OUTCOME 2 - TUTORIAL 1

Size: px
Start display at page:

Download "OUTCOME 2 - TUTORIAL 1"

Transcription

1 Unit 4: Heat Transfer and Combustion Unit code: K/60/44 QCF level: 5 Credit value: 5 OUTCOME - TUTORIAL Heat transfer coefficients Dimensional analysis: dimensionless groups; Reynolds, Nusselt, Prandtl, Stanton, Grashof numbers Heat transfer mechanism: description of flow in tubes, ducts and across surfaces; boundary layer; laminar and turbulent; forced and natural convection; fluid properties; flow parameters; boiling and condensation Determine heat transfer coefficients: Dittus-Boelter equation for forced convection in circular ducts and tubes, for various fluids, tube dimensions and flow parameters; use of charts and data for fluid properties You should judge your progress by completing the self assessment exercises. On completion of this tutorial the student should be able to do the following. This is the third tutorial in the series on heat transfer and covers some of the advanced theory of convection. The tutorials are designed to bring the student to a level where he or she can solve problems involving practical heat exchangers. On completion of this tutorial the student should be able to do the following. Explain the use of the overall heat transfer coefficient. Explain the factors involved in heat transfer. Apply dimensional analysis to heat transfer. Solve heat transfer problems for basic shapes. D.J.Dunn

2 DERIVATION AND CALCULATION OF HEAT TRANSFER COEFFICIENTS The surface heat transfer coefficients depend on many things such as shape and orientation of the surface, the velocity of the fluid and the properties of the fluid. The fluid properties also depend on the temperature. The velocity of the fluid is a major consideration and this varies with distance from the surface in the boundary layer and distance from the leading edge. All these factors are involved when deriving formula from basic principles. Perhaps the best place to start is with boundary layers. BOUNDARY LAYER - LAMINAR AND TURBULENT When a fluid flows over a surface, the velocity grows from zero at the surface to a maximum at distance. In theory, the value of is infinity but in practice it is taen as the height needed to obtain 99% of the mainstream velocity and this is very small. The boundary layer is important for the following reason. When a fluid is convecting heat to or from a solid surface, the heat transfer close to the surface is by conduction through the boundary layer. Outside the boundary layer the temperature is the bul temperature of the fluid but inside it decreases to the surface temperature. The diagram shows how the temperature varies from the hot fluid on one side of a wall to cold fluid on the other side. There is a boundary layer on both sides. Consider the hot side only. Using the conduction law from the bul fluid : The heat transfer at θ h to the surface at θ is Φ = (/δ)a( θ h - θ ) The heat transfer using the convection law is Φ = ha( θ h - θ ) Equating to find h we have h = /δ So the surface heat transfer depends on the thicness of the boundary layer and the thermal conductivity of the fluid. The boundary layer thicness depends on several factors such as the velocity and distance from the leading edge maing the calculation of h a lot less simple than implied above. The boundary layer shape is discussed next. BOUNDARY LAYER SHAPE There are many theories and formulae that describe the shape of the boundary and this is covered in fluid mechanics. The following is a summary. When the flow is laminar the boundary layer is a curve following the precise law δ dp uo u y μ dl δ When the flow is turbulent, the shape of the boundary layers waivers and the mean shapes are usually shown. D.J.Dunn

3 Comparing a laminar and turbulent boundary layer reveals that the turbulent layer is thinner than the laminar layer. When laminar flow occurs in a round pipe the boundary layer grows in three dimensions from the wall and meets at the middle. The velocity u in a pipe of radius R at any radius r is given by Δp u R r Δp is the pressure drop. 4 μ L There are many formulae and theories for the shape of the boundary layer such as that given by Prandtl. u = u(y/) /7 This law fits the turbulent case well for Reynolds numbers below 07: FORMATION OF BOUNDARY LAYER When a fluid first encounters a solid surface, the boundary layer grows with distance until it becomes fully formed. Eventually it changes from laminar to turbulent. This also affects the heat transfer. DIMENSIONLESS GROUPS One of the best ways to analyse how all the factors come together is the use of dimensional analysis and the dimensionless groups that they form. Those required to study this topic should refer to the fluid dynamics module. A dimensionless group is a combination of variables that have no overall dimensions when grouped in a certain pattern and when evaluated yields a number with no units. D.J.Dunn

4 LIST OF VARIABLES THAT AFFECT HEAT TRANSFER Dynamic viscosity μ Kinematic viscosity ν = μ /ρ Density ρ Thermal conductivity Specific heat capacity c p Temperature θ Mean velocity u o Characteristic length l or diameter D or distance from leading edge x. Coefficient of cubical expansion β There are many dimensionless groups for heat transfer and a summary is given next. Here is a summary of the groups that occur. ρuod uod ρuox uox REYNOLDS NUMBER Red or Rex μ ν μ ν This group occurs in studies of fluid friction and is widely used in determining whether the flow is laminar or turbulent. It may be based on pipe diameter D or distance from the edge of a surface x. hx NUSSELT NUMBER Nu x This group is very important for convection. The solution of h often depends on evaluating Nux first. cpμ PRANDTL NUMBER Pr This is a group that relates some of the thermal properties. βgρ x θ GRASHOF NUMBER Grx μ This is a group is important in convection because it determines how the buoyancy of the fluid is affected by temperature. STANTON NUMBER St h ρ u c p Nu Re Pr The following demonstrates that Nu = Pr Re DIMENSIONAL ANALYSIS Tutorials on dimensional analysis may be found in the modules on fluid mechanics. The following is the application of this method to heat transfer. There are many dimensionless groups for heat transfer. A dimensionless group is a combination of variables that have no overall dimension when grouped in a certain pattern and when evaluated yields a number with no units. The surface heat transfer coefficient h is a function of the following variables. Dynamic viscosity μ, density ρ, thermal conductivity, specific heat capacity c, temperature θ, mean velocity u and Characteristic length l D.J.Dunn 4

5 The solution to this problem is much easier if we use energy E as a base unit. The dimensions used here are: Length L Mass M Time T Temperature θ Energy E First convert the units into dimensions. h Watts/m K Energy/s m K E/(T L θ) μ g/m s M/(LT) ρ g/m M/L Watts/m K Energy/s m K E/(T L θ) c J/g K E/(M θ) θ K θ u m/s L/T l m L The general relationship is This may be represented as a power series h = (μ,ρ,,c,θ,u,l) h = constant μ a ρ b c c d θ e u f l g There are 8 quantities and 5 dimensions so there will be 8 5 = dimensionless groups. The solution is easier if told in advance that we solve a, b, c,e and g in terms of d and f Put in the dimensions. Any not present are implied index 0 ET - L - θ - M 0 = constant (ML - T - ) a (ML - ) b (ET - L - θ - ) c (EM - θ - ) d θ e (LT - ) f L g Equate dimensions on left and right of equality. Energy = c + d c = d Mass 0 = a + b d Hence b = d - a or a = d - b Length - = -a - b - c + f + g substitute to get rid of b and c - = -a (d - a) ( - d) + f + g - = -a d + a + d + f + g - = a d + f + g Temperature - = -c d + e substitute for c - = -(- d) - d + e Hence e = 0 Time - = -a - c - f substitute for c and a - = -( d - b) ( - d) f hence b = f Now finish with a = d - b = d - f From - = a d + f + g substitute for unnowns - = (d - f) d + f + g - = d - f d + f + g - = - f + g g = f - Next form the groups by substituting the indices into h = constant μ a ρ b c c d θ e u f l g h = constant μ d-f ρ f -d c d θ 0 u f l f- d f μ c ρ u l h l μ c ρ u l h const const l μ μ Nu = h l/ Pr =cμ/ Re = ρ u l/μ = u l/ν The Prandtl number is a function of fluid properties only and so may be looed up in tables at the appropriate temperature. d f D.J.Dunn 5

6 SOME STANDARD CASES Studies of fluids and boundary layers have led to formulae for the surface heat transfer coefficient under specified conditions. In the following you need to be conversant with tables of fluid properties in order to loo them up. Here are some of the better nown formulae. NATURAL CONVECTION WITH A VERTICAL SURFACE Nu x Pr Pr 0.95) 4 Gr 4 This has an approximate solution of h =.4 (ΔT/D) /4 when Gr is in the range 0 4 to 0 9 and h = 0.9 (ΔT/D) /4 when Gr is in the range 0 9 to 0 FORCED CONVECTION OVER A HORIZONTAL SURFACE Nu = 0. Pr / Re / (Ta/Ts) 0.7 TURBULENT FLOW THROUGH A PIPE (Dittus-Boelter Equation) Nu = 0.0 Re 0.8 Pr 0.4 NATURAL CONVECTION FROM A HORIZONTAL CYLINDER Nu 0.57Pr This has an approximate solution of h =.(ΔT/D) /4 4 - Pr 0.95 Gr 4 x WORKED EXAMPLE No. Air at 88 K and bul velocity 6 m/s flows over a flat horizontal plate with a temperature of 8 K at all points on its surface. Given that Nu = 0. Pr / Re / (Ta/Ts) 0.7 Calculate the heat transfer rate per metre width from both sides over the first 50 mm. Ta is the bul air temperature and Ts is the surface temperature. The fluid properties should be obtained at the mean temperature. SOLUTION Nu = 0. Pr / Re / (Tw/Ts) 0.7 Mean temperature is (88 + 8)/ = K From fluids tables Pr = 0.68 υ = 4.55 x 0-5 m /s Re = v l/υ = 6 x 0.5/ 4.55 x 0-5 = 9.9 x D.J.Dunn 6 = 4.9 x 0 - W/m K 8 Nu x h l 4.9 x0 Nu h W/m K l 0.5 Heat Transfer from one side = Φ = h A (Tw-Ts) =.64 x ( x 0.5) x (8-88) = W For two sides double the answer.

7 WORKED EXAMPLE No. Calculate the heat transfer to air at 5 o C by natural convection with a vertical surface 0.6 m tall and m wide maintained at 79 o C at all points. The Nusselt Number is given by Nux Pr Pr 0.95) 4 Grx4 β = coefficient of cubical expansion given by β = /T SOLUTION β = /T = /(7 + 5) = /88 Use the fluid tables for dry air at (5 o C) 88 K and atmospheric pressure Taing atmospheric pressure as.0 bar Gas constant R = 87 J/g K ρ = p/rt =.0 x 0 5 /(87 x 88) =.6 g/m This can be also be found in the tables. μ is the dynamic viscosity μ =.788 x 0-5 g/m s Pr = 0.69 Thermal conductivity =.5 x 0 - W/ m K Taing x as the height of the wall 9.8x.6 (0.6) x 88 βgρx θ 88 9 Grashof Number Grx x 0 5 μ.788 x 0 Nux Pr Pr 0.95) 4 Grx ) x Nux h x Nux x0 h W/m K x 0.6 This the value at height 0.6 m. We need the mean over the height and this is 4/ of the value h = (4/)5.9 = W/m K Heat Transfer from one side = Φ = h A (79-5) = x (0.6 x ) x (79-5) = 8 W D.J.Dunn 7

8 WORKED EXAMPLE No. Calculate the heat transfer to air at 5 o C by natural convection with a vertical surface 0.6 m tall and m wide maintained at 79 o C at all points. The Nusselt Number is given by Nux Pr Pr 0.95) 4 Grx4 β = coefficient of cubical expansion given by β = /T SOLUTION β = /T = /(7 + 5) = /88 Use the fluid tables for dry air at (5 o C) 88 K and atmospheric pressure Taing atmospheric pressure as.0 bar Gas constant R = 87 J/g K ρ = p/rt =.0 x 0 5 /(87 x 88) =.6 g/m This can be also be found in the tables. μ is the dynamic viscosity μ =.788 x 0-5 g/m s Pr = 0.69 Thermal conductivity =.5 x 0 - W/ m K Taing x as the height of the wall 9.8x.6 (0.6) x 88 βgρx θ 88 9 Grashof Number Grx x 0 5 μ.788 x 0 Nux Pr Pr 0.95) 4 Grx ) x Nux h x Nu x0 h W/m K x 0.6 This the value at height 0.6 m. We need the mean over the height and this is 4/ of the value h = (4/)5.9 = W/m K Heat Transfer from one side = Φ = h A (79-5) = x (0.6 x ) x (79-5) = 8 W D.J.Dunn 8

9 WORKED EXAMPLE No. 4 Dry saturated steam at 77 o C flows in a pipe with a bore of 50 mm with a mean velocity of 6 m/s. The pipe has a wall 7 mm thic and is covered with a layer of insulation 50 mm thic. The surrounding atmospheric air is at 7 o C. Calculate the heat transfer rate for m length. The Nusselt number is given by Nu = 0. Re 0.8 Pr 0.4 for pipe = 50 W/m K for insulation = 0.06 W/m K The surface heat transfer coefficient for a long horizontal cylinder is h =.(ΔT/D) /4 SOLUTION From the fluids table for d.s.s. at 77 o C we find Pr =.4 and v g = 0. m /g μ = 4.88 x 0-6 g m/s = W/m K D = 0.5 m u = 6 m/s Re = u D/μ v g = 04 for pipe = 50 W/m K for insulation = 0.06 W/m K Nu = 0.0 Re 0.8 Pr 0.4 = 9.9 Nu = h D/ = h = 9.9 x /0.5 = 0.89 W/m K Heat transfer = Φ per metre length From steam to pipe Φ = h A ΔT = h πd ΔT = 0.89 π x 0.5 ΔT = ΔT Through the pipe wall Φ = πδt/ln(d /D ) = π x 50 ΔT/ln(64/50) = 5 ΔT Through the insulation Φ = πδt/ln(d /D ) = π x 0.06 ΔT/ln(64/64) = 0.79 ΔT From the outer surface h =. (ΔT/D) /4 =. (ΔT/0.64) /4 =.84(ΔT) /4 Φ = h A ΔT =.84(ΔT) /4 π x 0.64 ΔT =.58(ΔT) 5/4 Because the surface temperature is unnown we need the heat transfer between the steam and the surface and the surface and the air. Steam to Surface Φ = U (77 T s ) = U (77 T s ) U is found from. 64 U = 0.7 U U Φ = 0.78(77 T s ) Surface to Air Φ =.57(T s 7) 5/4 Equate Φ = 0.7(77 T s ) =.57(T s 7) 5/4 Possibly the best way to solve this is by plotting 0.7(77 T s ) and.57(t s 7) 5/4 against temperature to find the temperature that maes them the same. This appears to be 45 o C D.J.Dunn 9

10 Φ = 0.7(77 T s ) = 0.7(77 45) = 0.4 W Φ =.57(T s 7) 5/4 =.57(45 7) 5/4 = 0.8 W Say 0.6 W SELF ASSESSMENT EXERCISE No.. Air at 00 K and bul velocity 8 m/s flows over a flat horizontal plate with a temperature of 900 K at all points on its surface. Given that Nu = 0. Pr / Re / (Ta/Ts) 0.7 Calculate the heat transfer rate per metre of width from one side over the first 00 mm and the first 00 mm. Ta is the bul air temperature and Ts is the surface temperature. The fluid properties should be obtained at the mean temperature. (897 W and 68 W). Calculate the heat transfer to air at o C by natural convection with a vertical surface m tall and m wide maintained at 0 o C at all points. Nux Pr β = coefficient of cubical expansion given by β = /T (676 W) The Nusselt Number is given by 4 4 Pr 0.95). Dry saturated steam at 5 bar flows in a pipe with a bore of 00 mm with a mean velocity of 4 m/s. The pipe has a wall 4 mm thic and is covered with a layer of insulation 60 mm thic. The surrounding atmosphere is at 0 o C. Calculate surface temperature of the lagging and the heat transfer rate for m length. The Nusselt number is given by Nu = 0.0 Re 0.8 Pr 0.4 for pipe = 55 W/m K for insulation = 0.08W/m K The surface heat transfer coefficient for a long horizontal cylinder is h =.(ΔT/D) /4 (0 o C and 6.4 W ) Grx D.J.Dunn 0

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

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

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

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

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

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 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

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

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

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

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

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

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

Chapter 7: Natural Convection

Chapter 7: Natural Convection 7-1 Introduction 7- The Grashof Number 7-3 Natural Convection over Surfaces 7-4 Natural Convection Inside Enclosures 7-5 Similarity Solution 7-6 Integral Method 7-7 Combined Natural and Forced Convection

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

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

Thermal and Fluids in Architectural Engineering

Thermal and Fluids in Architectural Engineering hermal and Fluids in Architectural Engineering 12. Convection heat transfer Jun-Seo Par, Dr. Eng., Prof. Dept. of Architectural Engineering Hanyang Univ. Where do we learn in this chaper 1. Introduction

More information

Lecture 30 Review of Fluid Flow and Heat Transfer

Lecture 30 Review of Fluid Flow and Heat Transfer Objectives In this lecture you will learn the following We shall summarise the principles used in fluid mechanics and heat transfer. It is assumed that the student has already been exposed to courses in

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

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

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

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

6.2 Governing Equations for Natural Convection

6.2 Governing Equations for Natural Convection 6. Governing Equations for Natural Convection 6..1 Generalized Governing Equations The governing equations for natural convection are special cases of the generalized governing equations that were discussed

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

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

Technological design and off-design behavior of heat exchangers 26

Technological design and off-design behavior of heat exchangers 26 Technological design and off-design behavior of heat exchangers 26 2.2 MODELING OF HEAT TRANSFER The overall heat transfer coefficient U depends on the distribution of thermal resistances in the exchanger.

More information

MECHANISM BEHIND FREE /NATURAL CONVECTION

MECHANISM BEHIND FREE /NATURAL CONVECTION CONVECTIVE HEAT TRANSFER By: Prof K. M. Joshi, Assi. Professor, MED, SSAS Institute of Technology, Surat. MECHANISM BEHIND FREE /NATURAL CONVECTION The stagnate layer of fluid in immediate vicinity of

More information

Empirical Co - Relations approach for solving problems of convection 10:06:43

Empirical Co - Relations approach for solving problems of convection 10:06:43 Empirical Co - Relations approach for solving problems of convection 10:06:43 10:06:44 Empirical Corelations for Free Convection Use T f or T b for getting various properties like Re = VL c / ν β = thermal

More information

ME 331 Homework Assignment #6

ME 331 Homework Assignment #6 ME 33 Homework Assignment #6 Problem Statement: ater at 30 o C flows through a long.85 cm diameter tube at a mass flow rate of 0.020 kg/s. Find: The mean velocity (u m ), maximum velocity (u MAX ), and

More information

FINITE ELEMENT ANALYSIS OF MIXED CONVECTION HEAT TRANSFER ENHANCEMENT OF A HEATED SQUARE HOLLOW CYLINDER IN A LID-DRIVEN RECTANGULAR ENCLOSURE

FINITE ELEMENT ANALYSIS OF MIXED CONVECTION HEAT TRANSFER ENHANCEMENT OF A HEATED SQUARE HOLLOW CYLINDER IN A LID-DRIVEN RECTANGULAR ENCLOSURE Proceedings of the International Conference on Mechanical Engineering 2011 (ICME2011) 18-20 December 2011, Dhaka, Bangladesh ICME11-TH-014 FINITE ELEMENT ANALYSIS OF MIXED CONVECTION HEAT TRANSFER ENHANCEMENT

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

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

Ben Wolfe 11/3/14. Figure 1: Theoretical diagram showing the each step of heat loss.

Ben Wolfe 11/3/14. Figure 1: Theoretical diagram showing the each step of heat loss. Condenser Analysis Water Cooled Model: For this condenser design there will be a coil of stainless steel tubing suspended in a bath of cold water. The cold water will be stationary and begin at an ambient

More information

FORMULA SHEET. General formulas:

FORMULA SHEET. General formulas: FORMULA SHEET You may use this formula sheet during the Advanced Transport Phenomena course and it should contain all formulas you need during this course. Note that the weeks are numbered from 1.1 to

More information

HEAT AND MASS TRANSFER. List of Experiments:

HEAT AND MASS TRANSFER. List of Experiments: HEAT AND MASS TRANSFER List of Experiments: Conduction Heat Transfer Unit 1. Investigation of Fourier Law for linear conduction of heat along a simple bar. 2. Study the conduction of heat along a composite

More information

5th WSEAS Int. Conf. on Heat and Mass transfer (HMT'08), Acapulco, Mexico, January 25-27, 2008

5th WSEAS Int. Conf. on Heat and Mass transfer (HMT'08), Acapulco, Mexico, January 25-27, 2008 Numerical Determination of Temperature and Velocity Profiles for Forced and Mixed Convection Flow through Narrow Vertical Rectangular Channels ABDALLA S. HANAFI Mechanical power department Cairo university

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

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

Circle one: School of Mechanical Engineering Purdue University ME315 Heat and Mass Transfer. Exam #2. April 3, 2014

Circle one: School of Mechanical Engineering Purdue University ME315 Heat and Mass Transfer. Exam #2. April 3, 2014 Circle one: Div. 1 (12:30 pm, Prof. Choi) Div. 2 (9:30 am, Prof. Xu) School of Mechanical Engineering Purdue University ME315 Heat and Mass Transfer Exam #2 April 3, 2014 Instructions: Write your name

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

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

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

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

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

NUMERICAL HEAT TRANSFER ENHANCEMENT IN SQUARE DUCT WITH INTERNAL RIB

NUMERICAL HEAT TRANSFER ENHANCEMENT IN SQUARE DUCT WITH INTERNAL RIB NUMERICAL HEAT TRANSFER ENHANCEMENT IN SQUARE DUCT WITH INTERNAL RIB University of Technology Department Mechanical engineering Baghdad, Iraq ABSTRACT - This paper presents numerical investigation of heat

More information

Dimensionless Numbers

Dimensionless Numbers 1 06.10.2017, 09:49 Dimensionless Numbers A. Salih Dept. of Aerospace Engineering IIST, Thiruvananthapuram The nondimensionalization of the governing equations of fluid flow is important for both theoretical

More information

Analysis, Design and Fabrication of Forced Convection Apparatus

Analysis, Design and Fabrication of Forced Convection Apparatus Analysis, Design and Fabrication of Forced Convection Apparatus Shajan K. Thomas 1, Vishnukumar C M 2, Vishnu C J 3, Alex Baby 4 Assistant Professor, Dept. of Mechanical Engineering, Toc H Institute of

More information

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA SCIENCE FOR TECHNICIANS OUTCOME 3 - ENERGY TUTORIAL 2 HEAT

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA SCIENCE FOR TECHNICIANS OUTCOME 3 - ENERGY TUTORIAL 2 HEAT EDEXCEL NATIONAL CERTIFICATE/DIPLOMA SCIENCE FOR TECHNICIANS OUTCOME 3 - ENERGY TUTORIAL 2 HEAT 3. Energy Mechanical work, energy and power: work - energy relationship, gravitational potential energy,

More information

10. Buoyancy-driven flow

10. Buoyancy-driven flow 10. Buoyancy-driven flow For such flows to occur, need: Gravity field Variation of density (note: not the same as variable density!) Simplest case: Viscous flow, incompressible fluid, density-variation

More information

طراحی مبدل های حرارتی مهدي کریمی ترم بهار HEAT TRANSFER CALCULATIONS

طراحی مبدل های حرارتی مهدي کریمی ترم بهار HEAT TRANSFER CALCULATIONS طراحی مبدل های حرارتی مهدي کریمی ترم بهار 96-97 HEAT TRANSFER CALCULATIONS ١ TEMPERATURE DIFFERENCE For any transfer the driving force is needed General heat transfer equation : Q = U.A. T What T should

More information

6. Laminar and turbulent boundary layers

6. Laminar and turbulent boundary layers 6. Laminar and turbulent boundary layers John Richard Thome 8 avril 2008 John Richard Thome (LTCM - SGM - EPFL) Heat transfer - Convection 8 avril 2008 1 / 34 6.1 Some introductory ideas Figure 6.1 A boundary

More information

Fundamental Concepts of Convection : Flow and Thermal Considerations. Chapter Six and Appendix D Sections 6.1 through 6.8 and D.1 through D.

Fundamental Concepts of Convection : Flow and Thermal Considerations. Chapter Six and Appendix D Sections 6.1 through 6.8 and D.1 through D. Fundamental Concepts of Convection : Flow and Thermal Considerations Chapter Six and Appendix D Sections 6.1 through 6.8 and D.1 through D.3 6.1 Boundary Layers: Physical Features Velocity Boundary Layer

More information

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

External Forced Convection. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

External Forced Convection. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. External Forced Convection Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Drag and Heat Transfer in External flow Fluid flow over solid bodies is responsible

More information

Internal Forced Convection. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Internal Forced Convection. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Internal Forced Convection Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Introduction Pipe circular cross section. Duct noncircular cross section. Tubes small-diameter

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

Advanced Heat and Mass Transfer by Amir Faghri, Yuwen Zhang, and John R. Howell

Advanced Heat and Mass Transfer by Amir Faghri, Yuwen Zhang, and John R. Howell Laminar external natural convection on vertical and horizontal flat plates, over horizontal and vertical cylinders and sphere, as well as plumes, wakes and other types of free flow will be discussed in

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

INDIAN INSTITUTE OF TECHNOOGY, KHARAGPUR Date: -- AN No. of Students: 5 Sub. No.: ME64/ME64 Time: Hours Full Marks: 6 Mid Autumn Semester Examination Sub. Name: Convective Heat and Mass Transfer Instructions:

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

Thermal engineering with QuickField

Thermal engineering with QuickField Thermal engineering with QuickField Vladimir Podnos Director of marketing and support, Tera Analysis Ltd. Thermal problems in QuickField Sergey Ionin Support engineer, Tera Analysis Ltd. Basics of the

More information

CONVECTIVE HEAT TRANSFER

CONVECTIVE HEAT TRANSFER CONVECTIVE HEAT TRANSFER Mohammad Goharkhah Department of Mechanical Engineering, Sahand Unversity of Technology, Tabriz, Iran CHAPTER 4 HEAT TRANSFER IN CHANNEL FLOW BASIC CONCEPTS BASIC CONCEPTS Laminar

More information

CHME 302 CHEMICAL ENGINEERING LABOATORY-I EXPERIMENT 302-V FREE AND FORCED CONVECTION

CHME 302 CHEMICAL ENGINEERING LABOATORY-I EXPERIMENT 302-V FREE AND FORCED CONVECTION CHME 302 CHEMICAL ENGINEERING LABOATORY-I EXPERIMENT 302-V FREE AND FORCED CONVECTION OBJECTIVE The objective of the experiment is to compare the heat transfer characteristics of free and forced convection.

More information

CHAPTER 4 BOUNDARY LAYER FLOW APPLICATION TO EXTERNAL FLOW

CHAPTER 4 BOUNDARY LAYER FLOW APPLICATION TO EXTERNAL FLOW CHAPTER 4 BOUNDARY LAYER FLOW APPLICATION TO EXTERNAL FLOW 4.1 Introduction Boundary layer concept (Prandtl 1904): Eliminate selected terms in the governing equations Two key questions (1) What are the

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

EXAMPLE SHEET FOR TOPIC 3 AUTUMN 2013

EXAMPLE SHEET FOR TOPIC 3 AUTUMN 2013 EXAMPLE SHEET FOR TOPIC ATMN 01 Q1. se dimensional analysis to investigate how the capillary rise h of a liquid in a tube varies with tube diameter d, gravity g, fluid density ρ, surface tension σ and

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

Temperature distribution and heat flow across the combustion chamber wall.

Temperature distribution and heat flow across the combustion chamber wall. ΜΕΤΑΔΟΣΗ ΘΕΡΜΟΤΗΤΑΣ ΣΤΟΝ ΚΥΛΙΝΔΡΟ (J.B. Heywood: Internal Combustion Engine Fundamentals McGraw Hill 1988) Temperature distribution and heat flow across the combustion chamber wall. Throughout each engine

More information

Numerical Heat and Mass Transfer

Numerical Heat and Mass Transfer Master Degree in Mechanical Engineering Numerical Heat and Mass Transfer 15-Convective Heat Transfer Fausto Arpino f.arpino@unicas.it Introduction In conduction problems the convection entered the analysis

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

cen29305_ch08.qxd 11/30/05 3:05 PM Page 451 INTERNAL FORCED CONVECTION CHAPTER 8 Liquid or gas flow through pipes or ducts is commonly used in heating

cen29305_ch08.qxd 11/30/05 3:05 PM Page 451 INTERNAL FORCED CONVECTION CHAPTER 8 Liquid or gas flow through pipes or ducts is commonly used in heating cen29305_ch08.qxd 11/30/05 3:05 PM Page 451 INTERNAL FORCED CONVECTION CHAPTER 8 Liquid or gas flow through pipes or ducts is commonly used in heating and cooling applications. The fluid in such applications

More information

Convective Heat and Mass Transfer Prof. A. W. Date Department of Mechanical Engineering Indian Institute of Technology, Bombay

Convective Heat and Mass Transfer Prof. A. W. Date Department of Mechanical Engineering Indian Institute of Technology, Bombay Convective Heat and Mass Transfer Prof. A. W. Date Department of Mechanical Engineering Indian Institute of Technology, Bombay Module No.# 01 Lecture No. # 41 Natural Convection BLs So far we have considered

More information

WTS Table of contents. Layout

WTS Table of contents. Layout Table of contents Thermal and hydraulic design of shell and tube heat exchangers... 2 Tube sheet data... 4 Properties of Water and Steam... 6 Properties of Water and Steam... 7 Heat transfer in pipe flow...

More information

Free Convective Heat Transfer From A Vertical Surface For The Case Of Linearly Varying Thermal Potential

Free Convective Heat Transfer From A Vertical Surface For The Case Of Linearly Varying Thermal Potential American Journal of Engineering Research (AJER) e-issn : 232-847 p-issn : 232-936 Volume-2, Issue-9, pp-71-75 www.ajer.org Research Paper Open Access Free Convective Heat Transfer From A Vertical Surface

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

HEAT EXCHANGER. Objectives

HEAT EXCHANGER. Objectives HEAT EXCHANGER Heat exchange is an important unit operation that contributes to efficiency and safety of many processes. In this project you will evaluate performance of three different types of heat exchangers

More information

PROBLEM h fg ρ v ρ l σ 10 3 T sat (kj/kg) (kg/m 3 ) (N/m) (K)

PROBLEM h fg ρ v ρ l σ 10 3 T sat (kj/kg) (kg/m 3 ) (N/m) (K) PROBLEM 10.9 KNOWN: Fluids at 1 atm: mercury, ethanol, R-1. FIND: Critical heat flux; compare with value for water also at 1 atm. ASSUMPTIONS: (1) Steady-state conditions, () Nucleate pool boiling. PROPERTIES:

More information

HEAT TRANSFER. Mechanisms of Heat Transfer: (1) Conduction

HEAT TRANSFER. Mechanisms of Heat Transfer: (1) Conduction HEAT TRANSFER Mechanisms of Heat Transfer: (1) Conduction where Q is the amount of heat, Btu, transferred in time t, h k is the thermal conductivity, Btu/[h ft 2 ( o F/ft)] A is the area of heat transfer

More information

INSTRUCTOR: PM DR MAZLAN ABDUL WAHID

INSTRUCTOR: PM DR MAZLAN ABDUL WAHID SMJ 4463: HEAT TRANSFER INSTRUCTOR: PM ABDUL WAHID http://www.fkm.utm.my/~mazlan TEXT: Introduction to Heat Transfer by Incropera, DeWitt, Bergman, Lavine 5 th Edition, John Wiley and Sons Chapter 9 Natural

More information

Chapter 7: External Forced Convection

Chapter 7: External Forced Convection Chapter 7: External Forced Convection Yoav Peles Department of Mechanical, Aerospace and Nuclear Engineering Rensselaer Polytechnic Institute Copyright The McGraw-Hill Companies, Inc. Permission required

More information

Outlines. simple relations of fluid dynamics Boundary layer analysis. Important for basic understanding of convection heat transfer

Outlines. simple relations of fluid dynamics Boundary layer analysis. Important for basic understanding of convection heat transfer Forced Convection Outlines To examine the methods of calculating convection heat transfer (particularly, the ways of predicting the value of convection heat transfer coefficient, h) Convection heat transfer

More information

Table of Contents. Foreword... xiii. Preface... xv

Table of Contents. Foreword... xiii. Preface... xv Table of Contents Foreword.... xiii Preface... xv Chapter 1. Fundamental Equations, Dimensionless Numbers... 1 1.1. Fundamental equations... 1 1.1.1. Local equations... 1 1.1.2. Integral conservation equations...

More information

Experimental Analysis for Natural Convection Heat Transfer through Vertical Cylinder

Experimental Analysis for Natural Convection Heat Transfer through Vertical Cylinder Experimental Analysis for Natural Convection Heat Transfer through Vertical Cylinder 1 Shyam S. Kanwar, 2 Manoj K. Yadav, Saurabh Sharma 3 1,2,3 Assistant Professor 1 Department of Mechanical Engg. 1 Institute

More information

6 Empirical and Practical

6 Empirical and Practical 6 Empirical and Practical Forced-Convection Relations for Heat Transfer CHAPTER 6-1 INTRODUCTION The discussion and analyses of Chapter 5 have shown how forced-convection heat transfer may be calculated

More information

Heat Transfer with Phase Change

Heat Transfer with Phase Change CM3110 Transport I Part II: Heat Transfer Heat Transfer with Phase Change Evaporators and Condensers Professor Faith Morrison Department of Chemical Engineering Michigan Technological University 1 Heat

More information

Chapter 10: Boiling and Condensation 1. Based on lecture by Yoav Peles, Mech. Aero. Nuc. Eng., RPI.

Chapter 10: Boiling and Condensation 1. Based on lecture by Yoav Peles, Mech. Aero. Nuc. Eng., RPI. Chapter 10: Boiling and Condensation 1 1 Based on lecture by Yoav Peles, Mech. Aero. Nuc. Eng., RPI. Objectives When you finish studying this chapter, you should be able to: Differentiate between evaporation

More information

J.P. Holman: 3.09) T sur := Use table 3-1 to determine the shape factor for this problem. 4π r S := T sphere := 30K r 1. S = m k := 1.

J.P. Holman: 3.09) T sur := Use table 3-1 to determine the shape factor for this problem. 4π r S := T sphere := 30K r 1. S = m k := 1. .P. Holman:.09) T ur : 0 Ue table - to determine the hape factor for thi problem. D :.m r : 0.5m π r S : T phere : 0 r D S 7.0 m :.7 m Ue eq. - to calculate the heat lo. q : S T phere T ur q 57.70 .P.

More information

V. MODELING, SIMILARITY, AND DIMENSIONAL ANALYSIS To this point, we have concentrated on analytical methods of solution for fluids problems.

V. MODELING, SIMILARITY, AND DIMENSIONAL ANALYSIS To this point, we have concentrated on analytical methods of solution for fluids problems. V. MODELING, SIMILARITY, AND DIMENSIONAL ANALYSIS To this point, we have concentrated on analytical methods of solution for fluids problems. However, analytical methods are not always satisfactory due

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

External Forced Convection :

External Forced Convection : External Forced Convection : Flow over Bluff Objects (Cylinders, Spheres, Packed Beds) and Impinging Jets Chapter 7 Sections 7.4 through 7.8 7.4 The Cylinder in Cross Flow Conditions depend on special

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 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

Heat Transfer Coefficient Solver for a Triple Concentric-tube Heat Exchanger in Transition Regime

Heat Transfer Coefficient Solver for a Triple Concentric-tube Heat Exchanger in Transition Regime Heat Transfer Coefficient Solver for a Triple Concentric-tube Heat Exchanger in Transition Regime SINZIANA RADULESCU*, IRENA LOREDANA NEGOITA, ION ONUTU University Petroleum-Gas of Ploiesti, Department

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

Natural Convection Systems

Natural Convection Systems C H A P T E R 6 Natural Convection Systems 6.1 Physical Mechanism Of Natural Convection Many familiar heat transfer applications involve natural convection as the primary mechanism of heat transfer. Some

More information

Internal Flow: Heat Transfer in Pipes

Internal Flow: Heat Transfer in Pipes Internal Flow: Heat Transfer in Pipes V.Vuorinen Aalto University School of Engineering Heat and Mass Transfer Course, Autumn 2016 November 15 th 2016, Otaniemi ville.vuorinen@aalto.fi First about the

More information

Chapter 8 INTERNAL FORCED CONVECTION

Chapter 8 INTERNAL FORCED CONVECTION Heat Transfer Chapter 8 INTERNAL FORCED CONVECTION Universitry of Technology Materials Engineering Department MaE216: Heat Transfer and Fluid bjectives Obtain average velocity from a knowledge of velocity

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

PROBLEM 7.2 1/3. (b) The local convection coefficient, Eq. 7.23, and heat flux at x = L are 1/2 1/3

PROBLEM 7.2 1/3. (b) The local convection coefficient, Eq. 7.23, and heat flux at x = L are 1/2 1/3 PROBLEM 7. KNOWN: Temperature and velocity of engine oil. Temperature and length of flat plate. FIND: (a) Velocity and thermal boundary layer thickness at trailing edge, (b) Heat flux and surface shear

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