TOPIC 2 [A] STEADY STATE HEAT CONDUCTION

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1 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 inner surface. Consider Heat transfer coefficient of 5 W/m 2 -K (between inside air and inside surface) and Heat transfer coefficient of 30 W/m2-K (between outside air and outside surface). The temperatures at the inside and outside air are 0 & 35 respectively. Calculate I. heat transfer rate II. steel-cork interface temp. 2. A storage chamber of interior dimensions 10 mx 8 mx 2.5 m high has its inside maintained at a temperature of 20 whilst the outside is at 25. The walls and ceiling of the chamber have three layers made of 60 mm thick board (k = 0.2 W m deg) on the inside 90 mm thick insulation (k = 0.04 W m deg) at the mid 240 mm thick concrete (k = 1.8 W m deg) on the outside Neglecting flow of heat through the floor, determine the rate at which heat can flow towards inside of the chamber. (D.S. Kumar, Example 3.13) 3. A steam pipe of 5 cm inside diameter and 6.5 cm outside diameter is insulated with a 2.75 cm radial thickness of high temperature insulation (k = 1.1 W/mK). The surface heat transfer coefficient for inside and outside surfaces are 4650 W/m 2 K and 11.5 W/m 2 K respectively. The thermal conductivity of the pipe material is 45 W/m K. If the steam temperature is 200 C and ambient air temperature 25 C, determine I. Heat loss per meter length of pipe II. III. Temperature at the interface Overall heat transfer coefficient 4. An 8 mm thick metal plate, having thermal conductivity 98.6 W m K is exposed to vapor at 100 on one side and cooling water at 30 on another side. The heat transfer coefficients are W m 2 K on vapor side and 2325 W m 2 K on water side. Determine the rate of heat transfer and drop in temperature on each side of the plate. Assume area of the plate as unity.(summer 2014)(Similar to D.S. Kumar, Example 3.40) Darshan Institute of Engineering and Technology, Rajkot 1

2 5. A steel tube of 5 cm inner diameter and 8 cm outer diameter(k = 16 W mk), is covered with an insulation of 3 cm thickness(k = 0.3 W mk). A hot gas at350, h = 400 W m 2 K flows. Calculate the heat loss from the tube for 20 meter length. Also calculate the temperature at the interface of insulation and steel. Outside air temperature is at30,h = 60 W m 2 K. (May-2012) (Similar to Mahesh Rathod, Example 3.29) 6. A refrigeration suction line having outer diameter 30 mm is required to be thermally insulated. The outside air convective heat transfer coefficient is 12 W m 2 K. The thermal conductivity of the insulating material is0.3 W mk. Determine: I. Whether the insulation will be effective II. Estimate the maximum value of thermal conductivity of insulating material to reduce heat transfer III. The thickness of cork insulation to reduce the heat transfer to 20% (k=0.04 W/m o C)(Summer 2013) ASSIGNMENT Theory 1. Derive an expression for three dimensional time dependent heat conduction with internal heat generation and constant thermal conductivity in cartesian coordinate system. Reduce it as i. Poisson equation ii. Fourier equation iii. Laplace equation (May-11, May-12, Winter-12, Winter-14, DEC-15, May-16) 2. Write the general heat conduction equation in cylindrical and reduce that equation for steady state heat conduction in radial direction and solve it to obtain temperature profile in radial direction through hollow cylinder. 3. Explain the following terms I. Radiation II. Thermal resistance (Summer-13, Winter-13, MAY-17, NOV-17, MAY-18) III. Thermal diffusivity (Dec-11, MAY-17, NOV-17) Darshan Institute of Engineering and Technology, Rajkot 2 IV. Thermal conductivity

3 4. What do you understand by critical radius of insulation? Draw rough sketch showing variation in heat transfer with respect to radius of insulation. Derive the equation for critical radius of insulation for cylinder. (May-12, Summer-13, Summer-14, Summer-15, MAY-16, MAY-17, MAY-18) Examples 1. A furnace wall is made up of two layers of thickness 250 mm, 100 mm with thermal conductivity of 1.65 and 9.2 W/m o C respectively. The inside is exposed to gases at 1250 o C with a convection coefficient of 25 W/m 2 o C and the inside surface is at 1100 o C, the outside surface is exposed to air at 25 o C with convection coefficient of 12 W/m 2 o C. The overall heat transfer coefficient. (MAY-18) 2. A steam pipe is covered with two layered of insulation, first layer being 3 cm thick and second 5 cm. The pipe is made of steel (k = 58 W/mK) having ID of 160 mm and OD of 170 mm. The inside and outside film coefficients are 30 and 5.8 W/m2K respectively. Calculate the heat loss per meter of pipe if the steam temperature is 300 C and air temperature 50 C. The thermal conductivity of two insulating materials are 0.17 and W/mK respectively. (DEC-16, MAY-17) Darshan Institute of Engineering and Technology, Rajkot 3

4 TOPIC 2 [B] FIN CLASS TUTORIAL 1. A long rod 12 mm square section made of low carbon steel protrudes into air at 35 C from a furnace wall at 200 C. The convective heat transfer coefficient is estimated at 22W/m 2 K. The conductivity of the material is 51.9 W/mK. Determine the location from the wall at which the temperature will be 60 C. Also calculate the temperature at 80 mm from base. 2. A temperature rise of 70 C in a circular shaft of 60 mm diameter is caused by amount of heat generated due to friction in the bearing mounted on the crankshaft. The thermal conductivity of the shaft material is 50 W/mK and the heat transfer coefficient is 10 W/m 2 K. Determine the amount of heat transfer through the shaft. Assume that the shaft is a rod of infinite length. 3. Calculate the amount of heat transfer through an iron fin of length 60mm, width 100mm and thickness 10mm. assume that the thermal conductivity of material is 210 kj/mh C and heat transfer coefficient is 40 kj/ m 2 h C and temperature at the base is 90 C. also calculate the temperature at tip of the fin, if the atmosphere temperature is 25 C. ASSIGNMENT Theory 1. Derive an expression for heat dissipation in rectangular Fin of uniform cross section which is insulated at tip. (Dec.-11, Winter-12, Winter-13, Winter-14, Dec.-15, MAY-16, MAY-18) 2. Derive the governing differential equation for temperature distribution of constant cross-sectional area fin. Hence derive expression for temperature distribution for long fin stating the assumption made. (Summer 2013, Summer 2015, DEC-16) 3. Why fins are used? Define effectiveness and efficiency of fin. For long fin with insulated tip, show that η of fin = tanh ml ml with usual notations (Summer 2014, DEC-16, MAY-17, NOV-17) Darshan Institute of Engineering and Technology, Rajkot 4

5 Examples 1. A fin 30 cm long and 10 cm diameter throughout is made of material A (Select Material from the table). The fin is attached to a plane heated wall at 200 temperature extends into surroundings at 25 and heat transfer coefficient of 120 W/m 2 -K. Find I. The rate of heat transfer from the fin II. The temperature distribution along the fin length at an interval of 5 cm from the base III. fin efficiency IV. fin effectiveness. For the following different condition I. The length of the fin is infinite II. The tip of the fin is insulated Assume that thermal radiation effect is negligible. SR. MATERIAL Thermal Conductivity BATCH NO. (W/mK) 1 Copper 393 AX1 2 Aluminium 240 AX2 3 Stainless Steel 17 AY1 4 Brass 137 AY2 5 Low carbon steel 56 ALL Darshan Institute of Engineering and Technology, Rajkot 5

6 TOPIC 2 [C] TRNASIENT HEAT CONDUCTION CLASS TUTORIAL 1. A solid copper sphere of 12cm diameter, initially at a uniform temperature 260 is suddenly dropped in a fluid which is maintained at a uniform temperature of 40. The convective heat transfer coefficient is 200 W m 2 K. The properties of copper are as follow: k = 385 W mk, Density = 8954 kg m 3, Sp. Heat = 383 J kgk Calculate the temperature of the copper block at 5min after immersion. 2. A solid sphere of 1 cm made up of steel is at initially at 300 temperature. Properties of steel: k = 60 W mk, Density = 7800 kg m 3, Sp. Heat = 434 J kgk Calculate the time required for cooling it up to 50 in the following two cases I. cooling medium is air at 25 with h = 20 W m 2 K II. cooling medium is water at 25 with h = 100 W m 2 K (Winter-2013) (Similar to D.S. Kumar, Example 6.7) ASSIGNMENT Theory 1. Explain lumped heat capacity method and state its assumptions. (MAY-16, MAY-17, MAY-18) 2. Differentiate between steady state and transient heat conduction. Explain two examples of heat conduction under unsteady state. (May-12, DEC-16) 3. What are Fourier and Biot Number? What is the physical significance of these numbers? (Winter-12, Winter-13, DEC-16) Examples 1. Estimate the time required to cook a carrot in boiling water at atmospheric pressure. The carrot is initially at room temp 32 C and the cooking requirement stipulates that a minimum temp. of 97 C is reached at the center of carrot. Treat the carrot as a long cylinder of 18 mm diameter and having the following properties: ρ=1025 kg/m3, Cp = 4000 J/kg K, k= 3.45 W/m-K, convective heat transfer coefficient h = 60 W/m2-K. (DEC-15) Darshan Institute of Engineering and Technology, Rajkot 6

7 2. An aluminum sphere weighing 6 kg and initially at temperature of 350 C is suddenly immersed in a fluid at 30 C with convective coefficient of 60 W/m2K. Estimate the time required to cool the sphere to 100 C. Take thermo physical properties of sphere as C = 900 J/kgK, ρ = 2700 kg/m3 k = 205 W/mK (MAY-16) Darshan Institute of Engineering and Technology, Rajkot 7

8 TOPIC 4 RADIATION CLASS TUTORIAL 1. Consider a 20-cm-diameter spherical ball at 800 K suspended in air as shown in Figure. Assuming the ball closely approximates a blackbody, determine (a) the total blackbody emissive power, (b) the total amount of radiation emitted by the ball in 5 min 2. The effective temperature of body having an area of 0.12 m 2 is 600. Calculate the following: I. The total rate of energy emission II. The intensity of normal radiation III. The wavelength of maximum monochromatic emissive power 3. Two very large parallel plates are maintained at uniform temperatures T1=800 K and T2=500 K and have emissivity ɛ1=0.2 and ɛ2=0.7, respectively, as shown in Figure. Determine the net rate of radiation heat transfer between the two surfaces per unit surface area of the plates. 4. A refractory material which has ɛ=0.4 at 1500K and ɛ=0.43 at 1420K is exposed to black surface wall at 1500K. What is the rate of gain of heat radiation per m 2 area? 5. Calculate the rate of heat transfer rate per m 2 area by radiation between the surfaces of two long cylinders having radii 100mm and 50mm respectively. The smaller cylinder being in the larger cylinder. The axis of the cylinders are parallel to each other and separated by distance of 20mm. The surface of inner and outer cylinders is Darshan Institute of Engineering and Technology, Rajkot 8

9 maintained at 127 and 27 respectively. The emissivity of both the surfaces is 0.5. Assume the medium between the two cylinders is non absorbing. 6. Liquid oxygen (boiling temperature= -182 ) is to be stored in the spherical container of 30cm diameter. The system is insulated by an evacuated space between inner space and surrounding 45cm inner diameter concentric sphere. For both sphere ɛ=0.03 and temperature of the outer sphere is 30. Estimate the rate of heat flow by radiation to the oxygen in the container. 7. A thin aluminum sheet with an emissivity of 0.1 on both sides is placed between two very large parallel plates that are maintained at uniform temperatures T1=800 K and T2=500 K and have emissivities ɛ1=0.2 and ɛ2=0.7, respectively. Determine the net rate of radiation heat transfer between the two plates per unit surface area of the plates and compare the result to that without the shield. ASSIGNMENT Theory 1. Define:(May 2011, Summer 2013, Summer 2015, DEC-16, NOV-17) I. Emissivity, II. III. IV. Radiosity, Black body Irradiation, V. Absorptivity, VI. VII. Grey body Solid angle. 2. Define total emissive power (Eb) and intensity of radiation (Ib). Show that Eb = π Ib 3. (a) Explain Wien s displacement law of radiation. (b) Explain Kirchoff s law of radiation. (DEC-15, MAY-17, MAY-18) (DEC-16, MAY-17, NOV-17) 4. What is Radiosity (J)? Show that the net radiant energy leaving the surface is given by (DEC-16) 5. What is radiation shield? Show that presence of n number of radiation shields reduces the radiation heat transfer by a factor of (n+1). (MAY-18) Darshan Institute of Engineering and Technology, Rajkot 9

10 Examples 1. Consider two large parallel plates, one at temperature at 727 C with emissivity 0.8 and other at 227 C with emissivity 0.4. An aluminium radiation shield with an emissivity of 0.05 on both sides is placed between two plates. Calculate reduction in heat transfer rate between two plates as a result of shield. (MAY-17) 2. An enclosure measures 1.5m* 1.5m with a height of 2m under steady state conditions, the wall and ceiling are maintained at 525 K and floor is at 400K. Determine net radiation to floor. Take emissivity of ceiling and wall = 0.85 and emissivity of floor = 0.75 (NOV-17) B.E. Semester V Darshan Institute of Engineering and Technology, Rajkot 10

11 1. Discuss and define: a) Natural and Forced Convection. CHAPTER 3 CONVECTION Theory b) Mean Film Temperature & Bulk Mean Temperature. ASSIGNMENT - CONVECTION 2. State the general equation for the rate of heat transfer by convection and hence define the coefficient of heat transfer. What are the various factors on which the value of this coefficient depends? 3. Define and discuss the following dimensionless numbers: a) Reynolds Number b) Prandtl Number c) Grashoff Number d) Nusselt Number. 4. Derive the generalized co-relation for natural convection by using Buckingham s π theorem method. 5. Derive the generalized co-relation for forced convection by using Buckingham s π theorem method. 6. Derive the momentum equation for hydrodynamic boundary layer over a flat plate. 7. Define and discuss the hydrodynamic and thermal boundary layers over a flat plate. Show the thickness of these layers for different Prandtl numbers. Examples 1. Calculate the rate of heat loss from a human body which may be considered as vertical cylinder 30 cm in diameter and 175 cm high in still air at 15 C. The skin temperature is 35 C and emissivity at the skin surface is 0.4. Neglect sweating and effect of clothing. Use Nu = 0.13 (Gr Pr) [Ans: W] [D.S. Kumar 11.15] 2. A nuclear reactor with its core constructed of parallel vertical plates 2.25 m high and 1.5 wide has been designed on free convection heating of liquid bismuth. Metallurgical considerations limit the maximum surface temperature of the plate to 975 C and the lowest allowable temperature of bismuth is 325 C. Estimate the maximum possible heat dissipation from both sides of each plate. The appropriate correlation for the convection coefficient is Nu = 0.13 (Gr Pr) 1/3. Where, the different parameters are evaluated as the mean film temperature. [Ans: 153 MW] [D.S. Kumar;11.6] 3. A sheet metal air duct carries air-conditioned air at an average temperature of 10 C. The duct size is 320mm x 200mm and length of the duct exposed to the surrounding air at 30 C is 15m long. Find the heat gain by the air in the duct. Assume 200mm side is vertical and top surface of the duct is insulated. Use the following correlation: Nu = 0.6 (Gr Pr) 0.25 for vertical surface, and Nu = 0.27 (Gr Pr) 0.25 for horizontal surface. [Ans: W] [R. K. Rajput; 8.5] Darshan Institute of Engineering and Technology, Rajkot 1

12 ASSIGNMENT - CONVECTION 4. A gas pipe is kept in an atmosphere of 20 C. The radius of pipe is 3.75cm and is lagged with insulation thickness of 2.5cm. The emissivity of the surface is 0.9.The length of pipe is 6 m. Surface temperature ts=80 C. Calculate (i) The total heat loss from pipe (ii) The overall heat transfer coefficient (iii) The heat transfer co efficient due to only radiation. For convection use co-relation, Nu =0.53(Gr.Pr) 1/4. [Ans: W; W/m 2 -K; W/m 2 -K] [GTU DEC 2013] 5. A spherical heater of 20cm diameter and at 60 C is immersed in a tank of water at 20 C. Determine the value of convective heat transfer coefficient & heat transfer rate by natural convection. For a sphere, the general correlation is Nu = (Ra) [Ans: W/m 2 -deg, W] [D.S. Kumar; 11.4] 6. Air at 30 C and at atmospheric pressure flows over a flat plate at a speed of 1.9 m/sec. If the plate is maintained at 90 C, calculate the heat transfer per unit width of the plate; assuming the length of the plate along the flow of air is 2 meters. Where local Nusselt number is given by,nu x = (Re x ) 1 2(Pr x ) 1 3 [Ans: W] 7. Air at 30 C and at atmospheric pressure is flowing over a flat plate with velocity 4 m/sec. If the plate is 2m long and the wall temperature is 70 C. Calculate the following at a location 2m from leading edge. a. Hydrodynamic boundary layer thickness. b. Local heat transfer co-efficient. [Ans: 13.90mm; W/m 2 K] 8. Air at 27 C and 1 atm flows over a flat plate at a velocity of 3 m/s. Calculate the boundary layer thickness at distances of 25 and 45 cm from the leading edge of the plate. Calculate the mass flow which enters the boundary layer between x = 25cm and x = 45cm. The viscosity of air at 27 C is 1.85E-05 kg/m-s. Assume parabolic velocity distribution and unit depth in z-direction. [Ans: 5.31mm; 7.125; kg/s] [4.17; P. K. NAG] 9. Water at 50 C enters 1.5 cm diameter and 3 m long tube with a velocity of 1.5 m/s. The tube wall is maintained at 100 C. Calculate the heat transfer coefficient and total amount of heat transferred if the water exit temperature is 70 C. The relevant properties of water are Pr = 3.15, ρ = 990 kg/m 3, ν = m 2 /s, Cp = 4184 J/kg-K, kf = 0.65 W/m-K. Use following correlation, Nu D = 0.023(Re D ) 0.8 (Pr) 0.4 Use following properties of fluid at required temperature, Example Temp ρ Cp ν x 10 Fluid K µ Pr No. C kg/m 3 KJ/kg-deg m 2 /sec W/m-deg kg/m-hr 1 Air Bismuth Air Air Water Air Air Darshan Institute of Engineering and Technology, Rajkot 2

13 CHAPTER 3 CONVECTION CLASS TUTORIAL 1. Calculate the rate of heat loss from a human body which may be considered as a vertical cylinder 300mm dia. and 1750 mm high. while standing in a 30 Km/hr wind at 10 C. The surface temperature of the human body is 30 C. The approximate corelation for laminar flow is Nu = 0.664(Re) 0.5 (Pr) 0.33 and the characteristic length is the diameter of human body. [Ans: W] 2. A hot square plate 40cm x 40cm at 100 C is exposed to atmospheric air at 20 C. Make calculations for the heat loss from both surfaces of the plate, if (a) plate is kept vertical (b) plate is kept horizontal. The following empirical correlations have been suggested: Nu = (Gr Pr) 0.33 for vertical position of plate, and Nu = 0.72 (Gr Pr) 0.25 for upper surface Nu = 0.35 (Gr Pr) 0.25 for lower surface [Ans: W] [D.S. Kumar 11.9, GTU - JAN 2013] 3. Estimate the heat transfer from a 40W incandescent bulb at 120 C to 20 C quiescent air. Approximate the bulb as a 50 mm dia. Sphere. What percentage of power is lost by free convection? The approximate co-relation is, N u = 0.60(G r P r ) [Ans: W; 19.62%] 4. A steam pipe 8 cm in diameter is covered with 3 cm thick layer of insulation which has a surface emissivity of 0.9.The surface temperature of the insulation is 80 C and the pipe is placed in atmospheric air at 24 C. Considering heat loss by both radiation and natural convection calculate: (1) The heat loss from the 7 m length of pipe. (2) The overall heat transfer coefficient & heat transfer co-efficient due to radiation alone. Use empirical correlation for horizontal cylinders as, Nu = 0.53(Gr. Pr) 0.25 [Ans: W; W/m 2 - C; W/m 2 - C][GTU DEC 2011] 5. Water at 10 C, flows over a flat plate (at 90 C) measuring 1 m X 1 m, with a velocity of 2 m/s. Determine, (a) The length of plate over which the flow is laminar (b) The rate of heat transfer up to the above length (c) The rate of heat transfer from the entire plate. Useful correlation: Nu = 0.332(Re x ) 1 2(Pr) 1 3 local Nusselt number for laminar flow Nu = [0.036(Re L ) ](Pr) 1/3 Average Nusselt number for mixed flow [Ans: 0.139m; KW; 471KW][GTU MAY 2013] 6. Air at 20 C is flowing over a flat plate which is 200mm wide and 500mm long. The plate is maintained at 100 C. Find the heat loss from the plate if the air is flowing Darshan Institute of Engineering and Technology, Rajkot 1

14 CLASS TUTORIAL parallel to 500mm side with 2m/s velocity. What will be the effect on heat transfer if the flow is parallel to 200mm side? For laminar flow over flat plate, use following correlation: Nu = (Re L ) 1 2(Pr) 1 3 [Ans: W, 85.6 W] [R. K. Rajput; 7.15] 7. Air at 20 C and at a pressure of 1 bar is flowing over a flat plate at a velocity of 3m/sec. If the plate is 280 mm wide and at 56 C, calculate the following quantities at x = 280 mm. a. Hydrodynamic boundary layer thickness b. Local and average friction coefficient c. Shearing stress due to friction d. Thickness of thermal boundary layer e. Local and average convective heat transfer coefficient f. Rate of heat transfer by convection g. Total drag force on the plate and h. Total mass flow rate through the boundary [Ans: Using Blasius Solution:-6.26mm; ; ; N/m 2 ; 7.05mm; 6.43W/m 2 K; 12.86W/m 2 K; 36.29W; N; kg/s] [4.6; P. K. NAG] 8. A plate of length 750mm has been placed longitudinally in a stream of crude oil which flows with a velocity of 5 m/sec. If the oil has a specific gravity of 0.8 and kinematic viscosity of 1 x 10-4 m 2 /sec, calculate, a. Boundary layer thickness at the middle of plate b. Shear stress at the middle of plate and c. Friction drag on one side of the plate. [Ans: m; N/m 2 ; N] 9. Air at 20 C and at atmospheric pressure flows at a velocity 4.5 m/s past a flat plate with a sharp leading edge. The entire plate surface is maintained at a temperature of 60 C. Assuming that the transition occurs at a critical Reynolds number of , find the distance from the leading edge at which the boundary layer changes from laminar to turbulent. At the location calculate: (1) thickness of hydrodynamic and thermal boundary layer, (2) Local and average heat transfer coefficients, (3) Heat transfer rate from both sides per unit width of plate. Use Nu xc = 0.332(Re xc ) 1/2 (Pr) 1/3 Assume cubic velocity profile and approximate method. [Ans: 12.34mm; 13.55mm; 3.05W/m 2 K; 6.1W/m 2 K; 917.4W] [GTU MAY 2012] [4.7; P. K. NAG] 10. The air at atmospheric pressure and temperature of 30 C flows over one side of plate of a velocity of 90 m/min. This plate is heated and maintained at 100 C over its entire length. Find out the following at 0.3 and 0.6 m from its leading edge. (1) Thickness of velocity boundary layer and thermal boundary layer. (2) Mass flow rate Darshan Institute of Engineering and Technology, Rajkot 2

15 CLASS TUTORIAL which enters the boundary layer between 0.3 m and 0.6 m per metre depth of plate. Assume unit width of plate. [Ans: 8.30mm; 9.119mm; 11.73mm; 12.88mm; kg/s] [GTU MAY 2012] Use following properties of fluid at required temperature, Example Temp ρ Cp ν x 10 Fluid K µ Pr No. C kg/m 3 KJ/kg-deg m 2 /sec W/m-deg kg/m-hr 1 Air Air Air Air Water Air Air Air Air Darshan Institute of Engineering and Technology, Rajkot 3

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17 CHAPTER 5 HEAT EXCHANGERS Theory ASSIGNMENT HEAT EXCHANGERS 1. Discuss various types of heat exchangers. Also discuss the importance of heat exchangers for industrial use. 2. What is mean by fouling factor? How does it affect the performance of a heat exchanger? 3. Explain difference between regenerator and recuperator. 4. Define: Overall heat transfer co-efficient, Heat capacity ratio, Number of transfer units. 5. Is it better to arrange for the flow in a heat exchanger to be parallel or counter flow? Explain with appropriate reasons. Also draw rough sketch of temperature distribution curve for condenser and evaporator type heat exchangers. 6. Derive equation of logarithmic mean temperature difference for Parallel flow heat exchanger. 7. Derive equation of logarithmic mean temperature difference for Counter flow heat exchanger. 8. Define effectiveness of heat exchanger. Derive equation for effectiveness of a Parallel flow heat exchanger. 9. Define effectiveness of heat exchanger. Derive the relationship between the effectiveness and number of transfer units for a counter flow heat exchangers. Examples 1. In a counter flow heat double pipe heat exchanger,water is heated from 25 C to 65 C by oil with specific heat of 1.45 kj/kg K and mass flow rate of 0.9 kg/s. The oil is cooled from 230 C to 160 C. If overall Heat transfer coefficient is 420 W/m 2 C. calculate following: a. The rate of heat transfer b. The mass flow rate of water, and c. The surface area of heat exchanger [Ans: 91.35KW, kg/s, 1.45 m 2 ] [GTU DEC-2013] 2. Dry saturated steam at 10 bar enters a counter-flow heat exchanger at the rate of 15 kg/s and leaves at 300 C. The entry of gas at 600 C is with mass flow rate of 25 kg/s. If the condenser tubes are 30 mm diameter and 3 m long, make calculations for the heating surface area and the number of tubes required. Neglect the resistance offered by the metallic tubes. Take the following properties for steam and gas: Darshan Institute of Engineering and Technology, Rajkot 1

18 ASSIGNMENT HEAT EXCHANGERS For steam: tsat = 180 C (at 10 bar); cps = 2.7 kj/kg-k; hs = 600 W/m 2 -deg For gas: cpg = 1 kj/kg-k; hg = 250 W/m 2 -deg. [Ans: m 2, 374] [14.20, D. S. Kumar] 3. A single pass shell and tube heat exchanger, consisting of a bundle of 100 tubes (inner diameter 25 mm and thickness 2 mm) is used for heating 8 kg/s of water from 25 C to 75 C with the help of steam condensing at atmospheric pressure on the shell side with condensing heat transfer co-efficient 5000 W/m 2 -deg. Make calculations for the overall heat transfer co-efficient based on the inner area and length of the tube bundle. Take fouling factor on the water side to be m 2 -deg/w per tube and neglect effect of fouling on the shell side and thermal resistance of the tube wall. The thermo-physical properties of water at the mean bulk temperature of 50 C are: ρ = 998 kg/m 3 ; cp = 4175 J/kg-deg; k = 0.65 W/m-deg; µ = 55 X 10-5 kg/m-s [Ans: W/m 2 -deg, 5.52 m] [14.27, D. S. Kumar] 4. Hot water at 2.5 kg/s and 100 C enters a concentric tube counter flow heat exchanger having a total area of 23m2. Cold water at 20 C enters at 5 kg/s and the overall heat transfer coefficient is 1000 W/m2K. Determine the total heat transfer rate and the outlet temperature of hot and cold fluids. [GTU DEC-2015] 5. Hot water having specific heat 4200 J/kg-K flows through a heat exchanger at the rate of 4 kg/min with an inlet temperature of 100 C. A cold fluid having a specific heat 2400 J/kg-K flows in at a rate of 8 kg/min and with inlet temperature 20 C. Make calculations for the maximum possible effectiveness if the fluid flow conforms to (a) parallel flow arrangement (b) counter flow arrangement. [Ans: 0.533, 1] [14.40, D. S. Kumar] 6. Oil (cp = 3.6 kj/kg- C) at 100 C flows at the rate of kg/h and enters into a concurrent heat exchanger. Cooling water (cp = 4.2 kj/kg- C) enters the heat exchanger at 10 C at the rate of kg/h. The heat transfer area is 10 m 2 and U = 1000 W/m 2 - C. Calculate the following: a. The outlet temperatures of oil and water; b. The maximum possible outlet temperature of water. [Ans: 71.2 C, 24.8 C, 40.5 C] [10.37, R. K. Rajput] Darshan Institute of Engineering and Technology, Rajkot 2

19 CHAPTER 5 HEAT EXCHANGERS CLASS TUTORIAL 1. Exhaust gases (Cp = 1.12 kj/kg-deg) flowing through a tubular heat exchanger at the rate of 1200 kg/hr are cooled from 400 C to 120 C. The cooling is affected by water (Cp = 4.18 kj/kg-deg) that enters the system at 10 C at the rate of 1500 kg/hr. If the overall heat transfer co-efficient is 500 kj/m 2 -hr-deg, what heat exchanger area is required to handle the load for (a) Parallel flow and (b) Counter flow arrangement? [Ans: m 2, m 2 ] [14.9, D. S. Kumar] 2. Calculate the surface area required for a heat exchanger which is required to cool 3600 kg/hr of benzene (Cp = 1.74 kj/kg-k) from 75 C to 45 C. The cooling water (Cp = 4.18 kj/kg-deg) at 15 C has a flow rate of 2500 kg/hr. consider the following arrangements: a. Single pass counter flow b. 1-4 exchanger (one shell pass and four tube passes) c. Cross flow single pass with water mixed and benzene unmixed. The overall heat transfer co-efficient for each configuration is approximated to be 0.3kW/m 2 -K. [Ans: 4.87 m 2, 5.29 m 2, 5.18 m 2 ] [14.35, D. S. Kumar] 3. A heat exchanger is to be designed to condense 8 kg/s of an organic liquid (tsat = 80 C; hfg = 600 kj/kg) with cooling water available at 15 C and at a flow rate of 60 kg/s. The overall heat transfer co-efficient is 480 W/m 2 -deg. Calculate: a. The number of tubes required. The tubes are to be of 25 mm outer diameter, 2 mm thickness and 4.85 m length. b. The number of tube passes. The velocity of the cooling water is not to exceed 2 m/s. [Ans: 478 tubes, 6 passes] [14.19, D. S. Kumar] 4. In a shell and tube heat exchanger, 6 kg/s of oil flows through the shell side. The oil enters at 105 C and leaves at 40 C. Water flows in the tubes, entering at 32 C and leaving at 50 C. In addition, Cpoil = 2282 J/kg-K and U = 416 W/m2-K. Determine number of tubes, if outer diameter of tubes is 100 mm, length of each tube is 1.9 m and take correction factor as [GTU MAY-2016, MAY 2017] 5. A counter flow heat exchanger is used to cool 2000 kg/hr of oil (cp = 2.5 kj/kg-k) from 105 C to 30 C by the use of water entering at 15 C. If the overall heat transfer co-efficient is expected to be 1.5 kw/m 2 K, make calculations for the water flow rate, the surface area required and the effectiveness of heat exchanger. Presume that the exit temperature of the water is not to be exceed 80 C. Use NTU-effectiveness approach. [Ans: kg/hr, 3.55 m 2, 0.833] [14.41, D. S. Kumar] 6. A tube type heat exchanger is used to cool hot water from 80 C to 60 C. The task is accomplished by transferring heat to cold water that enters the heat exchanger at 20 C and leaves at 40 C. Should this heat exchanger operate under counter flow or parallel flow conditions? Also determine the exit temperatures if the flow rates of fluids are doubled. [Ans: C, C] [14.47, D. S. Kumar] Darshan Institute of Engineering and Technology, Rajkot 1

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21 ASSIGNMENT BOILING & CONDENSATION CHAPTER 6 BOILING & CONDENSATION Theory 1. Discuss various regimes of pool boiling with neat sketch. OR Discuss in detail the various regimes in boiling and explain (i) the condition for the growth of bubbles and (ii) effect of bubble size on boiling. 2. Distinguish a. Sub-cooled and Saturated boiling b. Pool boiling and Forced convection boiling c. Nucleate and Film boiling. 3. What is condensation? When does it occur? Differentiate between film wise and drop wise condensation. Which type has better heat transfer coefficient? In condenser design which of condensation is usually selected and why? 4. Write note on influence of non-condensable gases on condensation. Darshan Institute of Engineering and Technology, Rajkot 1