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 CONDUCTION 1987: IIT Bombay A. Silver 1. A metallic slab of thickness 2R, initially at a B. Chrome-nickel steel uniform temperature Ti, throughout, is C. Aluminium immersed in...

 CONDUCTION 1987: IIT Bombay A. Silver 1. A metallic slab of thickness 2R, initially at a B. Chrome-nickel steel uniform temperature Ti, throughout, is C. Aluminium immersed in D. Carbon steel A. Large pool of fluid, at a temperature Tf , is 4. A steel ball of 5cm diameter at 200°C is flowing at a very larger velocity. suddenly placed in a controlled B. A large pool of fluid, at a temperature Tf , is environment maintained at 100°CHow flowing at a small velocity. much time is required for the ball to attain a It is required to obtain the temperature temperature of 150°C. distribution in the slab, in each of the above Internal cases. Write down the governing equation resistance can be neglected. that needs to be solved, together with all relevant initial and or boundary conditions 1990: IISC Bangalore necessary for the solution, in each of the 5. A hot fluid flows through a well-mixed above cases. Consider unidirectional stirred tank which is provided with a conduction only and neglect radiation effects. cooling jacket. The fluid in the cooling jacket can also be assumed to be well 1988: IIT Kharagpur mixed. Calculate the heat transfer area of 2. A thermo pane window consists of two the jacket required given the following sheets of glass each 6mm thick, separated by data, a layer of stagnant air also 6 mm thick. Find Hot fluid: Flow rate, Wh = 50 kg/s; Thi = the percentage reduction in heat loss from 205°C; this pane as compared to that of a single Cph = 2 kJ/kg°C; sheet of glass 6mm thickness. The Cold fluid: Flow rate, WC = 100 kg/s; temperature drops between inside and tin = 25°C, tout = 45°C; Cpc = 4 kJ/kg°C; outside remains same at 15°C. Thermal U = 2.5 kW/m2°C; conductivity of glass is 30 times that of air. 1989: IIT Kanpur 3. The thermal conductivity is minimum for:  1991: IIT Madras 1993: IIT Bombay 6. An industrial wall is constructed of 20 cm 9. A pipe is 20 mm inner diameter and 30 mm thick fireclay (k =1 W/m.°C). This is covered outer diameter is insulated with 35 mm on the outer surface with a 3 cm layer of thick insulation. Temperature of the bare insulating material (k = 0.075 W/m.°C). The pipe is 200 C. The thermal conductivity of innermost surface is at 940°C and the the insulating material is 0.15 W/m°C and outermost at 40°C. The steady state heat the convective heat transfer coefficient of transfer through the wall is ______________ outside air is 3 W/m2°C. The surface W/m2 and the temperature of the interface temperature is 30°C. The heat transfer between the fireclay and the insulating resistance of the metal pipe can be material is ________°C. neglected. 7. The Biot modulus for a 3 cm diameter I. Comment with reasoning about the sphere (k for the sphere = 5 W/m.°C) at 100 heat transfer rates with and without °C subjected to a convective air flow insulation resulting in an average convective heat II. If the same insulating material is used, transfer coefficient from the surface of 30 what is the minimum thickness above W/m2.°C is equal to _______________. which there is a reduction in heat loss 8. An aqueous solution (density =1000 kg/m3, as compared to the bare pipe? specific heat=4 kJ/kg⁰C) at 300K is III. For optimum design, what continuously fed at a flow rate of 1 m3/min conductivity of insulating material do to continuous flow stirred tank of volume you suggest for the conditions given in 1 containing a heater having capacity of the problem? 1000 kW. If the liquid in the tank is also at 1994: IIT Kharagpur 300k to start with, find the equation, which 10. A metal wire of 0. 1m dia and thermal predicts the exit temperature of the solution conductivity 200 W/m K is exposed to a as a function of time after the heater is fluid stream with a convective heat switched on. transfer coefficient of 100 W/m2 K. The Biot number is  A. 5.6 c. h/2k B. 0.0125 d. k/h C. 3.5 14. The critical radius r of insulation on a pipe is D. 0.0035 given by – 11. A. r = k / h (I)Nusselt (a) Convective B. r = k / 2h number resistance/Fluid C. r = h / k conduction D. r = 2k / h resistance (II) Biot Number (b) Fluid conduction 1996: IISC Bangalore resistance/Convect 15. A thermocouple junction may be ive resistance approximated as a sphere of diameter 2 (c) Solid conduction mm with thermal conductivity 30 resistance / W/(m.⁰C), density 8600 kg/m3 and Convective specific heat 0.4 kJ/(kg⁰C). The heat resistance transfer coefficient between the gas stream and the junction is 280 W/(m2.⁰C). 12. An asbestos pad, square in cross-section, How long will it take for the thermocouple measures 0.05 m on a side and increases to record 98 percent of the applied linearly to 0.1 m on the other end. The length temperature difference? of the pad is 0.15m 1997: IIT Madras 16. According to the kinetic theory, the thermal conductivity of a monoatomic gas is proportional to – A. T 13. Critical thickness of insulation for B. T0.5 Sphere a. h/k C. T1.5 D. T2 Cylinder b. 2k/h  17. At steady state, the temperature variation conductivity (k) of furnace wall and the in a plane wall, made of two different connective heat transfer coefficient (h) to solids I and II is shown below. be constant. II 19. A steel ball of 50 mm diameter is cooled by I exposing it to an air stream at 320 K. Under L L Then, the thermal conductivity of material I these conditions the connective heat A. is smaller than that of II transfer coefficient is 100 W/m2.K. B. is greater than that of II Estimate the time needed to cool the steel C. is equal to that of II ball from 1120 to 520 K. D. can be greater than or smaller than that of Properties of steel : Density = 8000 II kg/m3 and heat capacity = 450 J/kg.K. Due to the high thermal conductivity of 18. It is proposed to reduce the heat loss from a steel, there are no temperature gradients rectangular furnace wall by doubling its within the ball. wall thickness as shown in fig.. The temperature of the hot surface of the wall is 1998: IIT Delhi 723 K, and it loses heat from the other side 20. The variation of thermal conductivity of a exposed to air at 308 K. In case I, the metal with temperature is often temperature of the wall surface exposed to correlated using an expression of the air is 453 K. form –k=k0+aT, where k is the thermal conductivity, and T is the temperature (in K). The units of a in the SI system will be : A. W/m K B. W / m Estimate the % reduction in heat loss due C. W/m K2 D. None; a is just a to the doubling of wall thickness. Neglect number the radiation losses and assume 1-D 21. A long iron rod initially at a temperature conduction. Also assume the thermal of 200C has one end dipped in boiling  water (1000C) at time t = 0. The curved air at a temperature Ta = 200C. The pellets surface of the rod is insulated so that heat are falling at their terminal velocity ut = 6.9 conduction is one-dimensional in the axial m/s. The temperature within the pellets is direction. The temperature at a distance uniform at all times, and the initial 100 mm from the dipped end becomes temperature of the pellets is 800C. The heat 400C at t = 200 s. The same temperature is transfer coefficient for a pellet falling in air achieved at a distance 200 mm from the is h = 208 W/m2 K. dipped end at time. A. Obtain an expression for the change of A. t = 283 s B. t = 356 s temperature of a pellet with time [T(t)] C. t = 400 s D. t = 800 s B. Calculate the height of the tower for a 22. The wall of a cold storage unit comprises a pellet to cool to 600C. brick layer (thickness δB = 0.1 m, thermal 1999: IIT Bombay conductivity kB = 1.4 W/mK) and an inner 24. Rate of heat transfer through a pipe wall layer of polyurethane foam (thickness δp = is given by q= 2πk(Ti-To)2 lnriro for 0.05 m, thermal conductivity kp = 0.015 cylinders of very thin wall, q can be W/mK). Assume one dimensional heat approximated by transfer by conduction through the A. q= 2πk(Ti+To) 2 lnriro composite wall, and that the inner surface of B. q= 2πrikTi-T0(r0-ri) the polyurethane layer is at temperature TC C. q= 2πkTi-T0(r0-ri) and the outer surface of the brick layer is at D. q= 2πkTi-T0(r0-ri)/2 temperature Th. A. Derive an expression for the heat flux per 25. Walls of a cubical oven are of thickness L, unit area through the wall. and they are made of thermal B. Calculate the rate of heat gain when Tc = - conductivity K. The temperature inside 100C and Th = 400C. The surface area for the oven is 1000C and the inside heat heat transfer is 260 m2. transfer coefficient is 3K/L. If the wall temperature on the outside is held at 23. In the lower portion of a spray tower, urea pellets (diameter D = 2 mm) are cooled by  250C, what is the inside wall temperature C. 20 min, D. 40 min, in degree C? 28. A composite flat wall of a furnace is made of A. 35.5 B. 43.75 two materials A and B. The thermal C. 81.25 D. 48.25 conductivity of A is twice of that of material B, while the thickness of layer of A is half of 26. 150 kg of water is to be heated in a that of B. If the temperatures at the two steam-jacketed vessel from 250C to 800C. sides of the wall are 400 and 1200 K, then Steam is condensing at 1200C, and the the temperature drop (in K) across the layer heat transfer area is 0.25 m2. The heat of material A is transfer coefficients for condensation of A. 125 B. 133 steam and heating of water by convection C. 150 D. 160 are 1000 W/m2 0C and 500 W/m2 0C 29. The outside surface temperature of a pipe respectively. Write appropriate unsteady (radius = 0.1 m) is 400 K. The pipe is losing balance equations and find the time heat to atmosphere, which is at 300 K. The required for heating the water. Assume film heat transfer coefficient is 10 W/m2 K. that the specific heat of water in the To reduce the rate of heat loss, the pipe is temperature range of interest is 4.18 x insulated by a 50 mm thick layer of asbestos 103 J/Kg0C. (k = 0.5 W/m K). Calculate the percentage 2000: IIT Kharagpur reduction in the rate of heat loss. 27. A steel sphere of radius 0.1 m at 400K is 2001: IIT Kanpur immersed in an oil at 300K. If the centre of 30. The heat flux (from outside to inside) the sphere reaches 350K in 20 minutes, how across an insulating wall with thermal long will it take for a 0.05m radius steel conductivity k = 0.04 W/m K and sphere to reach the same temperature (at thickness 0.16 m is 10 W/m2. The the centre) under identical conditions? temperature of the inside wall is –50C. Assume that the convective heat transfer The outside wall temperature is coefficient is infinitely large. A. 250C, B. 300C A. 5 min, B. 10 min, C. 350C D. 400C  2002: IISC Bangalore the liquid to be 4 kJ/kg 0C, the time taken 31. A 10 cm diameter steam pipe, carrying for the liquid to reach desired steam at 180 0C, is covered with an temperature will be insulation (conductivity = 0.6 W/m 0C). A. 15 min B. 22 min It loses heat to the surroundings at 30 0C. C. 44 min D. 51 min Assume a heat transfer coefficient of 8.0 33. A composite wall consists of two plates A W/m2 0C for heat transfer from surface to and B placed in series normal to the flow of the surroundings. Neglect wall heat. The thermal conductivities are kA and resistance of the pipe and film resistance kB and the specific heat capacities are CpA of steam. If the insulation thickness is 2 and CpB, for plates A and B respectively. cm, the rate of heat loss from this Plate B has twice the thickness of plate A. At insulated pipe will be steady state, the temperature difference A. greater than that of the un-insulated across plate A is greater than that across steam pipe plate B when B. less than that of the un-insulated A. CpA > CpB B. Cp2 kB C. equal to that of the un-insulated steam pipe 2003: IIT Madras D. less than the steam pipe with 5 cm 34. Three solid objects of the same material insulation and of equal mass – a sphere, a cylinder (length = diameter) and a cube – are at 32. 1000 kg of liquid at 30 0C in a well-stirred 5000C initially. These are dropped in a vessel has to be heated to 1200C, using quenching bath containing a large immersed coils carrying condensing volume of cooling oil each attaining the steam at 1500C. The area of the steam bath temperature eventually. The time coils is 1.2 m2 and overall heat transfer required for 90% change of temperature coefficient to the liquid is 1500 W/m2 0C. is smallest for Assuming negligible heat loss to A. cube B. cylinder surrounding and specific heat capacity of  C. sphere D. equal for all the three coefficient from the right face is 10W/(m2K). At steady state, the 35. The inner wall of a furnace is at a temperature of the right face in °C is temperature of 700 0C. The composite A. 75.2 B. 11.2 wall is made of two substances, 10 and C. 63.8 D. 48.7 20 cm thick with thermal conductivities of 0.05 and 0.1 W m-1 0C-1 respectively. 38. A metal ball of radius 0.1 m at a uniform The ambient air is at 30 0C and the heat temperature of 90°C is left in air at 30°C. The transfer coefficient between the outer density and the specific heat of the metal are surface of wall and air is 20 W m-2 0C-1. 3000 kg/m3 and 0.4 kJ/g-K) respectively. The The rate of heat loss from the outer heat transfer coefficient is 50W/(m2K). surface in W m-2 is Neglecting the temperature gradient inside A. 165.4 B. 167.5 the ball, the time taken (in hour) for the ball C. 172.8 D. 175 to cool to 60 0C is A. 555 B. 57.5 36. For a given ambient air temperature with C. 0.55 D. 0.15 increase in the thickness of insulation of a hot cylindrical pipe, the rate of heat loss 2005: IIT Bombay from the surface would Common Data Questions: A. Decrease A liquid of mass 7 kg and specific heat 4 B. increase kJ/kg⁰C is contained in a cylindrical heater C. first decrease and then increase of diameter 0.15 m and height 0.40 m. The D. first increase and then decrease cylindrical surface of the heaters is exposed to air at 25°C while the end caps 2004: IIT Delhi are insulated, so that the heat transfer 37. The left face of a one-dimensional slab of takes place only through the cylindrical thickness 0.2 m is maintained at 80°C and surface. the right face is exposed to air at 30°C. The thickness of the wall of the heater = The thermal conductivity of the slab is 2mm. 1.2 W/(m-K) and the heat transfer  The wall thermal conductivity = 10W/(m- C. K) D. The heat transfer coefficient in the 41. A circular tube of outer diameter 5 cm and liquid=100 W/m2K inner diameter 4 cm is used to convey hot The heat transfer coefficient in air= 10 fluid. The inner surface of the wall of the W/m2 tube is at a temperature of 80°C while the The liquid is initially maintained at a outer surface of the wall of the tube is at temperature of 75 °C 25°C. What is the rate of heat transport At time t=0, the heater is switched off and across the tube wall per meter length of the the temperature of the liquid in the heater tube at steady state, if the thermal decreases due to heat loss across the conductivity of the tube wall is 10 W/(m- cylindrical surface. K)? 39. At time t=0, the heater is witched off and A. 13823 W/m B. 15487 W/m the temperature of the liquid in the C. 17279 W/m D. 27646W/m heater decreases due to heat loss across 42. A semi-infinite slab occupying the region x = the cylindrical surface. 0 and is at an initial temperature T0. What is the overall heat transfer At time t=0 , the surface of the, slab at x=0 is coefficient in W/m2K? brought into contact with a heat bath at a A. 1 B. 4.04 temperature TH. The temperature T(x,t) of C. 9.07 D. 10 the, slab rises according to the equation 40. What is the time required for the where x is temperature of the liquid to reduce to 50 position and t is time. The heat flux at the °C after the heater is switched off, surface x=0 is proportional to assuming lumped heat system analysis is A. B. valid? A. 7.874 C. D. B.  2006: IIT Kharagpur surface temperature Tso is 20 , the 43. A stagnant liquid film of 0.4 mm inner surface temperature Tsi is 600 thickness is held between two parallel and the oven air temperature is plates. The top plate is maintained at 40. For the following data : and the bottom plate is maintained at Thermal conductivities KA=20W/(m-K) 30. If the thermal conductivity of the and KC=25W/(m-K) liquid is 0.14 W/(m-K), then the steady Thickness LA=0.3m, LA=0.15m and state flux (in W/m2) assuming one- LC=0.15m Inner-wall heat transfer dimensional heat transfer, is coefficient h= 25W/(m-K), A. 3.5 B. 350 C. 3500 D. 7000 44. One dimensional steady state heat-transfer occurs from a flat vertical wall of length 0.1m into the adjacent fluid. The heat flux into this fluid is 21 W/m2. The wall thermal conductivity is 1.73 W/(m-K). If the heat The thermal conductivity KB in W/(m-K) transfer coefficient is 30 W/m2and the of the material B, is calculated as Nusselt number based on the wall length is A. 35 B. 1.53 20, then the magnitude of the temperature C. 0.66 D. 0.03 gradient at the wall on the fluid side (in K/m) is Linked Answer Questions: A. 0.7 B. 12.14 Consider steady one-dimensional heat C. 120 C. 140 flow in a plate of 20 mm thickness with a uniform heat generation of 80 MW/m3. 2007: IIT Kanpur The left and right faces are kept at 45. The composite wall of an oven consists of constant temperatures of 160⁰C and 120⁰C three materials A, B and C. Under steady respectively. The plate has a constant state operating conditions, the outer thermal conductivity of 200 W/m.K 46. The location of maximum temperature 50. A rectangular fin of length 12 cm, width 22 within the plate from its left face is cm and thickness 1.5 cm is connected to a A. 15 mm B. 10 mm tube at a temperature of 0⁰C. The thermal C. 5 mm D. 0 mm conductivity of the fin material is 150 W m-1 K-1. The tip of the fin is not insulated. Air at a 47. The maximum temperature within the temperature of 5⁰C is in contact with the fin. plate in ⁰C is The heat transfer coefficient between the fin A. 160 B. 165 and the air is 25 W m-2 K-1. The rate of heat C. 200 D. 250 transfer is 48. Heat is being transferred conductively A. 3.33 W B. 6.63 W from a cylindrical nuclear reactor fuel rod C. 9.13 W D. 15.23 of 50 mm diameter to water at 75⁰C, under 51. In order to reduce heat loss, a stream line with steady state condition, the rate of heat a tube diameter of 1.0 cm is insulated with generation within the fuel element is 106 material having thermal conductivity of 0.108 W/m3 and the convective heat transfer W m-1 K-1. Heat is dissipated from the outer coefficient is 1 kW/m2K, the outer surface surface of the insulating material by natural temperature of the fuel element would be convection with a heat transfer coefficient of A. 700 K B. 625 K 12 W m2 K-1 into the ambient at a constant C. 360 K D. 400 K temperature. The heat loss becomes maximum 49. A long glass cylinder of inner diameter = when the thickness of insulation is 0.03 m and outer diameter = 0.05 m A. 0.5 mm B. 2 mm carries hot fluid inside. If the thermal C. 4 mm D. 6.5 mm conductivity of glass = 1.05 W/mK, the 2008: IISC Bangalore thermal resistance (K/W) per unit length 52. Transient three-dimensional heat of the cylinder is conduction is governed by one of the A. 0.031 B. 0.077 following differential equations (⍺ = C. 0.17 D. 0.34 thermal diffusivity, K = thermal conductivity  and volumetric rate of heat generation) A. B. C. C. D. 53. The temperature profile for heat transfer from one fluid to another separated by a solid wall is D. 54. A metallic ball [ρ = 2700 kg/m3 and CP = 0.9 kJ/kg⁰C] of diameter 7.5 cm is allowed to A. cool in air at 25⁰C When the 125⁰C it is found to cool at the rate of 4⁰C/min. If thermal gradients inside the ball are neglected, the heat transfer coefficient (in W/m2⁰C) is A. 2.034 B. 20.34 C. 81.36 D. 203.4 55. Two plats of equal thickness (t) and cross- B. sectional are joined together to form a composite as shown in the figure. If the thermal conductivities of the plates are K  and 2 K, then the effective thermal A. =20 K/m, = 0 K/m conductivity of the composite is B. = 0 K/m, = 10 K/m C. =10 K/m, = 10 K/m D. = 0 K/m, = 20 K/m 57. The thermal conductivity of a common metal used in fabrication of food processing equipment is given as 120 BTU ft-1 h-1 °F-1. A. B. This value in J m-1 s-1 K-¹ will be C. D. A. 2.08 B. 20.8 C. 208 D. 280 56. Steady two-dimensional heat conduction takes place in the body shown in the 58. A cork slab of 100 mm thickness has one figure below. The normal temperature face at -12 °C and the other face at 21 °C. If gradients over surface P and Q can be the mean thermal conductivity (k) of the considered to be uniform. The cork is 0.042 J m-1 s-1 K-¹, the rate of heat temperature gradient at surface Q is transfer (Js-1) through one m² of the wall will be equal to 10 K/m. Surface P and Q are A. 13.9 B. 9.3 maintained at constant temperatures as C. 5.0 D. 2.5 shown in the figure, while the remaining Linked Answer Questions: part of the boundary is insulated. The A wall is heated uniformly at a volumetric body has a constant thermal conductivity heat generation rate of 1 kW/m3. The of 0.1 W/mK. The values of and at temperature distribution across the 1 m surface P are thick wall at a certain instant of time is given by: T(x) = a + bx + cx2  Where a = 900⁰C, b = -300⁰C/m, and c = - thermal conductivity of the material will 50⁰C/m2. be The wall has an area of 10 m2 (as shown A. 0.3 WK-1m-1 B. 35.1 WK-1m-1 in the figure) and a thermal conductivity C. 2.1 WK-1m-1 D. 9.5 WK-1m-1 of 40 W/m.K 62. Match the properties in Group 1 with the units in Group 2 Group 1 Group 2 (P) Thermal (1) J m-2 s-1 K-1 conductivity (Q) Heat transfer (2) J m-1 s-1 K1 coefficient (R) Specific heat (3) m2 s-1 (S) Diffusivity (4) J mol-1 K-1 59. The rate of heat transfer (in kW) into the wall (at x = 0) is A. P-1, Q-2, R-4, S-3 A. 900 B. 450 B. P-2, Q-3, R-1, S-4 C. 120 D. 60 C. P-2, Q-1, R-4, S-3 D. P-2, Q-4, R-3, S-1 60. The rate of change of energy storage (in kW) in the wall is 2009: IIT Roorkee A. 130 B. 120 63. During the transient convective cooling of a C. -10 D. -30 solid object, Biot number → 0 indicates A. Uniform temperature throughout the 61. The heat flow across the thickness to the object opposite surface of a plastic slab of B. Negligible convection at the surface of dimensions 0.1 m⨯0.1 m⨯0.05 m is 19 the object W. If the temperature difference between C. Significant thermal resistance within the the surface of the slab is 10 K, the object  D. Significant temperature gradient within 66. For the composite wall shown below the object (Case 1), the steady state interface temperature is 180. If the thickness of Common Data Question: layer P is doubled (Case 2), then the rate A slab of thickness L with one side (x = 0) of heat transfer (Assuming 1-dimensional insulated and the other side (X = L) conduction) is reduced by maintained at constant temperature T0 is shown below A. 20% B. 40% A uniformly distributed internal heat C. 50% D. 70% source produces heat in the slab at the rate of S W/m3 Assume the heat 67. A coolant fluid at 30ºC flows over a heated conduction to be steady and 1- flat plate maintained at a constant dimensional along the x-direction. temperature of 100ºC, the boundary layer temperature distribution at a given location 64. The heat flux at x = L is on the plate may be approximated as T = 30 + A. Zero B. SL/4 70 exp( - y) where y (in m) is the distance C. SL/2 D. SL normal to the plate and T is in ºC. If thermal 65. The maximum temperature in the slab conductivity of the fluid is 1.0 W/mK, the occurs at x equal to total convective heat transfer coefficient (in A. Zero B. W/m2K) at that location will be A. 0.2 B. 1 C. D. L C. 5 D. 10 68. An insulating material has a thermal A. M1 B. M2 conductivity of 0.03 Wm-¹ K-¹. If 60 mm of C. M3 D. M4 this material is applied as insulation on a 2010: IIT Guwahati heat transfer surface, the R-value of the 71. The figure below shows steady state insulation in m² K W-¹ is temperature profiles for one dimensional A. 1 B. 2 heat transfer within a solid slab for the C. 3 D. 6 following cases: P. Uniform heat generation with left surface 69. Convective heat transfer coefficient outside perfectly insulted an ice cream block is 10 W.m-²K-¹. Thermal conductivity of frozen ice cream is 0.3 W m-1 Q. Uniform heat generation with right surface K-¹. Convection takes place across a layer of perfectly insulated 10 mm of air for 5 minutes. If the density R. Uniform heat consumption with left and the specific heat capacity of ice cream surface perfectly insulated are respectively 600 kg m-3 and 2.5 kJ kg-1 K- S. Uniform heat consumption with right 1, then 0.33 is surface perfectly insulated A. Biot Number B. Nusselt Number C. Fourier Number D. Prandtl Number 70. A furnace wall consists of four layers of different materials, M1, M2, M3 and M4. If the layers are of equal thickness and the steady state temperature profile is, as shown below, then the material with the lowest thermal conductivity Match the profiles with appropriate cases. A. P-I, Q-III, R,-II, S-IV B. P-II, Q-III, R-I, S-IV C. P-I, Q-IV, R-II, S-III D. P-II, Q-IV, R-I, S-III 72. The interrelationship between thermal is increased to 120⁰C, then the percent conductivity, dynamic viscosity and increase in heat flux under steady state heat temperature of gas can be described as transfer is A. Dynamic viscosity and thermal A. 20.67 B. 40.00 conductivity decrease as temperature C. 59.99 D. 66.67 increases 2011: IIT Madras B. Dynamic viscosity decreases and 75. Heat is generated uniformly within a solid thermal conductivity increases as slab. The slab separates fluid 1 from fluid 2. temperature increases The heat transfer coefficients between the C. Dynamic viscosity and thermal solid slab and the fluid are h1 and h2 (h2 > conductivity decrease as temperature h1) respectively. The Steady state decreases temperature profile (T vs x) for one- D. Dynamic viscosity and thermal dimensional heat is correctly shown by, conductivity increase as temperature decreases 73. At steady state and when the inner and A. outer walls of a long hollow cylinder are kept at two different temperatures, the unidirectional temperature variation along the thickness of the wall is A. Linear B. Parabolic C. Logarithmic D. Constant B. 74. Two faces of a metal plate having thermal conductivity 17 W m-1 K-1 and thickness 10 mm are maintained at 80⁰C and 100⁰C. If the thickness of the plate is increased by 20% and the temperature of the hotter face  C. is h2. The critical thickness of insulation for maximum heat transfer rate is A. B. D. C. D. 78. A constant heat flux of 500 W m-2 is supplied to one face of a food material having a plate like structure with thickness 76. A pipe of 25 mm outer diameter carries of 10 mm. The thermal conductivity of the steam. The heat transfer coefficient food material is 1.5 W m-1 ⁰C-1. From the between the cylinder and surroundings is outer face of the food material, heat is 5 W/m2K. It is proposed to reduce the dissipated by convection into a fluid of 40⁰C heat loss from the pipe by adding temperature. The heat transfer coefficient of insulation having a thermal conductivity the fluid is 100 W m-2 ⁰C of the surface to of 0.05 W/m.K. Which one of the which the heat flux is supplied will be following statements is TRUE? A. 43.3 B. 45.3 A. The outer radius of the pipe is equal to C. 48.3 D. 54.3 the critical radius. B. The outer radius of the pipe is less 79. A plate shaped frozen food has a thickness of than the critical radius. 20 mm, average thermal conductivity of 2.58 C. Adding the insulation will reduce the W m-1 ⁰C-1, density of 1080 kg/m3, specific heat loss. heat of 3550 J/kg.⁰C, and uniform D. Adding the insulation will increase the temperature of - 20⁰C. The food material is heat loss. suddenly immersed in a well stirred hot water maintained at a constant temperature 77. A material having thermal conductivity k of 90⁰C. The heat transfer coefficient between insulates a spherical object of diameter d. the food material and hot water is 25 W m-2 The heat transfer coefficient between the ⁰C-1. The time required for the centre insulating material and the environment  temperature of the food material to reach statements is NOT true when the Biot 30⁰C in minutes is number is very small compared to 1? A. 3.9 B. 7.9 A. Conduction resistance in the solid is C. 15.5 D. 31.0 very small compared to convection resistance in the fluid 80. A furnace wall consists of two layers. The B. Temperature profile within the solid is inside layer of 450 mm is made of light nearly uniform weight bricks of thermal conductivity 1 C. Temperature drop in the fluid is W/m.K and outside layer of 900 mm is significant made of refractory of thermal D. Temperature drop in the Solid is conductivity 2 W/m.K. The hot face of the significant inside layer is at temperature 1300 K and 83. A solid sphere with initial temperature Ti is the cold face of the outer layer is at 400K. immersed in a large thermal reservoir of The temperature at the interface temperature To. The sphere reaches a between the two layers is steady temperature after a certain time t1. If A. 1000 K B. 850 K the radius of the sphere is doubled, the time C. 700 K D. 600 K required to reach steady- state will be PI: 2011: IIT Madras A. B. 81. If T(x, y, z) = x2 + y2 + 2z2 defines the C. 2t1 D. 4t1 temperature at any location (x, y, z), then 84. Heat generated at a steady rate of 100 W due the magnitude of the temperature gradient to resistance heating in a long wire (length = at point P (1, 1, 1) is 5 m, diameter = 2 mm). This wire is wrapped A. B. 4 with an insulation of thickness 1 mm that C. D. that has a thermal conductivity of 0.1 W/m.K. The insulated wire is exposed to air at 30⁰C. 2012: IIT Delhi The convective heat transfer between the 82. For heat transfer across a solid-fluid wire and surrounding air is characterized by interface, which one of the following a heat coefficient of 10 W/m2K. The  temperature (in ⁰C) at the interface the wire B. -100yz exp(-t-x² - y²) and the insulation is C. 100xz exp(-t-x² - y²) A. 211.2 B. 242.1 D. -100xz exp(-t-x² - y²) C. 311.2 D. 484.2 88. Which one of the following 85. The one-dimensional unsteady state heat configurations has the highest fin conduction equation in a hollow cylinder effectiveness? with a constant heat source q is A. Thin, closely spaced fins. If A and B are arbitrary B. Thin, widely spaced fins C. Thick, widely spaced fins constant, then the steady state solution to D. Thick, closely spaced fins the above equation is A. T(r) = 2013:IIT Bombay 89. Consider one-dimensional steady state heat B. T(r) = conduction, without heat generation, in a C. T(r) = plane wall; with boundary conditions as D. T(r) = shown in the figure below. The conductivity of the wall is given by k= k0+bT; where k0, 86. Hot metal at 1700 K is poured in a sand and b are positive constants and mould that is open at the top. Heat loss T is temperature. from the liquid metal takes place by A. Radiation only B. Radiation and conduction only C. Radiation and convection only D. Radiation, conduction and convection 87. The temperature field of a slab is given by x increases, the temperature gradient T = 400-50z exp(-t-x²-y²). The (dT/dx) will temperature gradient in y-direction is A. Remain constant A. 100yz exp(-t-x² - y²) B. Be zero  C. Increase 92. Consider one-dimensional steady state D. Decrease heat conduction along x-axis (0 ≤ x ≤ L), through a plane wall; with the boundary 90. Consider one-dimensional steady state heat surfaces (x=0 and x=L) maintained at conduction along x-axis (0≤x≤L), through a temperatures of 0°C and 100°C. Heat is plane wall the boundary surfaces (x=0 and generated uniformly throughout the wall. x= L) maintained at temperatures 0°C and Choose the CORRECT statement. 100°C. Heat is generated uniformly A. The direction of heat transfer will be throughout the wall. Choose the CORRECT from the surface at 100°C to the surface statement. at 0°C. A. The direction of heat transfer will be B. The maximum temperature inside the from the surface at 100°C to surface at wall must be greater than 100°C. 0°C. C. The temperature distribution is linear B. The maximum temperature inside the within the wall. wall must be greater than 100°C D. The temperature distribution is C. The temperature distribution is linear symmetric about the mid-plane of the wall. within the wall 93. A 40mm⨯40mm square polymer composite D. The temperature distribution is sample with 5 mm thickness (heat transfer symmetric about the mid- distance) exhibited a heat flow rate of 60W, plane of the wall when the temperatures of the warm and 91. A cold storage chamber is constructed cold surfaces were 90°C and 25°C with 10 mm mortar, 200 mm brick, 100 respectively. The thermal conductivity of mm insulation and 5 mm wood-board the sample in W.m-1.K-1 is having thermal conductivities of 0.8, 1.5, A. 5.67 B. 15.3 0.025 and 0.2 W m-¹ K-¹, respectively. The C. 2.88 D. 0.667 resistance of 4 K m² W-¹ is offered by A. Mortar B. Brick C. Insulation D. wood-board  2014: IIT Kharagpur with a fluid at 25°C and heat transfer 94. The bottom face of a horizontal slab of coefficient of 250 W/m2.K. The thickness 6 mm is maintained at 300. The temperature (in °C), at x = 0 is _______ top face is exposed to a flowing gas at 30. The thermal conductivity of the slab is 1.5W m-1K-1 and the convective heat transfer coefficient is 1.5W m-2K-1. At steady state, the temperature (in ) of top face is_______. 95. A brick wall of 20 cm thickness has thermal 97. Biot number signifies the ratio of conductivity of 0.7 W m-1K-1. An insulation A. Convective resistance in the fluid to of thermal conductivity 0.2 W m-1K-1is to be conductive resistance in the solid applied on one side of the wall, so that the B. Conductive resistance in the solid to heat transfer through the wall is reduced by convective resistance in the fluid 75%. The same temperature difference is C. Inertia force to viscose force in the maintained across the wall before and after fluid applying the insulation. The required D. Buoyancy force to viscose force in the thickness (in cm)of the insulation is _______. fluid 96. Consider one dimensional steady state heat conduction across a wall (as shown in figure below) of thickness 30 mm and thermal conductivity 15 W/m.K. At x = 0, a constant heat flux, q" = 1×105 W/m2 is applied. On the other side of the wall, heat is removed from the wall by convection 98. A material P of thickness 1 mm is sandwiched A. B. between two steel slabs, as shown in the C. D. figure below. A heat flux 10 kW/m2 is supplied to one of the steel slabs as shown. 100. Heat transfer through a composite wall is shown in figure. Both the sections of the wall have equal thickness (l). The P conductivity of one section is k and that of the other is 2k. The left face of the wall is at 600 K and the right face is at 300 K. The interface temperature Ti (in K) of the composite wall is _______. The boundary temperatures of the slabs are indicated in the figure. Assume thermal conductivity of this steel is 10 W/m.K. considering one-dimensional steady state heat conduction for the configuration, the thermal conductivity (k, in W/m.K) of material P is _________. 101. As the temperature increases, the 99. Consider a long cylindrical tube of inner and thermal conductivity of a gas outer radii, ri and r0 , respectively, length, L A. increases and thermal conductivity, k. Its inner and B. decreases outer surfaces are maintained at Ti and T0, C. remains constant respectively (Ti > TO). Assuming one- D. increases up to a certain temperature dimensional steady state heat conduction in and then decreases the radial direction, the thermal resistance 102. A plane wall has a thermal conductivity in the wall of the tube is of 1.15 W/m.K. If the inner surface is at  1100⁰C and the outer surface is at drop ( 2 − 3), in K, across the second 350⁰C, then the design thickness (in layer? _____________ meter) of the wall to maintain a steady heat flux of 2500 W/m2 should be _______ 103. A container having volume 282.7 cm3 and total surface area 245 cm2 is completely filled with milk whose initial temperature is 25⁰C. The continually stirred milk container is suddenly exposed to a steam bath at 105. A metallic sphere of 0.1 m diameter has 100⁰C. The overall heat transfer coefficient a thermal conductivity of 10 W/m-K. If between steam and milk is 1136 W m-2 K-1. the fluid flowing around it has a heat The properties of milk are: specific heat transfer coefficient of 10 W/m2-K and capacity = 3.9 kJ kg-1K-1, thermal thermal conductivity of 0.4 W/m-K, the conductivity = 0.54 W m-1K–1 and density = value of Biot number is ______ 1030 kg m-3. Neglecting thermal resistance and heat capacity of container walls, the 106. Two geometrically identical metallic necessary time required in seconds to heat bars are joined end to end (as shown in milk up to the temperature of 85⁰C, will be Fig.). Bars P and Q have thermal ____________. conductivities of 5 W/m-K and 10 W/m-K respectively. The free end of the 104. Consider a steady state heat flux across Bar P is kept at 40°C, while that of Bar Q a rectangular slab composed of two is at 10°C. layers of equal width as shown in the figure below. The thermal conductivities are in the ratio of. If the first layer experiences a temperature drop ( 1 The junction temperature (in °C) for − 2) of 50 K, what is the temperature steady state heat flow is _______ 107. A metallic sphere of 1 kg mass, with temperature. The opposite faces of the surface area of 0.0314 m2, is maintained block are maintained at constant but at an initial temperature of 50°C. The different temperatures: T(x = 0) > T(x = fluid circulating around the sphere is 1). Heat transfer is by steady state maintained at a temperature of 10°C. conduction in x-direction only. There is Specific heat of metallic sphere is 314 no source or sink of heat inside the block. J/kg-K and the heat transfer coefficient In the figure below, identify the correct between the fluid and the sphere is 10 temperature profile in the block. W/m2-K. The time taken (in seconds) for the sphere to cool down to 20°C is ________ 2015: IIT Kanpur 108. A heated solid copper sphere (of surface A. I B. II are A and volume V) is immersed in large C. III D. IV body of cold fluid. Assume the resistance 110. A 10 mm diameter electrical conductor to heat transfer inside the sphere to be is covered by an insulation of 2 mm negligible and heat transfer coefficient thickness. The conductivity of the (h),density , heat capacity (C), and insulation is 0.08 W/m-K and the thermal conductivity (K) to be constant. convection coefficient at the insulation Then, at time t, the temperature surface is 10 W/m²-K. Addition of difference between the sphere and the further insulation of the same material fluid is proportional to: will A. B. A. increase heat loss continuously C. D. B. decrease heat loss continuously C. increase heat loss to a maximum and 109. Consider a solid block of unit thickness then decrease heat loss for which the thermal conductivity decrease with an increase is  D. decrease heat loss to a minimum and figure, the critical radius of then increase heat loss insulation (in cm) is 111. A cylindrical uranium fuel rod of radius 5 mm in a nuclear reactor is generating heat at the rate of 4×107 W/m². The rod is cooled by a liquid (convective heat transfer coefficient 1000 W/m²-K) at 25°C. At steady state, the surface temperature (in K) of the rod is A. 308 B. 398 114. The wall of a cold storage is made up of C. 418 D. 448 four layers; concrete, brick, cardboard and paint with respective thickness of 5, 112. A brick wall (k=0.9 ) of thickness 0.18 60, 8 and 1 mm, and their m separates the warm air in a room from corresponding thermal conductivities the cold ambient air. On a particular are 0.8, 0.7, 0.04 and 0.15 W m–1 K–1. winter day, the outside air temperature The overall resistance of the wall to is -5°C and the room needs to be conduction heat transfer in m2 K W–1 is maintained at 27°C. The heat transfer _____. coefficient associated with outside air is 115. In a 1 m thick wall, the temperature 20. Neglecting the convective distribution at a given instant is T(x) = c0 resistance of the air inside the room, the + c1x + c2x2 where T is in ⁰C and x is in m. heat loss, in( ), is The constants are: c0 = 800⁰C, c1 = – A. 88 B. 110 250⁰C/m and c2 = –40⁰C/m2. The C. 128 D. 160 thermal conductivity of the wall is 50 W/mK and wall area is 5 m2. If there is a 113. If a foam insulation is added to a 4 cm heat source generating uniform outer diameter pipe as shown in the volumetric heating at the rate of 500 W/m3 inside the wall, then the rate of  change of energy storage in the wall, in conditions as shown in figure below. kW, is ________. The figure shows plate temperatures and the heat fluxes in the vertical 2016: IISC Bangalore direction. 116. A Composite wall is made of four different materials of construction in the fashion shown below. The A. resistance (in K/W) of each of the sections of the wall is indicated in the diagram. The overall resistance (in K/W, rounded B. off to the first decimal place) of the composite wall, in the direction of heat flow, is ______ 117. In an experimental setup, mineral oil is C. filled in between the narrow gap of two horizontal smooth plates. The setup has arrangements to maintain the plates at desired uniform temperatures. At these temperatures, ONLY the radiative heat flux is negligible. The thermal D. conductivity of the oil does not vary perceptibly in this temperature range. What is the steady state heat flux (in Wm-2 ) Consider four experiments at steady with the top plate at 70 0 C and the bottom state under different experimental plate at 40 0 C ?  A. 26 B. 39 120. A hollow cylinder has length L, inner C. 42 D. 63 radius r1, outer radius r2, and thermal conductivity k. The thermal resistance 118. Steady one-dimensional heat of the cylinder for radial conduction is conduction takes place across the faces 1 and 3 of a composite slab consisting of A. B. slabs A and B in perfect contact as shown in the figure, where kA, kB denote C. D. the respective thermal conductivities. Using the data as given in the figure, the 121. Two cylindrical shafts A and B at the interface temperature T2 (in °C) is same initial temperature are __________ simultaneously placed in a furnace. The surfaces of the shafts remain at the furnace gas temperature at all times after they are introduced into the furnace. The temperature variation in the axial direction of the shafts can be 119. A cylindrical steel rod, 0.01 m in assumed to be negligible. The data diameter and 0.2 m in length is first related to shafts A and B is given in the heated to 750⁰C and then immersed in a following Table. water bath at 100⁰C. The heat transfer Shaft Shaft coefficient is 250 W/m2-K. The density, Quantity A B specific heat and thermal conductivity Diameter (m) 0.4 0.1 of steel are ρ = 7801 kg/m3, c = 473 Thermal J/kg-K, and k = 43 W/m-K, respectively. Conductivity 40 20 The time required for the rod to reach (W/m.K) 300⁰C is ________ seconds. Volumetric Heat 2⨯106 2⨯107 Capacity (J/m3.K)  The temperature at the centreline of the 124. A long slender metallic rod of length L is shaft A reaches 400⁰C after two hours. The used as a fin. As shown in the figure time required (in hours) for the centreline below, the left end of the fin is kept at a of the shaft B to attain the temperature of constant temperature tb. The fin loses 400⁰C is_______ heat by convection to the atmosphere which is at a temperature ta(tad) and thermal conductivity k1 is heat from the fuel pellet is transferred joined with another rod of identical to the surrounding coolant by dimensions, but of thermal conductivity convection such that the pellet wall k2, to form a composite cylindrical rod temperature remains constant at 300 of length 2l. the heat transfer in radial. Neglecting the axial and azimuthal direction and contact resistance are dependence, the maximum temperature negligible. The effective thermal (in ⁰C in the pellet at steady state is conductivity of the composite rod is ______________ (rounded off to the nearest A. k1+ k2 B. integer). C. D. 136. A solid sphere of radius 1 cm and initial 138. One dimensional steady-state heat temperature of 250 C is exposed to a gas conduction takes place solid whose stream at 100 C For the solid sphere, 0 cross sectional area varies linearly in the density is 10 kg/m and the specific 4 3 the direction of heat transfer. Assume heat capacity is 500J/(kg K). The there is no heat generation in the solid  and the thermal conductivity of the 140. Steady state radial heat conduction material is constant and independent of through a hollow, infinitely long temperature. The temperature zirconia cylinder is governed by the distribution in the solid is following ordinary differential A. Quadratic B. logarithmic equation: C. Linear D. Exponential 139. Three slabs are joined together as shown in the figure. There is no thermal contact Where, T is the temperature and is the resistance at the interfaces. The center radial distance. The inner surface of the slab experiences a non-uniform internal hollow cylinder is maintained at 1473 K heat generation with an average value and the outer surface at 973 K. The rate equal to 10000 Wm-³, while the left and of heat loss per unit length through the right slabs have no internal heat outer surface of the hollow cylinder (in generation. All slabs have thickness equal W.m-¹, rounded off to the nearest to 1 m and thermal conductivity of each integer) is______________. slab is equal to 5 Wm-1K-1. The two Given: Inner radius of cylinder = 0.05 m; extreme faces are exposed to fluid with outer radius of cylinder = 0.07 m and heat transfer coefficient 100 Wm-² K-1 thermal conductivity of and bulk temperature 30 °C as shown. zirconia (k)=2 W.m-1.K-1. The heat transfer in the slabs is assumed 2020: IIT Delhi to be one dimensional and steady, and all 141. Consider an infinitely long rectangular properties are constant. If the left fin exposed to a surrounding fluid at a extreme face temperature T1, is constant temperature T0=20. measured to be 100 °C, the right extreme face temperature T2 ___________________°C.  The steady state one dimensional energy maintained at 1100⁰C respectively as balance on an element of the fin of shown in figure. thickness dx at a distance x from its base yields Where is the temperature of the find at the distance x from its base in. The value of m is 0.04 cm-1 and the temperature at the base is T0=227. The temperature (in ) at x=25cm is The brick wall is covered by an insulating _____(rounded off to 1 decimal place). material of thermal conductivity k2. The thickness of the insulation is 1/4th of the 142. A small metal bead (radius 0.5 mm), thickness of the brick wall. The outer initially at 100⁰C, when placed in a surface of the insulation is at 200⁰C. The stream of fluid at 20⁰C, attains a heat flux through the composite walls is temperature of 28⁰C in 4.35 seconds. 2500 W/m2. The value of k2 is ____________ The density and specific heat of the W/m.K (Round off to 2 decimal places). metal are 8500 kg/m3 and 400 J/kg.K, 144. Heat gain is occurring through a respectively. If the bead is considered as composite cold storage wall, made of lumped system, the convective heat brick and polyurethane foam insulation transfer coefficient (in W/m2.K) (thickness and thermal conductivity between the metal bead and the fluid values are given below). If the exposed stream is surfaces of brick and insulation are at A. 283.3 B. 299.8 45⁰C and 10⁰C, respectively, C. 148.0 D. 449.7 temperature at the interface of brick and insulation in ⁰C (round off to 1 143. In a furnace, the inner and outer sides of decimal place) is _____________ the brick wall (k1 = 2.5 W/m.K) are  Thermal 147. Consider a solid slab of thickness 2L and Thickness Material Conductivity uniform cross section A. The volumetric (mm) rate of heat generation within the slab is W/m.⁰C ġ (W m–3). The slab loses heat by Brick 100 0.30 convection at both the ends to air with Insulation 150 0.05 heat transfer coefficient h. Assuming steady state, one-dimensional heat transfer, the temperature profile within 145. Two solid spheres X and Y of identical the slab along the thickness is given by: diameter are made of different materials having thermal diffusivities 100⨯10-6 m2s-1 and 25⨯10-6 m2s-1 respectively. Both spheres are heated in a furnace where k is the thermal conductivity of the maintained at 1000 K. If the centre of the slab and Ts is the surface temperature. If sphere X reaches 800 K in 1 hour, time Ts = 350 K, ambient air temperature T∞ = required for the centre of sphere Y to 300 K, and Biot number (based on L as the reach 800 K is characteristic length) is 0.5, the maximum A. 1 hour B. 2 hours temperature in the slab is _________________ C. 4 hours D. 16 hours K (round off to nearest integer). 2021: IIT Bombay 148. An uninsulated cylindrical wire of 146. A straight fin of uniform circular cross radius 1.0mm produces electric heating section and adiabatic tip has an aspect at the rate of 5.0 W/m. the temperature ratio (length/diameter) of 4. If the Biot of the surface of the wire is 75⁰C when number (based on radius of the fin as placed in air at 25⁰C. When the wire is the characteristic length) is 0.04, the fin coated with PVC of thickness 1.0mm, efficiency is % (round off to nearest the temperature of the surface of the integer). wire reduces to 55⁰C. Assume that the heat generation rate from the wire and  the convection heat transfer coefficient 151. Ambient air flows over a heated slab are same for both insulated wire and having flat, top surface at y = 0. The local the coated wire. The thermal temperature (in Kelvin) profile within conductivity of PVC is _____________ the thermal boundary layer is given by W/m.K(round off to two decimal T(y) = 300 + 200 exp(−5y), where y is the places.) distance measured from the slab surface in meter. If the thermal conductivity of 149. A hot steel spherical ball is suddenly air is 1.0 W/m.K and that of the slab is dipped into a low temperature oil bath. 100 W/m.K, then the magnitude of Which of the following dimensionless temperature gradient |dT/dy| within the parameters are required to determine slab at y = 0 is _______________ K/m (round instantaneous center temperature of off to the nearest integer). the ball using a Heisler chart? A. Biot number and Fourier number 152. One-dimensional generalized heat B. Reynolds number and Prandtl number conduction equation representing C. Biot number and Froude number temperature distribution in a sphere, D. Nusselt number and Grashoff number based on thermal conductivity k, specific heat capacity Cp, density ρ, and 150. An infinitely long pin fin, attached to an energy generation E, can be written as isothermal hot surface, transfers heat at , where the a steady rate of 1 to the ambient air. If the thermal conductivity of the fin value of n is material is doubled, while keeping A. 1 B. 2 everything else constant, the rate of C. 3 D. 4 steady-state heat transfer from the in 153. One side of a solid food block of 10 cm becomes 2. The ratio 2/ 1 is thickness is subjected to a heating A. B. 2 medium having a film heat transfer C. D. coefficient of 70 W.(m2°C)-1. The other side of the food block is being cooled by  a medium having a film heat transfer D. 500 K, 0.5 K W-1 coefficient of 100 W.(m2°C)-1. The food 2022: IIT Kharagpur block is having a thermal conductivity 155. Consider a bare long copper wire of 1 of 0.2 W.(m°C)-1 and the contact area of mm diameter. Its surface temperature is the block available for heat transfer is 1 s and the ambient temperature is a ( s m2. Heat transfer rate in the block at > a). The wire is to be coated with a 2 steady state is 100 J.s-1. The mm thick insulation. The convective heat temperature difference between the transfer coefficient is 20 W m-2 K-1. two sides of the block in °C is ________. Assume that s and a remain [round off to 2 decimal places] unchanged. To reduce heat loss from the 154. One-dimensional steady-state wire, the maximum allowed thermal temperature distribution in two conductivity of the insulating material, in adjacent refractory blocks (with thermal W m-1K-1, rounded off to two decimal conductivities, k1 and k2) of unit cross- places, is sectional area are shown below. The A. 0.02 B. 0.04 temperature T1 and thermal contact C. 0.10 D. 0.01 resistance of the interface, respectively, 156. A cylindrical fin of diameter 24 mm is are: attached horizontally to a vertical planar wall. The heat transfer rate from the fin to the surrounding air is 60% of the heat transfer rate if the entire fin were at the wall temperature. If the fin effectiveness is 10, its length is ___________ mm (rounded off to the nearest integer). A. 200 K, 0.5 K W-1 B. 400 K, 1.0 K W-1 157. Consider a rod of uniform thermal C. 200 K, 0.25 K W-1 conductivity whose one end ( = 0) is  insulated and the other end ( = ) is process is ________ W/m2.K (round off to exposed to flow of air at temperature 2 decimal places). T∞ with convective heat transfer 159. Consider a solid slab (thermal coefficient h. The cylindrical surface of conductivity, k = 10 W∙m-1∙K-1) with the rod is insulated so that the heat thickness 0.2 m and of infinite extent in transfer is strictly along the axis of the the other two directions as shown in the rod. The rate of internal heat generation figure. Surface 2, at 300 K, is exposed to per unit volume inside the rod is given a fluid flow at a free stream as temperature (T∞) of 293 K, with a convective heat transfer coefficient (h) The steady state temperature at the mid- of 100 W∙m-2∙K-1. Surface 2 is opaque, location of the rod is given as TA. What diffuse and gray with an emissivity (Ɛ) will be the temperature at the same of 0.5 and exchanges heat by radiation location, if the convective heat transfer with very large surroundings at 0 K. coefficient increases to 2h? Radiative heat transfer inside the solid A. B. slab is neglected. The Stefan-Boltzmann C. D. constant is 5.67×10-8 W∙m-2∙K-4. The temperature T1 of Surface 1 of the slab, 158. Consider a one-dimensional steady heat under steady-state conditions, is conduction process through a solid slab _________ K (round off to the nearest of thickness 0.1 m. The higher integer). temperature side A has a surface temperature of 80⁰C, and the heat transfer rate per unit area to low temperature side B is 4.5 kW/m2. The thermal conductivity of the slab is 15 W/m.K. The rate of entropy generation per unit area during the heat transfer 160. Consider steady state, one-dimensional meter wall surface area, the heat heat conduction in an infinite slab of transfer rate in W is ____________. [round thickness 2 ( = 1 m) as shown in the off to one decimal place] figure. The conductivity ( ) of the 162. Apple juice flows through a steel pipe material varies with temperature as = having thermal conductivity of 50 W m-1 , where is the temperature in K, K-1. The outer surface of pipe is exposed and is a constant equal to 2 W∙m-1∙K-2. to ambient environment. The inside There is a uniform heat generation of diameter and thickness of the pipe are 3 1280 kW/m3 in the slab. If both faces of cm and 1.5 cm, respectively. The overall the slab are maintained at 600 K, then heat transfer coefficient based on inside the temperature at = 0 is ________ K (in area is 25 W m-2 K-1. If the internal integer). convective heat transfer coefficient is 30 W m-2 K-1, the external convective heat transfer coefficient (in W m-2 K-1) will be __________ (round off to two decimal places). 2023: IIT Kanpur 161. A walk-in deep freezer wall is made of 163. A copper ball and a steel ball having 120 mm thick brick layer on the outside diameters d1 and d2, respectively, are followed by 75 mm thick concrete and initially at a uniform temperature of 50 mm thick cork layers inside. The 200 ⁰C. Both the balls are exposed to the mean temperatures measured over atmosphere at 30 ⁰C. If both the balls inside and outside wall surfaces are −18 attain a temperature of 120 ⁰C after °C and 24 °C, respectively. The thermal equal exposure duration, then the ratio conductivity of brick, concrete and cork of d1 to d2 is ___________________ (rounded are 0.69, 0.76 and 0.043 W m-1 K-1, off to 3 decimal places). respectively. Considering one square  Assume Biot Number to be less than 0.1. A. P-II, Q-I, R-IV, S-III The thermo-physical properties of B. P-I, Q-II, R-III, S-IV copper and steel are given below: C. P-III, Q-IV, R-II, S-I D. P-IV, Q-I, R-III, S-II Specific Thermal Density 165. A slab of thickness , as shown in the Material heat conductivity Kg/m3 figure below, has cross-sectional area (J kg-1 (W m-1 ⁰C-1) and constant thermal conductivity. ⁰C-1) 1 and 2 are the temperatures at = Copper 8950 383 386 0 and = , respectively. Which one of Steel 7800 460 36 the following options is the CORRECT expression of the thermal resistance for 164. Match the quantities in Group 1 with steady-state one-dimensional heat their units in Group 2 listed in the table conduction? below. Group 1 Group 2 P. I. Thermal conductivity W. m−2K−1 A. B. Q. Convective heat transfer II. C. D. W. m−1K−1 coefficient 166. Consider a laterally insulated rod of length L and constant thermal R. III. W. K−1 Stefan-Boltzmann constant conductivity. Assuming one- dimensional heat conduction in the rod, S. Heat capacity rate IV. W. m−2K−4 which of the following steady-state temperature profile(s) can occur without internal heat generation?  A. B. A. ℎ = 10 Wm-2K-1, k = 100 Wm-1K-1, = 1 mm, TP = 350 K B. ℎ = 100 Wm-2K-1, k = 100 Wm-1K-1, = 1 m, TP = 325 K C. C. ℎ = 100 Wm-2K-1, k = 1000 Wm-1K-1, = 1 mm, TP = 325 K D. ℎ = 1000 Wm-2K-1, k = 1 Wm-1K-1, = 1 m, TP = 350 K D. 2024: IISC Bangalore 168. Critical thickness of insulation (rcr) for a pipe having thermal conductivity (k) and convective heat transfer coefficient (ho) is __________. 167. A very large metal plate of thickness A. 2k/ho and thermal conductivity is cooled by B. k/ho a stream of air at temperature ∞ = 300 C. ho/k K with a heat transfer coefficient ℎ, as shown in the figure. The centreline D. 2ho/k