2 Pro Probe (Manufacturer: Decagon Devices) Single needle probe: Can measure k Dual needle probe: Can measure k and = k / ( c p ) Sample Sample k: Thermal conductivity (W/m K); : Thermal diffusivity (m 2 /s) : Density (kg/m 3 ); c p : Specific heat (J/kg K) 11 Values of Thermal Conductivity (k) Good conductors of heat have high k values Cu: 401 W/m K Al: 250 W/m K Fe: 80 W/m K Stainless steel: 16 W/m K Insulators have very low (but positive) k values Paper: 0.05 W/m K Cork, fiberglass: 0.04 W/m K Cotton, styrofoam, expanded polystyrene: 0.03 W/m K Air: W/m K (lower k than insulators!) Foods and other materials have intermediate to low k values Foods: 0.3 to 0.6 W/m K (water: ~0.6 W/m K at room temperature) Glass: 1.05 W/m K; Brick: W/m K; Concrete: W/m K Plastics (commonly used): W/m K Thermally conductive plastics may have k > 20 W/m K 12 4

5 Empirical Correlations c p = (X w ) (X p ) (X c ) (X f ) (X a ) Heldman & Singh, 1981 k = 0.61 (X w ) (X p ) (X c ) (X f ) (X a ) Choi & Okos, 1984 w: water, p: protein, c: carbohydrates, f: fat, a: ash 13 Effect of Temperature on k,,, c p ) 14 Questions Q: When the same heating source is used to heat identical quantities of water and butter, which will be hotter after a certain time? Ans: Butter; because it has a lower specific heat Q: In winter, is a metallic park bench colder than a nearby wooden park bench? Ans: NO. A metallic bench has a higher thermal conductivity and hence conducts heat very well, thereby taking away the heat generated by our body very fast and making us feel colder. 15 5

6 Categories of Heat Transfer Steady state Temperatures at all points within the system remain constant over time The temperatures at different locations within the system may be different, but they do not change over time Strictly speaking, steady state conditions are uncommon Conditions are often approximated to be steady state Eg.: Temperature inside a room or refrigerator Unsteady state Temperature(s) at one or more points in the system change(s) over time Eg.: Temperature inside a canned food during cooking 16 Modes of Heat Transfer Conduction Translation of vibration of molecules as they acquire thermal energy Occurs in solids, liquids, and gases Heat transfer from hot plate to vessel/pot Heat transfer from surface of turkey to its center Convection Fluid currents developed due to temp. differences {within a fluid (liquid/gas) or between a fluid and a solid} or the use of a pump/fan Occurs in liquids and gases Heat transfer from hot vessel/pot to soup in it Radiation Emission & absorption of electromagnetic radiation between two surfaces (can occur in vacuum too) Occurs in solids, liquids, and gases Radiation from sun; reflective thermos flask; IR heating of buffet food 17 Conduction 18 6

7 Basics of Conduction Conduction involves the translation of vibration of molecules along a temperature gradient as they acquire thermal energy (mainly analyzed within solids; however, it takes place in liquids and gases also) Actual movement of particles does not occur Good conductors of electricity are generally good conductors of heat Thermal conductivity (k) is used to quantify the ability of a material to conduct heat 19 Fourier s Law of Heat Conduction Rate of heat transfer by conduction is given by Fourier s law of heat conduction as follows: Q = - ka ( T/ x) The negative sign is used to denote/determine the direction of heat transfer (Left to right or right to left) Q: Energy transferred per unit time (W) k: Thermal conductivity (W/m K); it is a +ve quantity A: Area of heat transfer (m 2 ) T: Temperature difference across the ends of solid (K) x: Distance across which heat transfer is taking place (m) Q/A: Heat flux (W/m 2 ) 20 Temperature Difference Across a Slab Slab: Q = ka ( T/ x) T = T 1 T 2 Heat flow For the same value of Q (example: use of a heater on one side of a slab), For insulators (low k), T 1 T 2 is large For good conductors (high k), T 1 T 2 is small For the same value of T 1 T 2 (example: fixed inside temperature of room and outside air temperature), For insulators (low k), Q is small For good conductors (high k), Q is large T 1 T 2 x Note: x and A are assumed to be the same in all of the above situations 21 7

8 Conduction Across a Slab or Cylinder Slab: Q = ka ( T/ x) Heat flow T 1 x T 2 Cylinder: Q = ka lm ( T/ r) r T 1 T 2 Heat flow k: Thermal conductivity (W/m K) A: Area across which heat transfer is taking place (m 2 ) T = T 1 T 2 : Temperature difference (K) A lm : Logarithmic mean area (m 2 ) 22 Logarithmic Mean Area (A lm ) r T 1 T 2 Heat flow r r o i L Slab: Area for heat transfer is same at both ends Cylinder Area at one end (outside) is A o (= 2 r o L) Area at other end (inside) is A i (= 2 r i L) Which area should be used in determining Q? A lm = (A o A i ) / ln (A o /A i ) = 2 L (r o r i ) / [ln (r o /r i )] Note: A o > A lm > A i 23 Logarithmic Mean Temp Diff ( T lm ) T w(o) T p(i) Double Tube Heat Exchanger Hot water T 1 T 2 Product T w(i) T p(o) T is NOT constant across the length of tube T 1 = T w(o) T p(i), T 2 = T w(i) T p(o) T lm = ( 1 2 ) / [ln ( 1 / 2 )] Note: T lm lies between T 1 and T 2 Subscripts: w for water; p for product, i for inlet, o for outlet 24 8

9 Convection 25 Basics of Convection It involves transfer of heat by movement of molecules of fluid (liquid or gas) due to Temperatures differences within a fluid or between a fluid and a solid object OR An external agency such as a pump or a fan Convection is a combination of Diffusion (Microscopic/molecular level) Random Brownian motion due to temperature gradient Advection (Macroscopic level) Heat is transferred from one place to another by fluid movement 26 Newton s Law of Cooling for Convection Rate of heat transfer by convection (for heating or cooling) is given by Newton s law of cooling as follows: Q = h A (T s -T ) Q: Energy transferred per unit time (W) h: Convective heat transfer coefficient -- CHTC (W/m 2 K) A: Surface area available for heat transfer (m 2 ) T = T s T : Temperature difference (K) T s : Surface temperature of solid object (K) T : Free stream (or bulk fluid) temperature of fluid (K) CHTC (h): Measure of rate of heat transfer by convection; NOT a property; depends on fluid velocity, surface characteristics (shape, size, smoothness), fluid properties (, k,, c p ) 27 9

10 Categories of Convection Free (or natural) convection Does not involve any external agency in causing flow Heat transfer between bottom of vessel and fluid in it Cooling of human body Cooling of radiator fluid in car engine during idling h air-solid : 5-25 W/m 2 K; h water-solid : W/m 2 K Forced convection External agency such as fan/pump causes flow Cooling of radiator fluid in car engine during motion Ice-cream freezer (Blast air) Stirring a pot of soup Heat transferred from computers (fan) h air-solid : W/m 2 K; h water-solid : 50-10,000 W/m 2 K h boiling water or steam to solid : 3, ,000 W/m 2 K 28 Free Convection Fluid comes into contact with hot solid Fluid temperature near solid increases Fluid density near solid decreases This results in a buoyancy force that causes flow Rate of heat transfer (Q & h) depends on Properties of fluid Dimensions of solid Temperature difference between fluid and solid N Nu = hd c /k f = f (N Gr, N Pr ) 29 Question Q: What is wind-chill factor? In winter, a thermometer reads -20 C when air is stationary. All of a sudden, a gust of wind blows. What will the thermometer read? Ans: -20 C. As wind speed increases, more heat is removed from our body due to an increase in h and hence Q. Thus, we feel colder than when the air is stationary. The air is NOT colder, we just feel colder since more heat is removed from our body and our body is unable to generate enough heat to replace the energy lost to the surroundings

11 Nusselt Number (N Nu ) h: Convective heat transfer coefficient (W/m 2 K) d c : Characteristic dimension (m) k f : Thermal conductivity of fluid (W/m K) Nusselt number represents a ratio of heat transfer by convection & conduction 31 Grashof (N Gr ) Number f : Coefficient of volumetric thermal expansion (K -1 ) g: Acceleration due to gravity (= 9.81 m/s 2 ) f : Density of fluid (kg/m 3 ) T s : Surface temperature of solid object (K) T : Free stream temperature of fluid (K) d c : Characteristic dimension of solid object (m) (Obtained from tables based on shape & orientation of solid object) f : Viscosity of surrounding fluid (Pa s) Grashof number represents a ratio of buoyancy and viscous forces 32 Prandtl Number (N Pr ) c p(f) : Specific heat of fluid (J/kg K) f : Viscosity of fluid (Pa s) k f : Thermal conductivity of fluid (W/m K) Prandtl number represents a ratio of momentum and thermal diffusivities 33 11

12 Properties of Air 34 Properties of Water 35 Free Convection (Plate) N Nu = hd c /k f = f (N Gr, N Pr ) N Nu = a (N Gr N Pr ) m ; N Ra = N Gr N Pr For vertical plate (d c = plate height) a = 0.59, m = (for 10 4 < N Ra < 10 9 ) a = 0.10, m = (for 10 9 < N Ra < ) For inclined plate (for N Ra < 10 9 ) Use same eqn as vertical plate & replace g by g cos in N Gr For horizontal plate (d c = Area/Perimeter) Upper surface hot a = 0.54, m = (for 10 4 < N Ra < 10 7 ) a = 0.15, m = (for 10 7 < N Ra < ) Lower surface hot a = 0.27, m = (for 10 5 < N Ra < ) 36 12

13 Free Convection (Cylinder) For vertical cylinder (d c = cylinder height) Similar to vertical plate if D 35L/(N Gr ) 0.25 For horizontal cylinder (d c = cylinder diameter) For 10-5 < N Ra < Free Convection (Sphere) For sphere, d c = D/2 Note 1: For all free convection situations, determine properties at the film temperature {T film = (T s + T )/2} unless otherwise specified Note 2: For all free convection scenarios, as the T between the fluid and surface of solid increases, N Gr increases. Thus, N Nu and h increase. 38 Forced Convection Fluid is forced to move by an external force (pump/fan) Rate of heat transfer (Q & h) depends on Properties of fluid Dimensions of solid h does NOT depend on Temperature difference between fluid and solid h strongly depends on Reynolds number When all system and product parameters are kept constant, it is flow rate (a process parameter) that strongly affects h N Nu = hd c /k f = f (N Re, N Pr ) 39 13

14 Categories of Convective Heat Transfer Coefficient for Forced Convection Between a moving fluid and a stationary solid object Transfer of heat from hot pipe to a fluid flowing in a pipe Generally depicted by h Between a moving fluid and a moving particle Transfer of heat from a hot fluid to a freely flowing particle in a suspension (particulate/multiphase food) Generally depicted by h fp 40 Forced Convection in a Pipe N Nu = hd c /k f = f (N Re, N Pr ) Three sub-categories of forced convection exist.. 1. Laminar flow (N Re < 2100) A. Constant surface temperature of pipe N Nu = 3.66 (for fully developed conditions) B. Constant surface heat flux N Nu = 4.36 (for fully developed conditions) C. Other situations (for entry region & fully developed) N Nu = 1.86 (N Re x N Pr x d c /L) 0.33 ( b / w ) Transitional flow (2100 < N Re < 4000) Friction factor (f) For smooth pipes: d c : ID of pipe, L: Length of pipe For non-smooth pipes, use Moody chart (graph of: f, N Re, /D) 41 Moody Diagram Friction Factor (f) Relative Roughness ( /D) Reynolds Number (N Re ) = 259 x 10-6 m for cast iron; x 10-6 m for drawn tubing; 152 x 10-6 m for galvanized iron; 45.7 x 10-6 m for steel or wrought iron 42 14

15 Forced Convection in a Pipe (contd.) 3. Turbulent flow (N Re > 4000) of a Newtonian fluid in a pipe, N Nu = (N Re ) 0.8 (N Pr ) 0.33 ( b / w ) 0.14 b: Viscosity of fluid based on bulk fluid temperature w : Viscosity of fluid based on wall temperature The term ( b / w ) is called the viscosity correction factor and can be approximated to 1.0 in the absence of information on wall temperature Note: For flow in an annulus, use same eqn with d c = 4 (A cs /W p ) = d io d oi d io : Inside diameter of outside pipe d oi : Outside diameter of inner pipe 43 h fp for Forced Convection over a Sphere N Nu = hd c /k f = f (N Re, N Pr ) similar to flow in a pipe N Nu = (N Re ) 0.5 (N Pr ) 0.33 For 1 < N Re < 70,000 and 0.6 < N Pr < 400 OR N Nu = 2 + [0.4(N Re ) (N Re ) ]{N Pr } 0.4 ( b / w ) 0.25 For 3.5 N Re 7.6 x 10 4, 0.71 N Pr 380, 1 < b / w < 3.2 Note: For all forced convection situations, use bulk temperature of fluid to determine properties (unless otherwise specified) 44 Radiation 45 15

16 Basics of Radiation Heat Transfer Rate of heat transfer by radiation is given by Stefan- Boltzmann law as follows: Q = σ A ε T 4 Q: Energy transferred per unit time (W) σ: Stefan-Boltzmann constant (= x 10-8 W/m 2 K 4 ) A: Surface area of object (m 2 ) ε: Emissivity of surface (ranges from 0 to 1.0) T: Temperature (K) 46 Infrared Thermometer Infrared thermometer can be used to non-invasively and remotely determine the surface temperature of an object Care should be exercised in ensuring that ONLY emitted energy is measured and NOT reflected energy (may have to use non-reflecting tape on metallic surfaces) The emissivity of some infrared thermometers can be adjusted; for others, a pre-set value of 0.95 is commonly programmed 47 Thermal Resistances to Heat Transfer 48 16

17 Thermal Resistances to Heat Transfer Conduction Slab: Q = ka ( T/ x) = T/[( x/ka)] Cylinder: Q = ka lm ( T/ r) = T/[( r/ka lm )] Driving force for heat transfer: T Thermal resistance to heat transfer: ( x/ka) or ( r/ka lm ) Convection Q = ha ( T) = T/[( /ha)] Driving force for heat transfer: T Thermal resistance to heat transfer: ( /ha) Units of thermal resistance to heat transfer: K/W 49 Thermal Resistances Conduction: Q = ka T/ x Single slab: Q = T/[( x/ka)] Multiple slabs: Q = T/[( x 1 /k 1 A) + ( x 2 /k 2 A) + ] Cylindrical shell: Q = T/[( r/ka lm )] Multiple cylindrical shells: Q = T/[( r 1 /k 1 A lm(1) ) + ( r 2 /k 2 A lm(2) )] Convection: Q = ha T Single convection: Q = T/[( /ha)] Multiple convections: Q = T/[( /h 1 A 1 ) + ( /h 2 A 2 ) + ] Combination of conduction and convection Multiple slabs Q = T/[( x 1 /k 1 A) + ( x 2 /k 2 A) + ( /h 1 A 1 ) + ( /h 2 A 2 ) + ] Multiple cylindrical shells Q = T/[( /h 1 A 1 ) + ( r 1 /k 1 A lm(1) ) + ( r 2 /k 2 A lm(2) ) + ( /h 2 A 2 )] Units of thermal resistance to heat transfer: K/W 50 V I R Electrical Analogy A current (I) flows because there is a driving force, the potential Difference (V), across the resistance (R) I = V/R Q = T/(Thermal Resistance) V I R 1 R 2 I = V/(R 1 + R 2 ) Q = T/(Sum of Thermal Resistances) Thermal resistances are additive (similar to electrical resistances) 51 17

18 k, h, U, Resistances, and Temperatures As thermal conductivity (k) increases, thermal resistance due to conduction ( x/ka) decreases Thus, temperature difference between center and surface of object decreases As convective heat transfer coefficient (h) increases, thermal resistance due to convection (1/hA) decreases Thus, temperature difference between the fluid and surface of the solid object decreases 52 Overall Heat Transfer Coefficient (OHTC) 53 What is Overall Heat Transfer Coefficient? OHTC (denoted by the symbol U ) refers to a single quantity that can be used to quantify the effect of all forms (conduction and convection) of heat transfer taking place in a system It facilitates the use of one equation (instead of individual equations for each conductive and convective heat transfer in the system) to determine the total heat transfer taking place in the system All thermal resistances in the system are added in order to facilitate this process 54 18

19 OHTC (or U) in Different Scenarios Three conductive heat transfers 1/(UA) = x 1 /(k 1 A) + x 2 /(k 2 A) + x 3 /(k 3 A) Two convective heat transfers 1/(UA) = 1/(h 1 A 1 ) + 1/(h 2 A 2 ) One conductive and one convective heat transfer 1/(UA) = x 1 /(k 1 A) + 1/(hA) Note 1: 1/UA > 1/hA; Thus, U < h Note 2: If there is no conductive resistance, U = h U: Overall heat transfer coefficient (W/m 2 K) 1/UA : Overall thermal resistance (K/W) 55 k, h, U, Resistances, and Temperatures As thermal conductivity (k) increases, thermal resistance due to conduction ( x/ka) decreases Thus, temperature difference between center and surface of object decreases As convective heat transfer coefficient (h) increases, thermal resistance due to convection (1/hA) decreases Thus, temperature difference between the fluid and surface of the solid object decreases As overall heat transfer coefficient (U) increases, overall thermal resistance (1/UA) decreases Thus, temperature difference between the two points across which heat transfer is taking place, decreases Thermal conductivity: W/m K Convective heat transfer coefficient: W/m 2 K Overall heat transfer coefficient: W/m 2 K Thermal resistance to heat transfer: K/W 56 Why Dress in Layers in Winter? Single jacket of thickness x: Q = T/[( x/ka)] Two jackets, each of thickness x/2: Q = T/[{( x/2)}/ka) + {( x/2)}/ka)] = T/[( x/ka)] If the above two expressions are identical, why is it better to wear two jackets, each of thickness x/2? Air trapped between the two jackets adds a convective thermal resistance. Thus, Q = T/[{( x/2)}/ka) + {( x/2)}/ka) + (1/hA)] Thus, total thermal resistance increases and Q decreases 57 19

20 Q Effect of Resistance on Temperature 95 C k x T Q h 5 C A heater is used to maintain the left end of the slab at 95 C Ambient air on right side is at 5 C What factors determine the magnitude of temperature at right end of slab? T is affected by 95 C at left AND 5 C at right Resistance to heat transfer from left (by conduction) is x/ka Resistance to heat transfer from right (by convection) is 1/hA If both resistances are equal, T = (95 + 5)/2 = 50 C If conductive resistance is less (occurs when k is high), T > 50 C If convective resistance is less (occurs when h is high), T < 50 C Note: The same Q flows through the slab and outside Thus, Q = ka (95 T)/ x = ha(t 5) 58 Heat Exchangers (HX) 59 Types of Heating Equipment Direct contact Steam injection, steam infusion Indirect contact (Other than plate, tubular, Shell & tube, SSHE) Retorts (Using hot water, steam, or steam-air for heating) Batch (Agitation: None, axial or end-over-end): With our w/o basket/crate Continuous (With agitation): Conventional, Hydrostatic Plate: Series, parallel, series-parallel Tubular: Double tube, triple tube, multi-tube Shell & tube: Single pass, multiple pass, cross-flow Scraped surface heat exchanger (SSHE) Alternative/Novel/Emerging Technologies Microwave and radio frequency heating Uses electromagnetic radiation; polar molecules heat up Ohmic heating Electric current in food causes heating; ions in food, cause heating 60 20

21 Pneumatically actuated Steam Steam Injection Intense, turbulent mixing of steam and product occurs. It results in rapid heating and dilution of product. A vacuum chamber is used downstream to evaporate steam that condensed into product. Pneumatically actuated Variable Gap Product 61 Steam in Steam Infusion Air out CIP in Product in Cooling water in/out This is a gentler process than steam injection. A vacuum chamber is used downstream to evaporate steam that condensed into product. Product out 62 Batch Retorts Static (with or without crates/baskets) Horizontal Vertical Rotary (axial or end-over-end rotation) End-over-end Rotation Rotary, end-over-end or reciprocating motion is used to mix the product and make the temperature distribution uniform Axial Rotation Reciprocating Shaka 63 21

22 Static & Rotary Retorts Raw canned foods are placed in basket Horizontal Basket Retort SuperAgi Retort Crateless Retort (Semi-Continuous) Problem: Cold spot identification 65 Conventional Continuous Rotary Retort 66 22

23 Hydrostatic Retort Height of water column provides enough pressure to prevent water from boiling at temperatures well above 100 C 67 Hydrostatic Retort/Sterilizer 68 Plate Heat Exchanger (PHE) Hot fluid flows on one side of plate and cold fluid flows on other side of plate. Heat transfer occurs across each plate. Simple, efficient, inexpensive; used for not too viscous fluids 69 23

24 PHEs (All channels in Parallel) Advantage Low pressure drop 1 X 4 1 X 4 Disadvantage Low heat transfer 70 PHEs (All Channels in Series) Advantage High heat transfer 4 X 1 4 X 1 Disadvantage High pressure drop 71 PHEs (Series & Parallel) Advantage Optimized pressure drop and heat transfer 2 X 2 1 X

25 Regeneration in a PHE Cold pasteurized product Hot pasteurized product Cooler Regenerator Heater Raw product Regeneration: Energy of hot pasteurized product is used to pre-heat cold raw product. Typical regeneration efficiency is ~90%. 73 Double Tube, Triple Tube, Multitube HX Heating from 1 side Heating from 2 sides 74 Shell & Tube: (One & Two Pass) Note: Presence of baffles creates cross-flow pattern (product and heating/cooling medium flow at right angles to one another) with uniform heat transfer throughout the heat exchanger. Baffles prevent shortcircuiting of heating medium directly from the inlet port to the outlet port

26 Scraped Surface Heat Exchanger (SSHE) Shaft with motor rotating it Blade Insulation Motor Blade Steam jacket Shaft Cross-sectional view Product Insulation Advantage: Mixing of viscous foods Disadvantage: Particle damage, uncertain residence time, cleaning Steam jacket Product 76 Double Tube Heat Exchanger (DTHE) Hot/Cold water Product Heat Transfer Double tube heat exchanger Two concentric tubes Product generally flows in inner tube Heating/cooling medium generally flows in outer tube (annulus) One stream gains heat while the other stream loses heat (hence, heat exchanger) Heat transfer takes place across wall of inner tube Both streams may flow in the same or opposite directions 77 Heat Transfer in a Double Tube HX (Hot water heating a product) T ho Product. T ci, m c, c p(c) Q = h o A o [T hot water -T wall (outside) ] h o h i Hot water. T hi, m h, c p(h) Q = ka lm [T wall (outside) -T wall (inside) ]/ r U Q = h i A i [T wall (inside) -T product ] r ii T co r oi L Subscripts for T: c for cold, h for hot, i for inlet, o for outlet 78 26

27 Heat Transfer from Hot Water to Product Convection From hot water to outside surface of inner tube Q = h o A o [T hot water -T wall (outside) ] Conduction From outside of inner tube to inside of inner tube Q = ka lm [T wall (outside) -T wall (inside) ]/ r Convection From inside surface of inner tube to bulk of product Q = h i A i [T wall (inside) -T product ] 79 Resistances to Heat Transfer from Hot Water to Product Product h o h i Hot water Convective resistance (1/h o A o ) Conductive resistance ( r/k A lm ) Convective resistance (1/h i A i ) U 80 Overall Heat Transfer Coefficient (U) Q = T / [(1/h o A o ) + ( r/ka lm ) + (1/h i A i )] Thermal resistances have been added Denominator: Total thermal resistance 1/UA lm = (1/h o A o ) + ( r/ka lm ) + (1/h i A i ) Thus, Q = UA lm T lm U: W/m 2 K U: Accounts for all modes of heat transfer from hot water to product U is NOT a property; it is NOT fixed for a HX; it depends on material properties, system dimensions, and process parameters 81 27

28 Determination of U: Theoretical Method 1/UA lm = (1/h o A o ) + ( r/ka lm ) + (1/h i A i ) h i and h o are usually determined using empirical correlations k is a material property of the tube of HX A i, A o, and A lm are determined based on dimensions (length & radii) of heat exchanger tubes Once A i, A o, A lm, h i, h o, and k are known, U is calculated using the above equation 82 Determination of U: Experimental Method (Hot Water as Heating Medium).. Q = m c c p(c) T c = m h c p(h) T h = UA lm T lm Assumption: Heat loss = zero Once the mass flow rates and temperatures of the product and hot water are experimentally determined, U can be calculated If there is heat loss, Q lost by hot water = Q gained by product + Q lost to outside 83 Tubular Heat Exchanger (Co- and Counter-Current) 1/UA lm = (1/h o A o ) + ( r/ka lm ) + (1/h i A i ) and Q = UA lm T lm Temperature h: Hot c: Cold i: Inlet o: Outlet Temperature h: Hot c: Cold i: Inlet o: Outlet Used only when rapid initial cooling is needed Most commonly used Lower heat transfer efficiency Higher heat transfer efficiency T co T ho always T co can be greater than T ho T btwn hot & cold fluid dec. along length T btwn hot & cold fluid does not A i = Inside surface area of inner pipe = 2 r ii L change significantly along length A o = Outside surface area of inner pipe = 2 r oi L A lm = Logarithmic mean area of inner pipe = (A o A i ) / [ln (A o /A i )] = 2 L (r oi r ii )/[ln (r oi /r ii )] T lm = Logarithmic mean temperature difference = ( T 1 T 2 )/[ln( T 1 / T 2 )] 84 28

29 Hot water Co-Current Arrangement. T hi, m h, c p(h) h o Q 2 Q 3 T ho Product. T ci, m c, c p(c) U h i Q 1 T co r ii r oi L r = r oi -r ii Q 1 : Energy transferred from heating medium to product (= energy gained by product) Q 2 : Energy lost by heating medium (= energy gained by product and surroundings) Q 3 : Energy transferred from heating medium to surroundings (= energy gained by surroundings) Note: Q 2 = Q 1 + Q 3 Common approximation: Q 3 = 0 (valid if HX is insulated) In this case,... Subscripts for m, c p, T, T: Q 1 = m c c p(c) ( T) c = Q 2 = m h c p(h) ( T) h = UA lm T lm h for hot, c for cold with 1/UA lm = 1/h i A i + r/ka lm + 1/h o A o i for inlet, o for outlet Note 1: ( T) c = (T co T ci ); ( T) h = (T hi T ho ) Note 2: ( T) 1 = (T hi T ci ); ( T) 2 = (T ho T co ) Subscripts for h, A: i for inside, o for outside 85 Counter-Current Arrangement Q 3 T ho Q 2 h o. T hi, m h, c p(h) Hot water Product. T ci, m c, c p(c) Q 1 h i U T co r ii r oi L r = r oi -r ii Q 1 : Energy transferred from heating medium to product (= energy gained by product) Q 2 : Energy lost by heating medium (= energy gained by product and surroundings) Q 3 : Energy transferred from heating medium to surroundings (= energy gained by surroundings) Note: Q 2 = Q 1 + Q 3 Common approximation: Q 3 = 0 (valid if HX is insulated) In this case,... Subscripts for m, c p, T, T: Q 1 = m c c p(c) ( T) c = Q 2 = m h c p(h) ( T) h = UA lm T lm h for hot, c for cold with 1/UA lm = 1/h i A i + r/ka lm + 1/h o A o i for inlet, o for outlet Note 1: ( T) c = (T co T ci ); ( T) h = (T hi T ho ) Note 2: ( T) 1 = (T ho T ci ); ( T) 2 = (T hi T co ) Subscripts for h, A: i for inside, o for outside 86 Insulation 87 29

30 Effect of Insulation Air has a lower k value than most insulating materials. Why do we use insulation then, to minimize heat loss from a heated pipe? Does the addition of insulation around a hot pipe surrounded by a cold fluid always decrease the heat loss from the pipe? Not always! Addition of insulation Increases the thermal resistance to heat transfer by conduction ( x/ka) Decreases the thermal resistance to heat transfer by convection (1/hA) The net effect may be an increase or decrease in heat loss 88 Heat Loss (Q) without and with Insulation Without Insulation With Insulation h o T T o o h o T i h i r 1 r 2 r 3 r 2 r 1 h i T i Q = T / [(1/h o A o ) + ( r/ka lm ) pipe + (1/h i A i )] Q = T / [(1/h o A o ) + ( r/ka lm ) insulation + ( r/ka lm ) pipe + (1/h i A i )] r pipe = r 2 r 1 and A o = 2 r 2 L r insulation = r 3 r 2 and A o = 2 r 3 L (A lm ) pipe = 2 L (r 2 r 1 ) / [ln (r 2 /r 1 )] (A lm ) insulation = 2 L (r 3 r 2 ) / [ln (r 3 /r 2 )] Adding insulation inc. conductive res. & dec. convective res. Setting dq/dr 3 = 0, and ensuring that d 2 Q/dr 32 is ve, yields Q max This happens when r 3 = k ins /h o = r critical = r c Thus, as insulation is added, heat loss increases till r 3 = k ins /h o ; then it decreases If r 2 > k ins /h o, heat loss decreases even if a small amount of insulation is added 89 Q ins /Q bare versus Thickness of Insulation 2 Outside Radius of Pipe = 2.25 cm 1.8 Q ins / Q bare k/h = 0.01 m k/h = 0.03 m k/h = 0.05 m k/h = 0.1 m Zero benefit Insulation Thickness (m) 90 30

31 Dimensionless Numbers in Heat Transfer 91 Dimensionless Numbers in Heat Transfer Reynolds number Nusselt number For circular cross-section pipes Prandtl number Grashof number 92 Dimensionless Numbers (contd.) Biot number Fourier number s = k/( c p ) = Thermal diffusivity (m 2 /s) Reynolds number: Ratio of inertial & viscous forces Nusselt number: Ratio of heat transfer by convection & conduction Prandtl number: Ratio of momentum & thermal diffusivities Grashof number: Ratio of buoyancy & viscous forces Biot number: Ratio of internal & external resistance to heat transfer Fourier number: Ratio of heat conduction & heat storage Subscripts: f for fluid & s for solid d c : Characteristic dimension = 4 (A cross-section )/(Wetted perimeter) D c : Distance between hottest and coldest point within solid object 93 31

32 Nusselt # (N Nu ) and Biot # (N Bi ) Both are denoted by hd/k Nusselt # Used in STEADY state heat transfer (to determine h ) d c : Characteristic dimension (= pipe diameter for flow in a pipe) k f : Thermal conductivity of FLUID Biot# Used in UNSTEADY state heat transfer (to determine the relative importance of conduction versus convection heat transfer) D c : Distance between hottest and coldest point in solid object k s : Thermal conductivity of SOLID 94 Unsteady State Heat Transfer (Heat Conduction to the Center of a Solid Object) 95 Basics of Unsteady State heat Transfer Temperature at one or more points in the system changes as a function of time Goal of unsteady state heat transfer Determine time taken for an object to attain a certain temperature OR Determine temperature of an object after a certain time Sometimes, it is used to determine h The dimensionless numbers that come into play for unsteady state heat transfer are Biot # (N Bi = hd c /k s and Fourier # (N Fo = s t/d c2 ) Note: s = k/( c p ) 96 32

33 Categories of Unsteady State Heat Transfer Categories are based on the magnitude of Biot # (N Bi = hd c /k s ) 1. Negligible internal (conductive) resistance N Bi < 0.1 (also called lumped capacitance/parameter method) 2. Finite internal and external resistances 0.1 < N Bi < Negligible external (convective) resistance N Bi > 40 D c for unsteady state heat transfer: Distance between points of maximum temperature difference within solid object D c for sphere: Radius of sphere D c for an infinitely long cylinder: Radius of cylinder D c for infinite slab with heat transfer from top & bottom: Half thickness of slab D c for an infinite slab with heat transfer from top: Thickness of slab 97 Modes of Heat Transfer from Air to the Center of a Sphere Consider hot air (at 100 C) being blown over a cold sphere (at 20 C) h 20 C 100 C air 20 C The two modes of heat transfer are Convection (external) Conduction (internal) 98 Significance of Magnitude of N Bi N Bi < 0.1 (Cat. #1) => Conductive resistance is low Occurs when k s is very high (metals) OR D c is very low t = 0 min t = 2 min 100 C air 100 C air 20 C 20 C 50 C 49 C N Bi > 40 (Cat. #3) => Convective resistance is low Occurs when h is very high (N Re is high) OR D c is large t = 0 min t = 2 min 100 C air 100 C air 20 C 20 C 95 C 55 C 99 33

34 Significance of Magnitude of N Bi (contd.) 0.1 < N Bi < 40 (Cat. #2) => Conductive and convective resistances are of same order of magnitude t = 0 min t = 2 min 100 C air 100 C air 20 C 20 C 70 C 45 C 100 Category #1 The above equation can be used to determine temperature, T, at time, t OR Based on time-temperature data, the equation can be used to determine h T i : Initial temperature of solid object (K) T : Temperature of surrounding fluid (K) h: Convective heat transfer coefficient (W/m 2 K) A: Surface area for heat transfer (m 2 ) : Density of solid object (kg/m 3 ) V: Volume of solid object (m 3 ) c p : Specific heat of solid object (J/kg K) Note: V = mass of object (kg) Shape Area Volume Brick 2 (LW+LH+WH) LWH Cylinder 2 RL + 2 R 2 R 2 L Sphere 4 R 2 (4/3) R 3 L: Length of brick or cylinder W, H: Width, height of brick resp. R: Radius of cylinder or sphere 101 Category #2 Need to use Heisler charts TR on y-axis and Fourier number (N Fo ) on x-axis Several straight lines based on different values of 1/N Bi Knowing temperature, T (and thus TR), and value of 1/N Bi, we can determine x-axis value (or N Fo ) and hence time, t OR Knowing time, t (and hence N Fo or x-axis value), and value of 1/N Bi, we can determine y-axis value (or TR) and hence temperature, T

35 Sample Heisler Chart /N Bi = k s /hd c = /N Bi = Note: s = k/( c p ) = Thermal diffusivity of solid object in m 2 /s 103 Heisler Chart (For Finite Sphere) TR [=(T-T )/(T i -T )] N Fo (= t/d c2 ) 104 Heisler Chart (For Infinite Cylinder) TR [=(T-T )/(T i -T )] N Fo (= t/d c2 )

36 Heisler Chart (For Infinite Slab) TR [=(T-T )/(T i -T )] N Fo (= t/d c2 ) 106 Category #3 Need to use Heisler charts to determine timetemperature relation These charts are a way to approximate the exact solution (equation) that represents how temperature (T) changes as a function of time (t) Similar approach as category #2 Since N Bi > 40, 1/N Bi is very small (~ 0) Thus, we use Heisler charts with the line corresponding to 1/N Bi = 0 Note: 1/N Bi = k/(hd c ) 107 Summary of Categories of Unsteady State Heat Transfer Category 1 Category 2 Category 3 N Bi N Bi < < N Bi < 40 N Bi > 40 This category is encountered when.. Resistance that is negligible T that is small Solution approach k is high OR D c is small Conductive (Internal) Btwn center and surface of solid Lumped parameter eqn. Neither k nor h are high and D c is not too small or too large None None Heisler chart(s) h is high OR D c is large Convective (External) Btwn fluid and surface of solid Heisler chart(s) (with 1/N Bi = 0)

37 Heisler Charts For a finite sphere For an infinitely long cylinder For a slab infinitely long in two dimensions & finite in one dimension Heat transfer in one dimension/direction only Temperature at ONLY center of object can be determined Use Gurney-Lurie charts for temperatures at other locations within object Rule of thumb: If one dimension of an object is at least 10 times another of its dimension, the first dimension is considered to be infinite in comparison to the other 109 Finite Objects Finite brick: Intersection of 3 infinite slabs Finite cylinder: Intersection of infinite cylinder & infinite slab 110 Finite Objects Finite objects (such as a cylinder or brick can be obtained as an intersection of infinite objects) Heisler charts have to be used twice or thrice respectively to determine temperatures for finite cylinder (food in a can) and finite brick (food in a tray) Note: (t) finite cylinder (t) infinite cylinder + (t) infinite slab (t) finite brick (t) infinite slab, width + (t) infinite slab, depth + (t) infinite slab, height

38 Calculations for Finite Cylinder (Heisler Chart) Infinite Cylinder Infinite Slab Characteristic dimension (D c ) Biot number (N Bi ) N Bi = h D c /k s 1/N Bi Thermal diffusivity ( ) s = k s / s c p(s) Fourier number (N Fo ) N Fo = s t/d c 2 Temperature ratio (TR) from Heisler chart (based on values of N Fo & 1/N Bi ) If both N Bi < 0.1, the lumped parameter method (eqn) can be used Solve for T from the above equation 112 Calculations for Finite Brick (Heisler Chart) Characteristic dimension (D c ) Biot number (N Bi ) N Bi = h D c /k s 1/N Bi Thermal diffusivity ( s ) s = k s / s c p(s) Fourier number (N Fo ) N Fo = s t/d 2 c Temperature ratio (TR) from Heisler chart (based on values of N Fo & 1/N Bi ) Infinite Slab #1 Infinite Slab #2 Infinite Slab #3 If all 3 N Bi < 0.1, the lumped parameter method (eqn) can be used Solve for T from the above equation 113 Temperature Ratio (TR) At time t = 0, T = T i and hence TR = 1 At time t =, T = T and hence TR = 0 Thus, TR starts off at 1.0 and can at best reach 0.0 Low values of TR (closer to 0.0) indicate a significant change in temperature (from T i ) of the object High values of TR (closer to 1.0) indicate a minimal change in temperature (from T i ) of the object

39 Summary Categories of steady state heat transfer Conduction, convection, radiation Conduction: Fourier s law of heat conduction Q = - ka ( T/ x); replace A & T by A lm & T lm resp. for cyl. Logarithmic mean area A lm = (A o A i ) / ln (A o /A i ) = 2 L (r o r i ) / [ln (r o /r i )] Logarithmic mean temperature difference T lm = ( 1 2 ) / [ln ( 1 / 2 )] Convection: Newton s law of cooling Q = h A ( T) Free convection: Due to density differences within a fluid; Forced convection: Due to external agency (fan/ pump) N Nu = f(n Gr & N Pr ) for free; N Nu = f(n Re & N Pr ) for forced 115 Summary (contd.) Thermal resistances to heat transfer by conduction ( x/ka) and convection (1/hA) are additive Overall heat transfer coefficient (U) combines the effect of all forms of heat transfer taking place between any two points in a system Q = UA lm T lm is the most generic form of equation for steady state heat transfer involving conduction and/or convection Tubular heat exchanger calculations are based on:.. Q = m p c p(p) T product = m hw c p(hw) T hot water (for no heat loss) = UA lm T lm 116 Summary (contd.) Thermal properties Specific heat: Important in determining T of an object Latent heat: Important in determining energy required for phase change Thermal conductivity: Important in determining rate of heat conduction in an object For unsteady state heat transfer, the lumped capacitance method (for N Bi < 0.1) or Heisler charts (for N Bi > 0.1) are used to establish time-temperature relations Heisler charts are applicable only for 1-D heat transfer to determine center temperature Use multiple 1-D objects to create 2-D or 3-D objects Characteristic dimension in unsteady state heat transfer Distance between the hottest and coldest point in object

1. Nusselt number and Biot number are computed in a similar manner (=hd/k). What are the differences between them? When and why are each of them used?

1. Nusselt number and Biot number are computed in a similar manner (=hd/k). What are the differences between them? When and why are each of them used? 1. Nusselt number and Biot number are computed in a similar manner (=hd/k). What are the differences between them? When and why are each of them used?. During unsteady state heat transfer, can the temperature

More information

Principles of Food and Bioprocess Engineering (FS 231) Exam 2 Part A -- Closed Book (50 points)

Principles of Food and Bioprocess Engineering (FS 231) Exam 2 Part A -- Closed Book (50 points) Principles of Food and Bioprocess Engineering (FS 231) Exam 2 Part A -- Closed Book (50 points) 1. Are the following statements true or false? (20 points) a. Thermal conductivity of a substance is a measure

More information

Review for Exam #2. Specific Heat, Thermal Conductivity, and Thermal Diffusivity. Conduction

Review for Exam #2. Specific Heat, Thermal Conductivity, and Thermal Diffusivity. Conduction Review for Exam # Speifi Heat, Thermal Condutivity, and Thermal Diffusivity Speifi heat ( p ) A measure of how muh energy is required to raise the temperature of an objet Thermal ondutivity (k) A measure

More information

Principles of Food and Bioprocess Engineering (FS 231) Problems on Heat Transfer

Principles of Food and Bioprocess Engineering (FS 231) Problems on Heat Transfer Principles of Food and Bioprocess Engineering (FS 1) Problems on Heat Transfer 1. What is the thermal conductivity of a material 8 cm thick if the temperature at one end of the product is 0 C and the temperature

More information

If there is convective heat transfer from outer surface to fluid maintained at T W.

If there is convective heat transfer from outer surface to fluid maintained at T W. Heat Transfer 1. What are the different modes of heat transfer? Explain with examples. 2. State Fourier s Law of heat conduction? Write some of their applications. 3. State the effect of variation of temperature

More information

Chapter 3 NATURAL CONVECTION

Chapter 3 NATURAL CONVECTION Fundamentals of Thermal-Fluid Sciences, 3rd Edition Yunus A. Cengel, Robert H. Turner, John M. Cimbala McGraw-Hill, 2008 Chapter 3 NATURAL CONVECTION Mehmet Kanoglu Copyright The McGraw-Hill Companies,

More information

Heat and Mass Transfer Unit-1 Conduction

Heat and Mass Transfer Unit-1 Conduction 1. State Fourier s Law of conduction. Heat and Mass Transfer Unit-1 Conduction Part-A The rate of heat conduction is proportional to the area measured normal to the direction of heat flow and to the temperature

More information

ELEC9712 High Voltage Systems. 1.2 Heat transfer from electrical equipment

ELEC9712 High Voltage Systems. 1.2 Heat transfer from electrical equipment ELEC9712 High Voltage Systems 1.2 Heat transfer from electrical equipment The basic equation governing heat transfer in an item of electrical equipment is the following incremental balance equation, with

More information

HEAT TRANSFER 1 INTRODUCTION AND BASIC CONCEPTS 5 2 CONDUCTION

HEAT TRANSFER 1 INTRODUCTION AND BASIC CONCEPTS 5 2 CONDUCTION HEAT TRANSFER 1 INTRODUCTION AND BASIC CONCEPTS 5 2 CONDUCTION 11 Fourier s Law of Heat Conduction, General Conduction Equation Based on Cartesian Coordinates, Heat Transfer Through a Wall, Composite Wall

More information

Thermal Systems. What and How? Physical Mechanisms and Rate Equations Conservation of Energy Requirement Control Volume Surface Energy Balance

Thermal Systems. What and How? Physical Mechanisms and Rate Equations Conservation of Energy Requirement Control Volume Surface Energy Balance Introduction to Heat Transfer What and How? Physical Mechanisms and Rate Equations Conservation of Energy Requirement Control Volume Surface Energy Balance Thermal Resistance Thermal Capacitance Thermal

More information

Heat Transfer Convection

Heat Transfer Convection Heat ransfer Convection Previous lectures conduction: heat transfer without fluid motion oday (textbook nearly 00 pages) Convection: heat transfer with fluid motion Research methods different Natural Convection

More information

Introduction to Heat Transfer

Introduction to Heat Transfer Question Bank CH302 Heat Transfer Operations Introduction to Heat Transfer Question No. 1. The essential condition for the transfer of heat from one body to another (a) Both bodies must be in physical

More information

Phone: , For Educational Use. SOFTbank E-Book Center, Tehran. Fundamentals of Heat Transfer. René Reyes Mazzoco

Phone: , For Educational Use. SOFTbank E-Book Center, Tehran. Fundamentals of Heat Transfer. René Reyes Mazzoco 8 Fundamentals of Heat Transfer René Reyes Mazzoco Universidad de las Américas Puebla, Cholula, Mexico 1 HEAT TRANSFER MECHANISMS 1.1 Conduction Conduction heat transfer is explained through the molecular

More information

Mechanical Engineering. Postal Correspondence Course HEAT TRANSFER. GATE, IES & PSUs

Mechanical Engineering. Postal Correspondence Course HEAT TRANSFER. GATE, IES & PSUs Heat Transfer-ME GATE, IES, PSU 1 SAMPLE STUDY MATERIAL Mechanical Engineering ME Postal Correspondence Course HEAT TRANSFER GATE, IES & PSUs Heat Transfer-ME GATE, IES, PSU 2 C O N T E N T 1. INTRODUCTION

More information

Chapter 11. Energy in Thermal Processes

Chapter 11. Energy in Thermal Processes Chapter 11 Energy in Thermal Processes Energy Transfer When two objects of different temperatures are placed in thermal contact, the temperature of the warmer decreases and the temperature of the cooler

More information

MYcsvtu Notes HEAT TRANSFER BY CONVECTION

MYcsvtu Notes HEAT TRANSFER BY CONVECTION www.mycsvtunotes.in HEAT TRANSFER BY CONVECTION CONDUCTION Mechanism of heat transfer through a solid or fluid in the absence any fluid motion. CONVECTION Mechanism of heat transfer through a fluid in

More information

C ONTENTS CHAPTER TWO HEAT CONDUCTION EQUATION 61 CHAPTER ONE BASICS OF HEAT TRANSFER 1 CHAPTER THREE STEADY HEAT CONDUCTION 127

C ONTENTS CHAPTER TWO HEAT CONDUCTION EQUATION 61 CHAPTER ONE BASICS OF HEAT TRANSFER 1 CHAPTER THREE STEADY HEAT CONDUCTION 127 C ONTENTS Preface xviii Nomenclature xxvi CHAPTER ONE BASICS OF HEAT TRANSFER 1 1-1 Thermodynamics and Heat Transfer 2 Application Areas of Heat Transfer 3 Historical Background 3 1-2 Engineering Heat

More information

Principles of Convection

Principles of Convection Principles of Convection Point Conduction & convection are similar both require the presence of a material medium. But convection requires the presence of fluid motion. Heat transfer through the: Solid

More information

Transient Heat Transfer Experiment. ME 331 Introduction to Heat Transfer. June 1 st, 2017

Transient Heat Transfer Experiment. ME 331 Introduction to Heat Transfer. June 1 st, 2017 Transient Heat Transfer Experiment ME 331 Introduction to Heat Transfer June 1 st, 2017 Abstract The lumped capacitance assumption for transient conduction was tested for three heated spheres; a gold plated

More information

UNIT II CONVECTION HEAT TRANSFER

UNIT II CONVECTION HEAT TRANSFER UNIT II CONVECTION HEAT TRANSFER Convection is the mode of heat transfer between a surface and a fluid moving over it. The energy transfer in convection is predominately due to the bulk motion of the fluid

More information

1. How much heat was needed to raise the bullet to its final temperature?

1. How much heat was needed to raise the bullet to its final temperature? Name: Date: Use the following to answer question 1: A 0.0500-kg lead bullet of volume 5.00 10 6 m 3 at 20.0 C hits a block that is made of an ideal thermal insulator and comes to rest at its center. At

More information

Convection. forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds.

Convection. forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds. Convection The convection heat transfer mode is comprised of two mechanisms. In addition to energy transfer due to random molecular motion (diffusion), energy is also transferred by the bulk, or macroscopic,

More information

Heat Transfer Predictions for Carbon Dioxide in Boiling Through Fundamental Modelling Implementing a Combination of Nusselt Number Correlations

Heat Transfer Predictions for Carbon Dioxide in Boiling Through Fundamental Modelling Implementing a Combination of Nusselt Number Correlations Heat Transfer Predictions for Carbon Dioxide in Boiling Through Fundamental Modelling Implementing a Combination of Nusselt Number Correlations L. Makaum, P.v.Z. Venter and M. van Eldik Abstract Refrigerants

More information

Heat and Mass Transfer Prof. S.P. Sukhatme Department of Mechanical Engineering Indian Institute of Technology, Bombay

Heat and Mass Transfer Prof. S.P. Sukhatme Department of Mechanical Engineering Indian Institute of Technology, Bombay Heat and Mass Transfer Prof. S.P. Sukhatme Department of Mechanical Engineering Indian Institute of Technology, Bombay Lecture No. 18 Forced Convection-1 Welcome. We now begin our study of forced convection

More information

Specific heat capacity. Convective heat transfer coefficient. Thermal diffusivity. Lc ft, m Characteristic length (r for cylinder or sphere; for slab)

Specific heat capacity. Convective heat transfer coefficient. Thermal diffusivity. Lc ft, m Characteristic length (r for cylinder or sphere; for slab) Important Heat Transfer Parameters CBE 150A Midterm #3 Review Sheet General Parameters: q or or Heat transfer rate Heat flux (per unit area) Cp Specific heat capacity k Thermal conductivity h Convective

More information

Transport processes. 7. Semester Chemical Engineering Civil Engineering

Transport processes. 7. Semester Chemical Engineering Civil Engineering Transport processes 7. Semester Chemical Engineering Civil Engineering 1. Elementary Fluid Dynamics 2. Fluid Kinematics 3. Finite Control Volume Analysis 4. Differential Analysis of Fluid Flow 5. Viscous

More information

S.E. (Chemical) (Second Semester) EXAMINATION, 2012 HEAT TRANSFER (2008 PATTERN) Time : Three Hours Maximum Marks : 100

S.E. (Chemical) (Second Semester) EXAMINATION, 2012 HEAT TRANSFER (2008 PATTERN) Time : Three Hours Maximum Marks : 100 Total No. of Questions 12] [Total No. of Printed Pages 7 Seat No. [4162]-187 S.E. (Chemical) (Second Semester) EXAMINATION, 2012 HEAT TRANSFER (2008 PATTERN) Time : Three Hours Maximum Marks : 100 N.B.

More information

Heat processes. Heat exchange

Heat processes. Heat exchange Heat processes Heat exchange Heat energy transported across a surface from higher temperature side to lower temperature side; it is a macroscopic measure of transported energies of molecular motions Temperature

More information

Introduction to Heat and Mass Transfer

Introduction to Heat and Mass Transfer Introduction to Heat and Mass Transfer Week 16 Merry X mas! Happy New Year 2019! Final Exam When? Thursday, January 10th What time? 3:10-5 pm Where? 91203 What? Lecture materials from Week 1 to 16 (before

More information

CALORIEMETRY. Similar to the other forms of the energy, The S.I unit of heat is joule. joule is represented as J.

CALORIEMETRY. Similar to the other forms of the energy, The S.I unit of heat is joule. joule is represented as J. CALORIEMETRY CALORIMETRY Heat is the kinetic energy due to random motion of the molecules of a substance is called heat energy. Heat is a an invisible energy, that causes in us the sensation of hotness

More information

Handout 10: Heat and heat transfer. Heat capacity

Handout 10: Heat and heat transfer. Heat capacity 1 Handout 10: Heat and heat transfer Heat capacity Consider an experiment in Figure 1. Heater is inserted into a solid substance of mass m and the temperature rise T degrees Celsius is measured by a thermometer.

More information

P5 Heat and Particles Revision Kinetic Model of Matter: States of matter

P5 Heat and Particles Revision Kinetic Model of Matter: States of matter P5 Heat and Particles Revision Kinetic Model of Matter: States of matter State Size Shape Solid occupies a fixed volume has a fixed shape Liquid occupies a fixed volume takes the shape of its container

More information

Convection Heat Transfer. Introduction

Convection Heat Transfer. Introduction Convection Heat Transfer Reading Problems 12-1 12-8 12-40, 12-49, 12-68, 12-70, 12-87, 12-98 13-1 13-6 13-39, 13-47, 13-59 14-1 14-4 14-18, 14-24, 14-45, 14-82 Introduction Newton s Law of Cooling Controlling

More information

S.E. (Chemical) (Second Semester) EXAMINATION, 2011 HEAT TRANSFER (2008 PATTERN) Time : Three Hours Maximum Marks : 100

S.E. (Chemical) (Second Semester) EXAMINATION, 2011 HEAT TRANSFER (2008 PATTERN) Time : Three Hours Maximum Marks : 100 Total No. of Questions 12] [Total No. of Printed Pages 7 [4062]-186 S.E. (Chemical) (Second Semester) EXAMINATION, 2011 HEAT TRANSFER (2008 PATTERN) Time : Three Hours Maximum Marks : 100 N.B. : (i) Answers

More information

Thermal Effects. IGCSE Physics

Thermal Effects. IGCSE Physics Thermal Effects IGCSE Physics Starter What is the difference between heat and temperature? What unit is thermal energy measured in? And what does it depend on? In which direction does heat flow? Heat (Thermal

More information

: HEAT TRANSFER & EVAPORATION COURSE CODE : 4072 COURSE CATEGORY : B PERIODS/ WEEK : 5 PERIODS/ SEMESTER : 70 CREDIT : 5 TIME SCHEDULE

: HEAT TRANSFER & EVAPORATION COURSE CODE : 4072 COURSE CATEGORY : B PERIODS/ WEEK : 5 PERIODS/ SEMESTER : 70 CREDIT : 5 TIME SCHEDULE COURSE TITLE : HEAT TRANSFER & EVAPORATION COURSE CODE : 4072 COURSE CATEGORY : B PERIODS/ WEEK : 5 PERIODS/ SEMESTER : 70 CREDIT : 5 TIME SCHEDULE MODULE TOPIC PERIODS 1 Conduction,Fourier law,variation

More information

TankExampleNov2016. Table of contents. Layout

TankExampleNov2016. Table of contents. Layout Table of contents Task... 2 Calculation of heat loss of storage tanks... 3 Properties ambient air Properties of air... 7 Heat transfer outside, roof Heat transfer in flow past a plane wall... 8 Properties

More information

PAPER 2 THEORY QUESTIONS

PAPER 2 THEORY QUESTIONS PAPER 2 THEORY QUESTIONS 1 Fig. 1.1 shows the arrangement of atoms in a solid block. Fig. 1.1 (a) End X of the block is heated. Energy is conducted to end Y, which becomes warm. (i) Explain how heat is

More information

Experiment 1. Measurement of Thermal Conductivity of a Metal (Brass) Bar

Experiment 1. Measurement of Thermal Conductivity of a Metal (Brass) Bar Experiment 1 Measurement of Thermal Conductivity of a Metal (Brass) Bar Introduction: Thermal conductivity is a measure of the ability of a substance to conduct heat, determined by the rate of heat flow

More information

Examination Heat Transfer

Examination Heat Transfer Examination Heat Transfer code: 4B680 date: 17 january 2006 time: 14.00-17.00 hours NOTE: There are 4 questions in total. The first one consists of independent sub-questions. If necessary, guide numbers

More information

Tutorial 1. Where Nu=(hl/k); Reynolds number Re=(Vlρ/µ) and Prandtl number Pr=(µCp/k)

Tutorial 1. Where Nu=(hl/k); Reynolds number Re=(Vlρ/µ) and Prandtl number Pr=(µCp/k) Tutorial 1 1. Explain in detail the mechanism of forced convection. Show by dimensional analysis (Rayleigh method) that data for forced convection may be correlated by an equation of the form Nu = φ (Re,

More information

Chapter 9 NATURAL CONVECTION

Chapter 9 NATURAL CONVECTION Heat and Mass Transfer: Fundamentals & Applications Fourth Edition in SI Units Yunus A. Cengel, Afshin J. Ghajar McGraw-Hill, 2011 Chapter 9 NATURAL CONVECTION PM Dr Mazlan Abdul Wahid Universiti Teknologi

More information

University of Rome Tor Vergata

University of Rome Tor Vergata University of Rome Tor Vergata Faculty of Engineering Department of Industrial Engineering THERMODYNAMIC AND HEAT TRANSFER HEAT TRANSFER dr. G. Bovesecchi gianluigi.bovesecchi@gmail.com 06-7259-727 (7249)

More information

Unit 11: Temperature and heat

Unit 11: Temperature and heat Unit 11: Temperature and heat 1. Thermal energy 2. Temperature 3. Heat and thermal equlibrium 4. Effects of heat 5. Transference of heat 6. Conductors and insulators Think and answer a. Is it the same

More information

* Defining Temperature * Temperature is proportional to the kinetic energy of atoms and molecules. * Temperature * Internal energy

* Defining Temperature * Temperature is proportional to the kinetic energy of atoms and molecules. * Temperature * Internal energy * Defining Temperature * We associate temperature with how hot or cold an object feels. * Our sense of touch serves as a qualitative indicator of temperature. * Energy must be either added or removed from

More information

Latest Heat Transfer

Latest Heat Transfer Latest Heat Transfer 1. Unit of thermal conductivity in M.K.S. units is (a) kcal/kg m2 C (b) kcal-m/hr m2 C (c) kcal/hr m2 C (d) kcal-m/hr C (e) kcal-m/m2 C. 2. Unit of thermal conductivity in S.I. units

More information

Convection Workshop. Academic Resource Center

Convection Workshop. Academic Resource Center Convection Workshop Academic Resource Center Presentation Outline Understanding the concepts Correlations External Convection (Chapter 7) Internal Convection (Chapter 8) Free Convection (Chapter 9) Solving

More information

Chapter 11. Energy in Thermal Processes

Chapter 11. Energy in Thermal Processes Chapter 11 Energy in Thermal Processes Energy Transfer When two objects of different temperatures are placed in thermal contact, the temperature of the warmer decreases and the temperature of the cooler

More information

High temperature He is hot

High temperature He is hot Lecture 9 What is Temperature and Heat? High temperature He is hot Some important definitions * Two objects are in Thermal contact with each other if energy can be exchanged between them. Thermal equilibrium

More information

Energy in Thermal Processes. Heat and Internal Energy

Energy in Thermal Processes. Heat and Internal Energy Energy in Thermal Processes Heat and Internal Energy Internal energy U: associated with the microscopic components of a system: kinetic and potential energies. The larger the number of internal degrees

More information

PHYSICAL MECHANISM OF NATURAL CONVECTION

PHYSICAL MECHANISM OF NATURAL CONVECTION 1 NATURAL CONVECTION In this chapter, we consider natural convection, where any fluid motion occurs by natural means such as buoyancy. The fluid motion in forced convection is quite noticeable, since a

More information

Analyzing Mass and Heat Transfer Equipment

Analyzing Mass and Heat Transfer Equipment Analyzing Mass and Heat Transfer Equipment (MHE) Analyzing Mass and Heat Transfer Equipment Scaling up to solving problems using process equipment requires both continuum and macroscopic knowledge of transport,

More information

Demonstrate understanding of aspects of heat

Demonstrate understanding of aspects of heat Demonstrate understanding of aspects of heat Heat Transfer Temperature - temperature is a measure of the average kinetic energy of the particles making up an object (measured in C or K) 0 K = -273 o C

More information

Introduction to Heat and Mass Transfer. Week 14

Introduction to Heat and Mass Transfer. Week 14 Introduction to Heat and Mass Transfer Week 14 HW # 7 prob. 2 Hot water at 50C flows through a steel pipe (thermal conductivity 14 W/m-K) of 100 mm outside diameter and 8 mm wall thickness. During winter,

More information

THERMAL PROPERTIES OF MATTER

THERMAL PROPERTIES OF MATTER CHP # 8 HERMA PROPERIES OF MAER Q.1 Differentiate between heat and temperature? (Ans) Heat It can be defined as "the sum of kinetic energy of the molecules present in a substance is called heat". Heat

More information

Chapter 11: Heat Exchangers. Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University

Chapter 11: Heat Exchangers. Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University Chapter 11: Heat Exchangers Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University Objectives When you finish studying this chapter, you should be able to: Recognize numerous types of

More information

Chapter 14 Temperature and Heat

Chapter 14 Temperature and Heat Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 14 Temperature and Heat Thermodynamics Starting a different area of physics called thermodynamics Thermodynamics focuses on energy rather than

More information

Thermodynamics. Thermodynamics is the study of the collective properties of a system containing many bodies (typically of order 10 23!

Thermodynamics. Thermodynamics is the study of the collective properties of a system containing many bodies (typically of order 10 23! Thermodynamics Thermodynamics is the study of the collective properties of a system containing many bodies (typically of order 10 23!) Chapter18 Thermodynamics Thermodynamics is the study of the thermal

More information

PHYSICAL MECHANISM OF CONVECTION

PHYSICAL MECHANISM OF CONVECTION Tue 8:54:24 AM Slide Nr. 0 of 33 Slides PHYSICAL MECHANISM OF CONVECTION Heat transfer through a fluid is by convection in the presence of bulk fluid motion and by conduction in the absence of it. Chapter

More information

Chapter 1 INTRODUCTION AND BASIC CONCEPTS

Chapter 1 INTRODUCTION AND BASIC CONCEPTS Heat and Mass Transfer: Fundamentals & Applications 5th Edition in SI Units Yunus A. Çengel, Afshin J. Ghajar McGraw-Hill, 2015 Chapter 1 INTRODUCTION AND BASIC CONCEPTS Mehmet Kanoglu University of Gaziantep

More information

MODULE CODE: ENGG08021 INTRODUCTION TO THERMOFLUIDS. Date: 15 January 2016 Time: 10:00 12:00

MODULE CODE: ENGG08021 INTRODUCTION TO THERMOFLUIDS. Date: 15 January 2016 Time: 10:00 12:00 School of Engineering & Computing Session 2015-16 Paisley Campus Trimester 1 MODULE CODE: ENGG08021 INTRODUCTION TO THERMOFLUIDS Date: 15 January 2016 Time: 10:00 12:00 Attempt FOUR QUESTIONS IN TOTAL

More information

AP PHYSICS 2 WHS-CH-14 Heat Show all your work, equations used, and box in your answers! 1 108kg

AP PHYSICS 2 WHS-CH-14 Heat Show all your work, equations used, and box in your answers! 1 108kg AP PHYSICS 2 WHS-CH-4 Heat Show all your work, equations used, and box in your answers! James Prescott Joule (88 889) James Prescott Joule studied the nature of heat, and discovered its relationship to

More information

TEMPERATURE. 8. Temperature and Heat 1

TEMPERATURE. 8. Temperature and Heat 1 TEMPERATURE Heat is the energy that is transferred between objects because of a temperature difference Terms such as transfer of heat or heat flow from object A to object B simply means that the total

More information

LECTURE NOTES. Heat Transfer. III B. Tech II Semester (JNTUA-R15) CHADALAWADA RAMANAMMA ENGINEERING COLLEGE (AUTONOMOUS)

LECTURE NOTES. Heat Transfer. III B. Tech II Semester (JNTUA-R15) CHADALAWADA RAMANAMMA ENGINEERING COLLEGE (AUTONOMOUS) LECTURE NOTES on Heat Transfer III B. Tech II Semester (JNTUA-R15) Mr. K.SURESH, Assistant Professor CHADALAWADA RAMANAMMA ENGINEERING COLLEGE (AUTONOMOUS) Chadalawada Nagar, Renigunta Road, Tirupati 517

More information

TOPIC 2 [A] STEADY STATE HEAT CONDUCTION

TOPIC 2 [A] STEADY STATE HEAT CONDUCTION TOPIC 2 [A] STEADY STATE HEAT CONDUCTION CLASS TUTORIAL 1. The walls of a refrigerated truck consist of 1.2 mm thick steel sheet (k=18 W/m-K) at the outer surface, 22 mm thick cork (k=0.04 W/m-K) on the

More information

True/False. Circle the correct answer. (1pt each, 7pts total) 3. Radiation doesn t occur in materials that are transparent such as gases.

True/False. Circle the correct answer. (1pt each, 7pts total) 3. Radiation doesn t occur in materials that are transparent such as gases. ME 323 Sample Final Exam. 120pts total True/False. Circle the correct answer. (1pt each, 7pts total) 1. A solid angle of 2π steradians defines a hemispherical shell. T F 2. The Earth irradiates the Sun.

More information

Heat Transfer Modeling using ANSYS FLUENT

Heat Transfer Modeling using ANSYS FLUENT Lecture 1 - Introduction 14.5 Release Heat Transfer Modeling using ANSYS FLUENT 2013 ANSYS, Inc. March 28, 2013 1 Release 14.5 Outline Modes of Heat Transfer Basic Heat Transfer Phenomena Conduction Convection

More information

Lectures on Applied Reactor Technology and Nuclear Power Safety. Lecture No 6

Lectures on Applied Reactor Technology and Nuclear Power Safety. Lecture No 6 Lectures on Nuclear Power Safety Lecture No 6 Title: Introduction to Thermal-Hydraulic Analysis of Nuclear Reactor Cores Department of Energy Technology KTH Spring 2005 Slide No 1 Outline of the Lecture

More information

Unit B-4: List of Subjects

Unit B-4: List of Subjects ES312 Energy Transfer Fundamentals Unit B: First Law of Thermodynamics ROAD MAP... B-1: The Concept of Energy B-2: Work Interactions B-3: First Law of Thermodynamics B-4: Heat Transfer Fundamentals Unit

More information

M1. (a) range of speeds 1. moving in different directions accept random motion 1. internal energy 1. density = mass / volume 1. (d) / 0.

M1. (a) range of speeds 1. moving in different directions accept random motion 1. internal energy 1. density = mass / volume 1. (d) / 0. M. (a) range of speeds moving in different directions accept random motion (b) internal energy (c) density = mass / volume (d) 0.00254 / 0.04 0.8 accept 0.8 with no working shown for the 2 calculation

More information

HEAT TRANSFER. PHI Learning PfcO too1. Principles and Applications BINAY K. DUTTA. Delhi Kolkata. West Bengal Pollution Control Board

HEAT TRANSFER. PHI Learning PfcO too1. Principles and Applications BINAY K. DUTTA. Delhi Kolkata. West Bengal Pollution Control Board HEAT TRANSFER Principles and Applications BINAY K. DUTTA West Bengal Pollution Control Board Kolkata PHI Learning PfcO too1 Delhi-110092 2014 Contents Preface Notations ix xiii 1. Introduction 1-8 1.1

More information

Forced Convection: Inside Pipe HANNA ILYANI ZULHAIMI

Forced Convection: Inside Pipe HANNA ILYANI ZULHAIMI + Forced Convection: Inside Pipe HANNA ILYANI ZULHAIMI + OUTLINE u Introduction and Dimensionless Numbers u Heat Transfer Coefficient for Laminar Flow inside a Pipe u Heat Transfer Coefficient for Turbulent

More information

Chapter 7: External Forced Convection. Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University

Chapter 7: External Forced Convection. Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University Chapter 7: External Forced Convection Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University Objectives When you finish studying this chapter, you should be able to: Distinguish between

More information

Review: Conduction. Breaking News

Review: Conduction. Breaking News CH EN 3453 Heat Transfer Review: Conduction Breaking News No more homework (yay!) Final project reports due today by 8:00 PM Email PDF version to report@chen3453.com Review grading rubric on Project page

More information

Convection. U y. U u(y) T s. T y

Convection. U y. U u(y) T s. T y Convection Heat transfer in the presence of a fluid motion on a solid surface Various mechanisms at play in the fluid: - advection physical transport of the fluid - diffusion conduction in the fluid -

More information

Physics Mechanics

Physics Mechanics 1 Physics 170 - Mechanics Lecture 35 Heat 2 Definition and Units of Heat Heat is a form of energy, and therefore is measured in joules. There are other units of heat, the most common one is the kilocalorie:

More information

Level 7 Post Graduate Diploma in Engineering Heat and mass transfer

Level 7 Post Graduate Diploma in Engineering Heat and mass transfer 9210-221 Level 7 Post Graduate Diploma in Engineering Heat and mass transfer 0 You should have the following for this examination one answer book non programmable calculator pen, pencil, drawing instruments

More information

There are four phases of matter: Phases of Matter

There are four phases of matter: Phases of Matter HEAT SCIENCE There are four phases of matter: Phases of Matter There are four phases of matter: Phases of Matter Animation States of Matter Solids Solids: Are rigid, crystalline Hold their shape Have little

More information

Physical Science Chapter 5 Cont3. Temperature & Heat

Physical Science Chapter 5 Cont3. Temperature & Heat Physical Science Chapter 5 Cont3 Temperature & Heat What are we going to study? Heat Transfer Phases of Matter The Kinetic Theory of Gases Thermodynamics Specific Heat (Capacity) Specific Heat Latent Heat

More information

Summary of Dimensionless Numbers of Fluid Mechanics and Heat Transfer

Summary of Dimensionless Numbers of Fluid Mechanics and Heat Transfer 1. Nusselt number Summary of Dimensionless Numbers of Fluid Mechanics and Heat Transfer Average Nusselt number: convective heat transfer Nu L = conductive heat transfer = hl where L is the characteristic

More information

Lecture 28. Key words: Heat transfer, conduction, convection, radiation, furnace, heat transfer coefficient

Lecture 28. Key words: Heat transfer, conduction, convection, radiation, furnace, heat transfer coefficient Lecture 28 Contents Heat transfer importance Conduction Convection Free Convection Forced convection Radiation Radiation coefficient Illustration on heat transfer coefficient 1 Illustration on heat transfer

More information

S6. (a) State what is meant by an ideal gas...

S6. (a) State what is meant by an ideal gas... IB PHYSICS Name: DEVIL PHYSICS Period: Date: BADDEST CLASS ON CAMPUS TSOKOS CHAPTER 3 TEST REVIEW S1. Thermal energy is transferred through the glass windows of a house mainly by A. conduction. B. radiation.

More information

Chapter 11. Important to distinguish between them. They are not interchangeable. They mean very different things when used in physics Internal Energy

Chapter 11. Important to distinguish between them. They are not interchangeable. They mean very different things when used in physics Internal Energy Chapter 11 Energy in Thermal Processes Energy Transfer When two objects of different temperatures are placed in thermal contact, the temperature of the warmer decreases and the temperature of the cooler

More information

4.1. Physics Module Form 4 Chapter 4 - Heat GCKL UNDERSTANDING THERMAL EQUILIBRIUM. What is thermal equilibrium?

4.1. Physics Module Form 4 Chapter 4 - Heat GCKL UNDERSTANDING THERMAL EQUILIBRIUM. What is thermal equilibrium? Physics Module Form 4 Chapter 4 - Heat GCKL 2010 4.1 4 UNDERSTANDING THERMAL EQUILIBRIUM What is thermal equilibrium? 1. (, Temperature ) is a form of energy that flows from a hot body to a cold body.

More information

Countercurrent heat exchanger

Countercurrent heat exchanger Countercurrent heat exchanger 1. Theoretical summary The basic operating principles and the simplified calculations regarding the counter current heat exchanger were discussed in the subject Chemical Unit

More information

Overall Heat Transfer Coefficient

Overall Heat Transfer Coefficient Overall Heat Transfer Coefficient A heat exchanger typically involves two flowing fluids separated by a solid wall. Heat is first transferred from the hot fluid to the wall by convection, through the wall

More information

4.1. Physics Module Form 4 Chapter 4 - Heat GCKL UNDERSTANDING THERMAL EQUILIBRIUM. What is thermal equilibrium?

4.1. Physics Module Form 4 Chapter 4 - Heat GCKL UNDERSTANDING THERMAL EQUILIBRIUM. What is thermal equilibrium? 4.1 4 UNDERSTANDING THERMAL EQUILIBRIUM What is thermal equilibrium? 1. ( Heat, Temperature ) is a form of energy that flows from a hot body to a cold body. 2. The SI unit for ( heat, temperature) is Joule,

More information

Introduction to Heat and Mass Transfer. Week 14

Introduction to Heat and Mass Transfer. Week 14 Introduction to Heat and Mass Transfer Week 14 Next Topic Internal Flow» Velocity Boundary Layer Development» Thermal Boundary Layer Development» Energy Balance Velocity Boundary Layer Development Velocity

More information

Convective Mass Transfer

Convective Mass Transfer Convective Mass Transfer Definition of convective mass transfer: The transport of material between a boundary surface and a moving fluid or between two immiscible moving fluids separated by a mobile interface

More information

The experimental determination of the thermal conductivity of melting chocolate: thermal resistance analogies and free convection boundary conditions

The experimental determination of the thermal conductivity of melting chocolate: thermal resistance analogies and free convection boundary conditions Advanced Computational Methods and Experiments in Heat Transfer XIII 505 The experimental determination of the thermal conductivity of melting chocolate: thermal resistance analogies and free convection

More information

General Physics (PHY 2130)

General Physics (PHY 2130) General Physics (PHY 2130) Lecture 34 Heat Heat transfer Conduction Convection Radiation http://www.physics.wayne.edu/~apetrov/phy2130/ Lightning Review Last lecture: 1. Thermal physics Heat. Specific

More information

HEAT TRANSFER BY CONVECTION. Dr. Şaziye Balku 1

HEAT TRANSFER BY CONVECTION. Dr. Şaziye Balku 1 HEAT TRANSFER BY CONVECTION Dr. Şaziye Balku 1 CONDUCTION Mechanism of heat transfer through a solid or fluid in the absence any fluid motion. CONVECTION Mechanism of heat transfer through a fluid in the

More information

Name Class Date. What are three kinds of energy transfer? What are conductors and insulators? What makes something a good conductor of heat?

Name Class Date. What are three kinds of energy transfer? What are conductors and insulators? What makes something a good conductor of heat? CHAPTER 14 SECTION Heat and Temperature 2 Energy Transfer KEY IDEAS As you read this section, keep these questions in mind: What are three kinds of energy transfer? What are conductors and insulators?

More information

Answer: The relation between kelvin scale and Celsius scale is TK =TC => TC=TK

Answer: The relation between kelvin scale and Celsius scale is TK =TC => TC=TK Question The triple points of neon and carbon dioxide are 24.57 K and 216.55 K respectively. Express these temperatures on the Celsius and Fahrenheit scales. Answer: The relation between kelvin scale and

More information

Chapter 1 Heating Processes

Chapter 1 Heating Processes Chapter 1 Heating Processes Section 1.1 Heat and temperature Worked example: Try yourself 1.1.1 CALCULATING THE CHANGE IN INTERNAL ENERGY A student places a heating element and a paddle wheel apparatus

More information

Thermal Unit Operation (ChEg3113)

Thermal Unit Operation (ChEg3113) Thermal Unit Operation (ChEg3113) Lecture 3- Examples on problems having different heat transfer modes Instructor: Mr. Tedla Yeshitila (M.Sc.) Today Review Examples Multimode heat transfer Heat exchanger

More information

Chapter 10: Steady Heat Conduction

Chapter 10: Steady Heat Conduction Chapter 0: Steady Heat Conduction In thermodynamics, we considered the amount of heat transfer as a system undergoes a process from one equilibrium state to another hermodynamics gives no indication of

More information

SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT B.Tech. [SEM V (ME-51, 52, 53, 54)] QUIZ TEST-1 (Session: )

SHRI RAMSWAROOP MEMORIAL COLLEGE OF ENGG. & MANAGEMENT B.Tech. [SEM V (ME-51, 52, 53, 54)] QUIZ TEST-1 (Session: ) QUIZ TEST-1 Time: 1 Hour HEAT AND MASS TRANSFER Note: All questions are compulsory. Q1) The inside temperature of a furnace wall ( k=1.35w/m.k), 200mm thick, is 1400 0 C. The heat transfer coefficient

More information

Department of Mechanical Engineering ME 96. Free and Forced Convection Experiment. Revised: 25 April Introduction

Department of Mechanical Engineering ME 96. Free and Forced Convection Experiment. Revised: 25 April Introduction CALIFORNIA INSTITUTE OF TECHNOLOGY Department of Mechanical Engineering ME 96 Free and Forced Convection Experiment Revised: 25 April 1994 1. Introduction The term forced convection refers to heat transport

More information

DEPARTMENT OF MECHANICAL ENGINEERING. ME 6502 Heat and Mass Transfer III YEAR-V SEMESTER

DEPARTMENT OF MECHANICAL ENGINEERING. ME 6502 Heat and Mass Transfer III YEAR-V SEMESTER ME650 HEAT AND MASS TRNSFER MARKS & 16 MARKS QUESTION AND ANSWER ME 650 Heat and Mass Transfer III YEAR-V SEMESTER NAME :. REG.NO :. BRANCH :... YEAR & SEM :. 1 ME650 HEAT AND MASS TRNSFER MARKS & 16 MARKS

More information