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 contact (b) Heat content of one body must be more than that of the other (c) One of the bodies must have a high value of thermal conductivity (d) There must exist a temperature difference between the bodies 2. Consider system A at uniform temperature t and system B at another uniform temperature T (t > T). Let the two systems be brought into contact and be thermally insulated from their surroundings but not from each other. Energy will flow from system A to system B because of (a) Temperature difference (b) Energy difference (c) Mass difference (d) Volumetric difference 3. Which of the following law do not govern heat transfer? (a) First Law of Thermodynamics (b) Second Law of Thermodynamics (c) Zeroth Law of Thermodynamics (d) Newton law of motion 4. The literature of heat transfer generally recognizes distinct modes of heat transfer. How many modes are there? a) One b) Two c) Three d) Four 5. Heat transfer in liquids and gases is essentially due to (a) Conduction (b) Convection (c) Radiation (d) Conduction and convection put together
6. Conduction is a process of heat transfer from (a) a hot body to a cold body, in a straight line, without affecting intervening medium (b) one particle of the body to another without the actual motion of the particles (c) one particle of the body to another by the actual motion of the heated particles (d) none of the above 7. Unit of rate of heat transfer is (a) Joule (b) Newton (c) Pascal (d) Watt 8. Which statement is true regarding steady state condition? (a) There is a variation in temperature in the course of time (b) Heat exchange is constant (c) It is a function of space and time coordinates (d) Internal energy of the system changes 9. An oil cooler in a high performance engine has an outside surface area 0.12 m 2 and a surface temperature of 65 degree Celsius. At any intermediate time air moves over the surface of the cooler at a temperature of 30 degree Celsius and gives rise to a surface coefficient equal to 45.4 W/ m 2 K. Find out the heat transfer rate? (a) 238.43 W (b) 190.68 W (c) 543.67 W (d) 675.98 W 10. The rate equation used to describe the mechanism of convection is called Newton s law of cooling. So rate of heat flow by convection doesn t depend on (a) Convective heat transfer coefficient (b) Surface area through which heat flows (c) Time (d) Temperature potential difference 11. Which of the following is an example of forced convection? (a) Chilling effect of cold wind on a warm body (b) Flow of water in condenser tubes (c) Cooling of billets in the atmosphere (d) Heat exchange on cold and warm pipes 12. A radiator in a domestic heating system operates at a surface temperature of 60 degree Celsius. Calculate the heat flux at the surface of the radiator if it behaves
as a black body (a) 697.2 W/m 2 (b) 786.9 W/m 2 (c) 324.7 W/m 2 (d) 592.1 W/m 2 13. The appropriate rate equation for convective heat transfer between a surface and adjacent fluid prescribed by. 14. The radiation energy emitted by a surface depends upon of its absolute temperature. 15. Heat transfer takes place according to law of thermodynamics. 16. The radiation energy emitted by a surface depends upon of its absolute temperature. 17. Heat transfer in liquids and gases is essentially due to. 18. How does heat transfer differ from thermodynamics? Is it true to say that heat transfer is essentially thermodynamics with rate equations added? 19. Write some examples to illustrate the importance of heat transfer in various fields of engineering. 20. What is the driving force for heat transfer? 21. Establish governing law of heat transfer through solid. 22. Cite an analogy that would be useful in fixing the concepts of heat conduction, convection and radiation. 23. Does any convection process involve conduction to some extent? Explain. 24. What is the difference between natural and forced convection? 25. Write the rate equations for the three modes of heat transfer. Define the symbols used and give the units for each. 26. Define thermal contact resistance. 27. Explain mechanism of heat transfer by conduction. 28. What will be your response to a person who states that heat cannot be transferred in a vacuum? 29. State by giving illustration that in practice the transfer of heat is combined effect of conduction, convection and radiation. 30. A person who sits in front of a fireplace feels warm. Through which process or processes of heat transfer does he receives heat. 31. If cooling coils in the refrigerator are placed at the bottom in place of the top then what will happen? Why? 32. Mention the assumptions, on which Fourier s law of heat transfer was established. 33. Explain Newton s law of cooling. 34. A temperature rise of 60 0 C in a circular shaft of 60 mm diameter is caused by the amount of heat generated due to friction. The thermal conductivity of the shaft material is 50 W/m 0 C and heat transfer coefficient is 6.5 W/m 2 0 C. Determine amount of heat transferred through 2 m long shaft. 35. The outer surface of 0.4 m thick concrete wall (20 m x 6m) is kept at a temperature of 10 0 C while the inner surface is kept at 50 0 C. Thermal
conductivity of the concrete is 1.2 w/m- K. Determine the thermal resistance of the wall and heat loss through it. 36. An electronic tube has a mean surface temperature of 55 0 C. Its surface area is 150 cm 2. The temperature of surface is 25 0 C. Calculate the heat lost from the tube by radiation. 37. The wind velocity outside a 20 cm solid brick wall is 7m/s. The thermal conductivity of the brick wall is 0.60 W/m-K. The inside temperature is 21 0 C and the outside one is -6.5 0 C. The film coefficient between the brick and air, at a speed of 7 m/s and a temperature of-6.5 0 C, is 39.8 W/m 2 -K and that for the inside a condition is 17 W/m 2 -K. Find the overall heat transfer coefficient and the rate of heat transfer. 38. Consider two black parallel surfaces; assume the radiant energy from each surface is completely absorbed by other surface. The temperature of one is 204.5 0 C and of the other is 21 0 C. The value of Stefan-Boltzmann constant is 5.6697 x 10-8 W/m 2 -K 4. Find the rate of heat transfer in W/m 2 and the equivalent radiation coefficient. Heat conduction 39. The amount of heat flow through a body by conduction is (a) dependent upon the material of the body (b) directly proportional to the surface area of the body (c) directly proportional to the temperature difference on the two faces of the body (d) inversely proportional to the thickness of the body (e) all of the above 40. Heat conduction in gases is due to (a) electromagnetic waves (b) motion of electrons (c) mixing motion of the different layers of the gas (d) elastic impact of molecules 41. Thermal conductivity of solid metals with rise in temperature. (a) decreases (b) increases (c) remains same (d) ) unpredictable 42. Which of the following has highest thermal conductivity? (a) boiling water (b) melting ice (c) steam (d) solid ice
43. Cork is a good insulator because (a) it is flexible and can be cast into rolls (b) ) it can be powdered (c) it is porous (d) ) its density is low 44. Arrange thermal conductivity of materials in ascending order. Copper, steel, brick and aluminium (a) Copper, steel, brick, aluminium (b) Brick, aluminium, copper, steel (c) Brick, steel, aluminium, copper (d) Steel, copper, brick, aluminium 45. Choose the false statement (a) Thermal conductivity is always higher in the purest form of metal (b) Heat treatment causes considerable variation in thermal conductivity (c) Thermal conductivity of a damp material is considerably higher than the thermal conductivity of the dry material and water taken individually (d) Thermal conductivity decreases with increase in the density of the substance 46. Thermal conductivity of non-metallic amorphous solids with decrease in temperature. (a) Decreases (b) Increases (c) remains constant (d) unpredictable 47. Temperature distribution for a plane wall, for steady state heat flow and constant value for thermal conductivity, is (a) logarithmic (b) parabolic (c) linear (d) any of above 48. A composite plane wall is made up of two different materials of the same thickness and having thermal conductivities of kl and k2 respectively. The equivalent thermal conductivity of the slab is. (a) k1+k2 (b) k1k2 (c) (k 1+ k 2 ) k 1 k 2 k 1 k 2 (d) (k 1 + k 2 )
49. The steady state temperature distribution in a very large thin plate with uniform surface temperatures will be (a) Linear (b) Parabolic (c) Hyperbolic (d) logarithmic 50. The heat flow equation through a sphere of inner radius r1 and outer radius r2 is to be written in the same form as that for heat flow through a plane wall. For wall thickness (r2 r1) the equivalent mean radius for the spherical shell is (a) (b) (c) (d) r1 r 2 2 r 1 r 2 r 1 r 2 r1 r2 r log e r 2 1 51. Heat transfer in liquids and gases is essentially due to (a) Conduction (b) Convection (c) Radiation (d) Conduction and Convection put together 52. For steady state and constant value of thermal conductivity, the temperature distribution associated with radial conduction through a cylinder is (a) Linear (b) Logarithmic (c) Parabolic (d) Exponential 53. 2 The relation T 0 is referred to as (a) Fourier s heat conduction equation (b) Laplace equation (c) Poisson s equation (d) Lumped parameter solution for transient conduction 54. The radial heat transfer rate through hollow cylinder increases as the ratio of outer radius to inner radius (a) decreases (b) increases
(c) constant (d) none of the above 55. Two insulating materials (in two layers) are used to insulate a steam pipe, best result would be obtained if (a) inferior insulation is put over pipe (first layer) and better one over it (second layer). (b) better insulation is put over pipe (first layer) and Inferior one over it (second layer). (c) any material as inner layer (d) unpredictable 56. Thermal diffusivity is a (a) dimensionless parameter (b) Mathematical formula (c) Function of temperature (d) All of above 57. Thermal conductivity is maximum for which substance (a) Silver (b) Ice (c) Aluminum (d) Diamond 58. Materials having crystalline structure have a value of thermal conductivity than the substance in the amorphous form. 59. 2 1 T For an isotropic and homogeneous material, the expression is the T equation for unsteady state heat flow with no internal heat generation. 60. The reciprocal of thermal resistance is called. 61. Thermal conductivity is always in the purest form of metal. 62. Is there any relation between thermal conductivity and electrical conductivity of metals? If yes, explain. 63. Suggest factors affecting thermal conductivity of substance. 64. Derive general heat conduction equation in cartesian coordinates for constant thermal conductivity. And define thermal diffusivity through it. State assumptions made for it. 65. Derive general heat conduction equation in cartesian coordinates. State assumptions made for it. Also simplify it for the case of: No internal heat generation. One dimensional heat transfer 66. How the thermal conductivity of metals vary with temperature and pressure? Which are the exceptions? 67. Point out and explain the various factors which affect the thermal conductivity of a material.
68. What is thermal conductivity? How does it vary with temperature & pressure in solids, liquids & gases? 69. Derive equation for heat transfer by combined mode through a two layer composite wall. Also mention assumptions made for it. 70. Derive equation for heat transfer by conduction through hollow cylinder. Also mention assumptions made for it. 71. Define thermal diffusivity and give its physical significance in heat transfer through conduction. 72. Prove that for a hollow composite cylinder made of m hollow shells enveloping each other the following equation will give rate of heat transfer q m m m1 T1 Tm 1 2l 1 r log e k m r m1 m Where l is the cylinder length, T1 and Tm+1 are the inner and outer surface temperature of composite shell. Assume k1, k2..km are the values of thermal conductivities of 1 st, 2 nd and m th shell and r1, r2..rm+1 be the various radii of this composite cylinder accordingly. A hollow cylinder placed in cold atmosphere contains hot fluid. Develop an equation for prediction of heat transfer by conduction through hollow cylinder. Also mention assumptions made for it. 73. Derive an expression for heat flow through a composite sphere taking into account the film heat transfer coefficients on the inside and outside surface of the sphere. 74. The insulated steam pipe of 16 cm diameter is covered with 4 cm thick layer of insulation (k=0.9 W/m-deg) and carries process steam. Determine the percentage change in the rate of heat loss if an extra 2 cm thick layer of lagging (k=1.25 W/m-deg) is provided. Given that surrounding temperature remains constant and the heat transfer coefficient for both the configuration is 12 W/m 2 -deg. 75. An insulated wall constructed of common brick 20 cm thick and plaster 2.5 cm thick with intermediate layer of loosely packed rock-wool. The outer surfaces of the brick and plaster are at a temperature of 600 0 C and 50 0 C respectively. Calculate the thickness of insulation required in order that the heat loss per square meter shall not exceed 600 W. The conductivities of brick, rock-wool and plaster are 0.32, 0.045 and 0.7 W/m 0 C respectively. 76. A cold storage room has walls made of 220 mm of brick on the outside, 90 mm of plastic foam, and finally 16 mm of wood on the inside. The outside and inside air temperatures are 25 C and -3 C respectively. If the inside and outside heat transfer coefficients are respectively 30 and 11 W/m 2 C, and the thermal conductivities of brick, foam and wood are 0.99, 0.022 and 0.17 W/m C
respectively, determine: (i) The rate of heat removal by refrigeration if the total wall area is 85 m 2 (ii) The interface temperature of the brick & foam. 77. A metal plate of 4 mm thickness (k = 95.5 W/m C) is exposed to vapour at 100 C one side and cooling water at 25 C on the opposite side. The heat transfer coefficients on vapour side and water side are 14500 W/m 2 C and 2250 W/m 2 C respectively. Determine: (i) The rate of heat transfer, (ii) The overall heat transfer coefficient, and (iii) Temperature drop at each side of heat transfer. 78. A plane slab of thickness 60 cm is made of a material of thermal conductivity k = 17.5 W/m deg. The left side of the slab absorbs a net amount of radiant energy from a radiant source at the rate q = 530 W/m 2. If the right hand face of the slab is at a constant temperature T2 = 38 0 C, set up an expression for temperature distribution within the slab as a function of relevant space coordinates. Therefrom work out the temperature at the mid plane of the slab and the maximum temperature within slab. It may be presumed that the temperature distribution is steady and there is no heat generation. 79. A wall of a furnace is made up of inside layer of silica brick 120 mm thick covered with a layer of magnesite brick 250 mm thick. The temperatures at the inside surface of silica brick wall and outside surface of magnesite brick wall are 725 C and 110 C respectively. The contact thermal resistance between the two walls at the interface is 0.0035 C/W per unit area. If thermal conductivities of silica and magnesite bricks are 1.7 W/m C and 5.8 W/m C calculate: (i) The rate of heat loss per unit area of walls, and (ii) The temperature drop at the interface. 80. A furnace wall is composed of 220 mm of fire brick, 150 mm of common brick, 50 mm of 85% magnesia and 3 mm of steel plate on the outside. If the inside surface temperature is 1500 0 C and outside surface temperature is 90 0 C, estimate the temperatures between layers and calculate the heat loss in kj/h m 2. Assume, k (for fire brick) = 4 kj/m h 0 C k (for common brick) = 2.8 kj/m h 0 C k (for 85% magnesia) = 0.24 kj/m h 0 C k (for steel) = 240 kj/m h 0 C 81. An exterior wall of a house is made of 0.1 m layer of common brick (k = 0.7 W/m C) followed by 0.04 m layer of gypsum plaster (k = 0.48 W/m C). Find heat loss through 8.7 m 2 area of wall, if external and internal temperatures are 42 and 15 C respectively. If 58.2 mm thick loosely packed rock wool insulation (k = 0.065 W/m c) is added find effect of it on heat loss through wall in percentage. 82. A two layer wall made of metal plate of 5 mm thickness (k = 95.5 W/m 0 C) followed by insulation layer of 12 mm thickness (k = 0.55 W/m 0 C) is exposed to vapour at 120 0 C one side and cooling water at 25 0 C on the opposite side. The heat transfer coefficients on vapour side and water side are 1050 W/m 2 0 C and 225 W/m 2 0 C respectively. Determine: (i) The rate of heat transfer, and (ii)
Temperature drop at each side of heat transfer 83. Two slabs, each 100 mm thick and made of materials with thermal conductivities of 16 W/m-deg and 1600 W/m-deg are placed in contact which is not perfect. Due to roughness of surfaces, only 40% of area is in contact and air fills 0.02 mm thick gap in the remaining area. If the extreme surfaces of the arrangement are at temperatures of 250 0 C and 30 0 C, determine the heat flow through the composite system, the contact resistance and temperature drop in contact. Take thermal conductivity of air as 0.032 W/m-deg and assume that half of the contact (of the contact area) is due to either metal. 84. A 3 mm thick metal plate, having thermal conductivity k = 98.6 W/m-deg, is exposed to vapor at 100 0 C on one side and cooling water at 30 0 C on the opposite side. The heat transfer coefficients are hi= 14200 W/m 2 -deg on the vapor side; h0=2325 W/ m 2 -deg on the water side Determine the rate of heat transfer, the overall heat transfer coefficient and drop in temperature at each side of heat transfer. 85. A wall of a furnace is made up of inside layer of silica brick 120 mm thick covered with a layer of magnesite brick 250 mm thick. The temperatures at the inside surface of silica brick wall and outside surface of magneside brick wall are 725 C and 110 C respectively. The contact thermal resistance between the two walls at the interface is 0.0035 C/W per unit area. If thermal conductivities of silica and magnesite bricks are 1.7 W/m C and 5.8 W/m C, calculate: (i) The rate of heat loss per unit area of walls, and (ii) The temperature drop at the interface. 86. A carbon steel (K = 54 W/m 0 C) rod with a cross section of an equilateral triangle (each side 5 mm) is 80 mm long. It is attached to a plane wall which is maintained at a temperature of 400 0 C, the surrounding temperature is 50 0 C and convective heat transfer coefficient is 90 W/m 2 0 C. Compute heat dissipated by rod. 87. A 5 m long 140 mm inner diameter and 160 mm outer diameter pipe (K=240 W/m 0 C) carrying saturated steam at 150 0 C, is covered by a layer of lagging of thickness of 40 mm (K= 0.8 W/m 0 C). Later, an extra layer of lagging 10 mm thick (K = 1.2 W/m 0 C) is added. If the surrounding temperature is 32 0 C and heat transfer coefficient inside pipe is 30 W/m 2 0 C and outside pipe is 10 W/m 2 0 C, (It is assumed that heat transfer coefficient for outside remains same for both the lagging materials) determine the percentage change in the rate of heat loss due to extra lagging layer. 88. A 10 m long insulated steam pipe (k = 250 W/m C) with inside diameter 25 mm and outside diameter of 30 mm is to be covered with two layers of insulation, each having thickness of 20 mm. The thermal conductivity of one material is 0.2 and the other is 1.0 W/m C. Steam temperature is 300 C and steam side heat transfer coefficient is 35 W/m 2 C. Surrounding temperature is 30 C and heat transfer coefficient is 36 W/m 2 C. Assuming that the heat transfer coefficient on outer-side is same for both insulating materials. Find out heat loss. If poor insulation is placed next to pipe, calculate effect on heat loss.
89. A 5 m long 200 mm ID and 240 mm OD steam pipe (k = 240 W/m C) carrying steam at 300 C. It is covered with 40 mm thick insulation (k = 2 W/m C). Inside and outside heat transfer coefficient are 40 & 10 W/m 2 C respectively. Surrounding air temperature is 30 C. Determine the quantity of heat loss and interface temperatures. 90. The hot combustion gases at 150 0 C flow through a hollow cylindrical pipe of 10 cm inner diameter and 12 cm outer diameter. The pipe is located in a space at 30 0 C and the thermal conductivity of the pipe material is 200 W/m K. Neglecting surface heat transfer coefficients, calculate the heat loss through the pipe per unit length and the temperature at a point halfway between the inner and outer surface. What should be the surface area normal to the direction of heat flow so that the heat transfer through the pipe can be determined by considering material of the pipe as a plane wall of same thickness? 91. A steam pipe ( k = 45 W/ m C) having 70 mm inside diameter and 85 mm outside diameter is lagged with two insulation layers; the layer in contact with the pipe is 35 mm asbestos ( k = 0.15 W/m C) and it is covered with 25 mm thick magnesia insulation ( k = 0.075 W/m C). The heat transfer coefficients for the inside and outside surfaces are 220 W/m 2 C and 65 W/m 2 C respectively. If the temperature of steam is 350 C and the ambient temperature is 30 C, Calculate : (1) The steady loss of heat for 50 m length of the pipe; (2) The overall heat transfer coefficients based on inside and outside surfaces of the lagged steam main. 92. A spherical shaped vessel of 1.4 m inner diameter is 90 mm thick. Find the rate of heat leakage, if the temperature difference between the inner and outer surfaces is 220 0 C. Thermal conductivity of the material of the sphere is 0.083 W/m 0 C. 93. An aluminium sphere contains steam at 110 C. The sphere (k= 185 W/m C) has an inner diameter of 100 mm and outer diameter of 120 mm. The sphere is located in a room where the ambient air temperature is 30 C and the convective heat transfer coefficient between the sphere and air is 15 W/m 2 C. Determine the heat transfer rate. To reduce the heat loss from the sphere, it is covered with a 50 mm thick layer of insulation (k= 0.20 W/m C). Determine the heat transfer rate from the insulated sphere. Assume that the convective resistance of the steam is negligible. 94. A sphere (inner diameter = 150 mm and outer diameter = 160 mm) having thermal conductivity 58 W/m 0 C is covered with two layers of insulation, of thickness 30 mm and 50 mm respectively and thermal conductivities 0.18 W/m 0 C and 0.09 W/m 0 C respectively. The temperature of inner surface of sphere is 320 0 C and that of the outer surface of the insulation layers is 40 0 C. Determine the quantity of heat loss per hour from sphere and interface temperatures. 95. The thermal conductivity of a material is to be determined by fabricating the material into the shape of a hollow sphere, placing an electric heater at the center and measuring the surface temperature with thermocouples when steady state
conditions have been attained. The sphere has internal radius 3 cm, external radius 8 cm and the corresponding temperatures are 95 0 C and 85 0 C when an electric input to heater is 10 watts. Determine the experimental value of thermal conductivity and the temperature at a point halfway through the wall. Critical Thickness 96. When the thickness of insulation is less than the critical thickness of insulation, the heat transfer from an insulated pipe will be than that from a bare pipe. 97. It is desired to increase the heat dissipation rate over the surface of an electric device of spherical shape of 5 mm radius exposed to convection with h = 10 W/m 2 deg by encasing it in a spherical sheath of conductivity k = 0.04 W/m 2 deg. For maximum heat flow, the radius of sheath should be. 98. Upto the critical radius of insulation (a) Heat loss decreases with addition of insulation (b) Heat loss increases with addition of insulation (c) There occurs a decrease in heat flux (d) Conduction heat loss is more than convection heat loss 99. Derive equation for critical radius for an insulated cylindrical body. Also mention assumptions made for it. 100. Derive equation for critical radius for a spherical body. Also mention assumptions made for it. 101. Explain meaning of critical radius for insulation. Develop equation for critical radius for insulation on spherical body. 102. What is critical insulation thickness? Can you give a physical explanation of its existence? Does a critical thickness exist for every insulated cylindrical surface? 103. What do you mean by optimum insulation thickness? What are the more important factors that should be taken into account while determining this thickness? 104. Derive equation for critical insulation radius for a hollow cylinder. 105. A small electric heating application uses wire of 2 mm diameter with 0.8 mm thick insulation (k =0.12 W/m C). The heat transfer coefficient (ho) on the insulated surface is 35 W/m 2 C. Determine the critical thickness of insulation in this case and the percentage change in the heat transfer rate if the critical thickness is used. Wire is at 135 C and surrounding air is at 32 C. 106. A 5 m long steam pipe (K = 240 W/m 0 C) having 200 mm ID and 240 mm OD, is carrying steam at 300 0 C. It is covered with 40 mm thick insulation (K= 2 W/m 0 C). Inside and outside heat transfer coefficient are 40 & 10 W/m 2 0 C respectively. Surrounding air temperature is 30 0 C. If the insulation thickness is critical, find % change in heat loss. 107. A cable of 10 mm outside is to be laid in an atmosphere of 25 0 C (h0 = 12.5 W/m 2 - deg) and its surface temperature is likely to be 75 0 C due to heat generated within it. How would the heat flow from the cable be affected if it is insulated with rubber having thermal conductivity k = 0.15 W/m-deg?
108. A small electric heating application uses wire of 2 mm diameter with 0.8 mm thick insulation (k = 0.12W/m C). The heat transfer coefficient (ho) on the insulated surface is 35 W/m 2 C. Determine the critical thickness of insulation in this case and the percentage change in the heat transfer rate if the critical thickness is used. Wire is at 135 C and surrounding air is at 32 C. 109. A wire of 6.5 mm diameter at temperature of 60 C is to be insulated by a material having k = 0.174 W/m C. Convection heat transfer coefficient (ho) = 8.722 W/m 2 C. The ambient temperature is 20 C. To maximize heat loss, what is the minimum thickness of insulation is required? Find heat loss per meter length. Extended surface (Fins) 110. On a heat transfer surface, fins are provided to. 111. On a heat transfer surface, fins are provided to (a) Increase temperature gradient so as to enhance heat transfer (b) Increase turbulence in flow for enhancing heat transfer (c) Increase surface area to promote the rate of heat transfer (d) Decrease the pressure drop of the fluid 112. Fin efficiency is defined as the ratio of the heat transferred across the fin surface to the theoretical heat transfer across an equal area held at (a) Temperature of fin end (b) Constant temperature equal to that of base (c) Average temperature of the fin (d) None of the above 113. Addition of insulating material does not always bring about a decrease in the heat transfer rate for geometries with non-constant cross section area. Comment upon the validity of this statement. A pipe of outside diameter 20 mm is to be insulated with asbestos which has a thermal conductivity of 0.1 W/m-deg. The local coefficient of convective heat to the surroundings is 5 W/m 2 deg. Comment upon the utility of asbestos as the insulating material. What should be the minimum value of thermal conductivity of insulating material to reduce heat transfer? 114. Mention the most common types of fins and sketch them. Proceed to develop expression for temperature distribution and total heat flow rate under steady state conditions for an infinitely long fin. 115. A ladle is attached with a rectangular handle (fin) with insulated end (tip). Derive equation for heat transfer through it. Also mention assumptions made for it. 116. Proceed to develop expression for temperature distribution and heat dissipation from a fin insulated at the tip. Set up the relation between fin effectiveness and fin efficiency. 117. Derive general equation for heat flow through rectangular fin. Also mention assumptions made for it. 118. A reactor is provided rectangular fin to improve heat release rate. If the end of the
fin is insulated, how can we measure heat loss? Develop an equation for heat loss calculation through the given fin. Also mention assumptions made for it. 119. The aluminium square fins (0.5 mm x 0.5 mm) of 12 mm length are provided on a surface of semi conductor electronic device to carry 1 W of energy generated by electronic device. The temperature at the surface of the device should not exceed 85 C when surrounding temperature is 40 C. Heat transfer coefficient = 15 W/m 2 C; Thermal conductivity of aluminium = 200 W/m C. Find number of fins required to carry out above duty. Neglect the heat loss from the end of fins. 120. Explain the dependency of thermal conductivity with temperature. 121. Explain in detail the effect of variable conductivity. Also derive the equation for the same for the case of plane wall, tube and the sphere. 122. The wall of a cold room is composed of three layers. The outside layer is of brick 20 cm thick, the middle layer is of cork 10cm thick, and the inside layer is of cement 5 cm thick. The temperature of the outside air is 25 0 C and that inside air is -20 0 C. The film coefficient (h0) for outside air and brick is 45.4 W/m 2-0 C and the film coefficient (hi) for outside air and cement is 17 W/m 2-0 C. Find: (a) The rate of heat flow under steady state conditions. (b) The temperature on the exposed surfaces of the wall. (c) Thermal resistance of the wall. 123. In a single experiment with a 2 cm thick sheet of pure copper having one face maintained at 500 0 C and the other at 300 0 C. The measured heat flux per unit area is 3.633MW/m 2 (1 MW =10 6 W.) A reported value of k for this material at 150 0 C is 371.9 W/m-K. Determine an expression for k(t) of form k = k0(1 + bɵ) 124. A thick wall copper cylinder has an inside radius of1cm and an outside radius of1cm.the inner and outer surface temperatures are held at 305 0 C and 295 0 C, respectively. Assume k varies linearly with temp., with k0 and b the same as in problem -1. Determine the heat loss per length. 125. A plane wall has thickness b and its two surfaces are maintained at temp. T1 and T2. If the thermal conductivity of the wall material varies according to k= k0(1 + ct + dt 2 ),develop an expression for the steady one dimensional heat flow. 126. A steam pipe having an outside diameter of 2 cm is to be covered with two layers of insulations; each having a thickness of 1cm.The average conductivity of one material is five times that of the other. Assuming that the inner and outer surface temperature of the composite insulation is fixed. Calculate by how much percentage that heat transfer will be reduced when the better insulating material is next to the pipe than when it is away from the pipe. 127. An electric wire 1 m diameter dissipates 500 W/m in air stream at 100 0 C. If the heat transfer coefficient is 370 W/m 2 -k, determine the temperature of the wire. The temperature variation in the wire may be neglected. An insulation having k =
0.277 W/m-k is then added to the wire, thereby increasing its outer diameter to 1.5 mm. Determine the new wire temperature and explain the physical significance of it. 128. Steel pipe 25 mm ID and 33mm OD and insulated with rock wool carries steam at 178 0 C. If the surrounding air temperature is 21 0 C. Calculate the rate of heat loss from one-meter length of pipe. The thickness of insulation is 38 mm. Thermal conductivity of steel and rock wool are 10.74 and 0.0418 cal/s-m- 0 C, respectively.the inside and outside heat transfer coefficient are 1356.17 and 2.7133 cal/sm 2-0 C, respectively. Contact resistance between the pipe and insulation may be neglected. 129. A furnace wall made up of steel 1 cm thick lined on inside with silica brick 15 cm thick, on the outside with magnesite brick 15 cm thick. The temperature on the inside edge of the wall is 700 0 C and on the outside is 15 0 C. Calculate the quantity of the heat passed in kcal/hr-m 2 and the temperature at the interface of the steel wall and the magnesite brick. It is required to reduce the heat flow to 1000 kcal/hr-m 2 by means of air gap between steel plate and magnesite brick. Estimate the width of this gap. Thermal conductivity if kcal/hr-m- 0 C are 14.5, 1.4, 4.5, and 0.029 for steel, silica brick, magnesite brick and air, respectively. 130. A pin fin 2.5 mm diameter is made of copper (k = 396 W/m-k). it protrudes from a wall maintained at 95 0 C and placed in 25 0 C air. The convective heat Transfer coefficient over the fin is 10 W/m 2 -k. Calculate the heat loss for the two cases: Fin length = 25 mm Infinite fin length. Convection 131. The physically signifies the ratio of temperature gradient at the surface to a reference temperature gradient. 132. The characteristic dimension used in estimating the Reynolds number is the hydraulic diameter defined as times the cross sectional area divided by the wetted perimeter. 133. At prandtl number equal to, the temperature distribution will be identical to the velocity distribution. 134. For a given value of Nusselt number, the convective surface coefficient (h) is proportional to thermal conductivity (k) of the fluid and proportional to the significant length (l). 135. Prandtl number essentially represents the ratio of to. 136. Based on dimensional analysis Nu = C (Re) m (Pr) n
The values of constant C, m and n are evaluated. 137. For free convection over inclined plates, Grashoff number is multiplied by where ϴ is the angle of inclination from the vertical and use vertical plate constants. 138. number represents the ratio of kinematic viscosity to thermal diffusivity. 139. Heat transmission is directly linked with the transport of medium itself i.e. there is actual motion of heated particles during (a) conduction only (b) convection only (c) radiation only (d) conduction as well as radiation 140. Forced convection in a liquid bath is caused by (a) density difference brought about by temperature gradients (b) molecular energy interaction (c) flow of electrons in random fashion (d) intense stirring by an external agency 141. Which dimensionless number has a significant role in forced convection? (a) Prandtl number (b) Reynolds number (c) Mach number (d) Peclet number 142. Differentiate between mechanisms of heat transfer by free and forced convection. 143. It is better to install air conditioner in the higher portion of the wall. Please explain this statement with reasons. 144. In which mode of heat transfer is the convection heat transfer coefficient usually higher, natural convection or forced convection? Why? 145. How does turbulent flow differ from laminar flow? For which flow is the heat transfer coefficient higher? 146. If cooling coils in the refrigerator are placed at the bottom in place of the top then what will happen? Why? 147. Why is the heating coil of an electric kettle placed near the bottom of the vessel? 148. Set up the relationship between local heat transfer coefficient and average heat transfer coefficient for flow past a stationary flat plate. 149. Mention some of the areas where free and force convection mechanisms are predominant. 150. Differentiate between mechanisms of heat transfer by free and forced convection. Mention some of the areas where these mechanisms are predominant. 151. Give a general equation for the rate of heat transfer by convection and hence define the coefficient of heat transfer. List the various factors on which the value of this coefficient depends. 152. An electric heater of exposed surface area 0.09 m 2 and output 600 W is designed
to operate fully submerged in water. Calculate the surface temperature of the heater when the water is at 37 0 C and the surface coefficient of heat transfer is 285.3 W/m 2 -deg. How this value will be affected if the heater is mistakenly operated at 37 0 C in air with a surface co-efficient of 8.5 W/m 2 -deg? 153. Set up the relationship between local heat transfer coefficient and average heat transfer coefficient for flow past a stationary flat plate. The temperature profile at a particular location in a thermal boundary layer is prescribed by an expression of the form: T( y) A By Cy 2 Where A, B and C are constants. Set up an expression for the corresponding heat transfer coefficient. 154. The temperature profile at a particular location on the surface of plate is prescribed by the identities: ts t y Sin ts t 0. 015 If thermal conductivity of air is stated to be 0.03 W/m-deg, determine the value of convective heat transfer coefficient. 155. A 5 cm diameter steel pipe maintained at a temperature of 60 0 C is kept in a large room where the air and wall temperatures are 25 0 C. If the surface emissivity of the steel is 0.7, calculate the total heat loss per unit length of pipe if convective heat transfer coefficient is 6.5 W/m 2 - deg. Comment on the result. 156. Air enters a rectangular duct measuring 30 cm 40 cm with a velocity of 8.5 m/s and a temperature of 40 0 C. The flowing air has a thermal conductivity 0.0242 kcal/m hr 0 C, kinematic viscosity 16.95 10-6 m 2 /s and from empirical correlation the Nusselt number has been approximated to be 425. Work out the equivalent diameter of the flow passage, the flow Reynolds number and the convective heat flow coefficient. 157. Define the Nusselt number. How it is related to temperature gradient in the fluid immediately in contact with the solid surface? Mention the various approaches which have suggested for estimating the value of Nusselt number. 158. Using Dimensional analysis (Buckingham s PI-Theorem) demonstrate that the following dimensionless parameters are possible combinations of the appropriate variables describing forced convection Vx c p hx, k, k Name these groups and discuss their physical significance. 159. Show by dimensional analysis (Buckingham π-theorem method) that data for forced convection may be correlated by an equation of the form Nu (Re,Pr)
160. hat data for forced convection may be correlated by an equation of the form St (Re,Pr) 161. Explain in detail the mechanism of free convection. Show by dimensional analysis (Buckingham π-theorem) that for problems in heat transfer involving free convection only, the Nusselt number Nu = the Prandtl number Pr = C p k hl k and the Grashof number Gr = can be expressed as a function of 3 2 l gt 2 162. List the variables that affect the forced heat transfer coefficient. Using dimensional analysis (Buckingham π-theorem), demonstrate that the following dimensionless parameters are possible combinations of the appropriate variables describing forced convection. h Vc P ; Vl ; c P K Name these groups. 163. Experimental results for heat transfer over a thin flat plate were found to be correlated by an expression of the form 164. Nu x 0.332 x Re 0.5 Pr 0. 33 Where Nux is the local value of Nusselt number at a position x measured from the leading edge of the plate. Obtain an expression for the ratio of the average heat transfer coefficient to the local coefficient. 0.5 Pr 0.332Re 33 Obtain an expression Nu x x for heat transfer over a thin flat plate. Nux is the local value of Nusselt number at a position x measured from the leading edge of the plate. 165. Show that t for Pr > 1 t for Pr = 1 t for Pr < 1 0. t respectively and Pr stands for the Prandtl number 166. Derive the relationship for the local and average skin friction coefficient for a flat df smooth plate at zero incidences. Assume the value 0. 332. d 0
167. Define the local and average skin friction coefficient for a flat smooth plate at zero incidences. Establish the following relations for laminar boundary layer over the plate. (i) Local skin friction coefficient c x 1.328 Re 0.664 (ii) Average drag coefficient c f l df Assume the value 0. 332. d 0 168. Calculate the rate of heat loss from a human body which may be considered as a vertical cylinder 30 cm in diameter and 175 cm high in still air at 15 0 C. The skin temperature is 35 0 C and emissivity at the skin surface is 0.4. Neglect sweating and effect of clothing. The thermo-physical properties of air at 25 0 C are: γ = 15.53 10-6 m 2 /s; k = 0.0263 W/m-deg; Pr = 0.7 Use the following correlation Nu 0.13 Gr Pr 0. 33 169. A vertical plate is under free convection with ambient still air at 20 0C. If the plate is heated from one side and maintained at 80 0C workout the local heat transfer coefficient at 20 cm from the lower edge. What would be the average value of convective coefficient over the 20 cm length? Following correlation for the local Nusselt number. 0.25 Re pr Nu x 0.52 ( Gr Pr) 0.95 pr x 0.25 The thermo physical properties of air at 50 0 C are: ρ = 1.093 kg/m 3 Pr = 0.698 k = 10.17 10-2 kj/m hr K γ = 17.95 10-6 m 2 /s 170. A motor cycle cylinder consists of 10 fins; each 15 cm outside diameter (do) and 7.5 cm inside diameter (di). Calculate the rate of heat dissipation from the cylinder fins when motor cycle is stationary. The atmospheric air is at 20 0 C and the average fin temperature is 480 0 C. The relevant thermo physical properties at the average temperature of 250 0 C are: ρ = 0.674 kg/m 3 CP = 1038 J/kg K k = 0.427 W/m K Pr = 0.677 γ = 40.61 x 10-6 m 2 /s The approximate value of heat transfer coefficient may be evaluated by idealing
the fins as a single horizontal flat plate of the same area. Use following correlations: For Horizontal flat plate: Free convection : Laminar flow : Nu= 0.54 (Gr Pr) 1/4 Characteristic dimension = 0.9 do. 171. A hot surface plate 40 cm 40 cm at 100 C is exposed to atmospheric air at 20 C. Make calculations for the heat loss from both surface of the plate if (a) the plate is kept vertical (b) the plate is kept horizontal. The following empirical correlations have been suggested: Gr Pr 0. 33 Gr Pr 0. 25 Gr Pr 0. 25 Nu 0.125 Nu 0.72 for vertical position of plate and for upper surface Nu 0.35 for lower surface Where the air properties are evaluated at the mean film temperature. Thermo-physical properties of air are at 60 C ρ = 1.06 kg/m 3 k = 0.028 W/m K Cp= 1.008 kj/kg K γ = 18.97 10-6 m 2 /s 172. Saturated steam at 110 0 C flows inside a copper pipe (thermal conductivity 450 W/m K) having an internal diameter of 10 cm and an external diameter of 12 cm. The heat transfer coefficient on the steam side is 12000 W/m 2 K and that on the outside surface of pipe is 18 W/m 2 K. Determine the heat loss from the pipe if it is located in space at 25 0 C. How this heat loss would be affected if the pipe is lagged with 5 cm thick insulation of thermal conductivity 0.22 W/m K. 173. Air at a temperature of 25 0 C is blown across a flat plate at a mean velocity of 7.5 m/s. If the plate surface temperature is 575 0 C, make calculations for the heat transferred per meter width from both sides of the plate over distance of 20 cm from the leading edge. For heat transfer from a plate with large temperature between the plate and the fluid, the local Nusselt number is given by: Nu x 0 1/ 3 1/ 2 T.332 Pr Re s T a 0.117 Where all the properties are at the mean film temperature, Ts and Ta are the absolute temperature of the plate surface and the free stream of air in K respectively. The characteristic linear dimension is the distance from the leading edge. The thermo physical properties of air at 300 0 C are: ρ = 0.615 kg/m 3 CP = 1.0465 kj/kg K k = 0.1659 kj/m hr K µ = 29.724 10-6 kg/ m s 174. A thin walled duct of 0.5 m diameter has been laid in an atmosphere of quiescent
air at 15 0 C and conveys a particular gas at 205 0 C. The boundary layer flow is laminar and the convective coefficient of heat transfer is given by: 0.25 t h W/m 2 -deg 1.37 l Where l is the length of the duct in meters. How this value of convective coefficient compares with that computed from the following non-dimensional correlation for laminar flow natural convection for a large vertical cylinder Gr Pr 0. 25 Nu 0.57 Base your calculations on one meter length of the duct. Also estimate the convective heat loss from the duct. The thermo physical properties of air at mean film temperature are: γ = 24.10 10-6 m 2 /s; k = 31.94 10-3 W/m-deg; Pr = 0.704 175. A square channel with a side 10 mm and length 1.5 m carries water with a velocity of 5 m/s. Measurements indicate that lengthwise mean temperature of water is 30 0 C whilst the inner surface of channel is at 80 0 C. Calculate the convective coefficient of heat transfer from the channel wall to the water. Use the correlation: 0.25 0 0.8 0.43 Pr Nu.021Re Pr Pr w Where the thermo-physical properties pertain to those at the mean bulk temperature of water. Prw corresponds to the value of Prandtl number at the channel surface temperature and equivalent diameter is the reference dimension. The physical properties of water at 30 0 C are: ρ = 995.07 kg/m 3 ; cp = 4174 J/kg K; k = 0.6172 W/m K; μ = 2.88 kg/m-hr; Pr = 5.42 At wall: temperature tw = 80 0 C and Prw = 2.21 176. Estimate the heat transfer from a 40 W incandescent bulb at 125 0 C to 25 0 C in quiescent air. Approximate the bulb as a 50 mm diameter sphere. What percentage of the power is lost by free convection? The appropriate correlation for the convection coefficient is Nu = 0.60 (Gr Pr) 0.25 Where the different parameters are evaluated at the mean film temperature and the characteristics length is the diameter of the sphere. The thermo physical properties of air are at 75 0 C: γ = 20.55 10-6 m 2 /s k = 0.03 W/m-deg Pr = 0.693 177. 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 consideration limits the maximum surfaces temperature of the plate
to 975 0 C and the lowest allowable temperature of bismuth is 325 0 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 The thermo physical properties of bismuth are at 650 0 C: μ = 3.12 kg/m-hr ρ = 10 4 kg/m 3 C p = 150.7 J/kg-deg k = 13.2 W/m-deg. 178. Estimate the heat transfer from a 40 W incandescent bulb at 125 0 C to 25 0 C in quiescent air. Approximate the bulb as a 50 mm diameter sphere. What percentage of the power is lost by free convection? The appropriate correlation for the convection coefficient is Nu 0.60 Gr Pr 0. 25 Where the different parameters are evaluated at the mean film temperature and the characteristics length is the diameter of the sphere. The thermo physical properties of air at mean film temperature are at: γ = 20.55 10-6 m 2 /s; k = 0.03 W/m-deg; Pr = 0.693 179. A metallic cylinder of 12.5 mm diameter and 95 mm length was heated internally by an electrical heater, and was subjected to cross flow of air in a low speed wind tunnel. Under a specific set of operating conditions, the following data were recorded: Velocity and temperature of free stream air = 10 m/s and 25.5 0 C respectively Average temperature of cylinder surface = 128.5 0 C Power dissipation by heater = 45 W If 15% of the power dissipation is lost through the insulated end pieces of the cylinder, determine the experimental value of the convective heat transfer coefficient. How this value compares with the convection coefficient obtained by using the correlation: 0 0.6 0.36 Pr Nu.26Re Pr Pr S 0.25 Where all properties, except PrS are evaluated at the mean bulk (free stream) temperature of air. k = 0.0264 W/m K; γ = 15.85 10-6 m 2 /s; and Pr = 0.706 PrS is the prandtl number of air evaluated at the average temperature of cylinder
surface; PrS = 0.691 180. A thin walled vertical duct a circular cross-section is 0.4 m in diameter. That duct carries a gas at 470 K and the surrounding air may be considered still at 290 K. Determine the heat transfer rate from one meter length of the duct assuming that the boundary layer is laminar. The general non-dimensional correlation for laminar flow, natural convection from large vertical cylinders is: Nu 0.56 Gr Pr 0. 25 The fluid properties are to be evaluated at film temperature which is defined as the average of the bulk fluid and wall temperature. The heat transfer coefficient is to be prescribed by the relation: T h C l 0.25 W/m 2 K where the length parameter (l) is in meter. Calculate the value of constant C which would give the same heat transfer rate. At the film temperature, the thermophysical properties of the gas are: ρ = 0.9315 kg/m 3 ; cp = 1.012 kj/kg K; μ = 22.016 10-6 kg/m s k = 3.2215 10-2 W/m K 181. What factors affect the value of convection coefficient for water flowing inside a circular tube? Within a condenser shell, water flows through one hundred thin walled circular tubes (diameter = 22.5 mm and length 5 m) which have been arranged in parallel. The mass flow rate of water is 65 kg/s and its inlet and outlet temperatures are known to be 22 0 C and 28 0 C respectively. Predict the average convection coefficient associated with water flow. The thermo-physical properties of water at mean bulk temperature are: ρ = 996.65 kg/m 3 ; μ = 903.01 10-6 kg/m s cp = 4.1776 kj/kg K; k = 2.1893 kj/m 2 hr K Use the Correlation:.8 0.40 Nu 0.023Re 0 Pr 182. A hot surface plate 40 cm 40 cm at 100 C is exposed to atmospheric air at 20 C. Make calculations for the heat loss from both surface of the plate if (a) the plate is kept vertical (b) the plate is kept horizontal. The following empirical correlations have been suggested: Gr Pr 0. 33 Gr Pr 0. 25 Nu 0.125 Nu 0.72 for vertical position of plate and for upper surface