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UNIT ± I Determine the the heat flow across a plane wall of 10 cm thickness with a thermal conductivity conductivit y 0 0 of 8.5 W/m.K. When the surface temperatures are steady & at 200 C & 50 C. The wall area is 2m 2. Also find the temperature gradient in flow direction. (Ans: 25500 W, 1500 0C/m) A pipe of outer diameter 10 cm & inner diameter 8 cm, whose thermal conductivity is expressed as K = (5+0.01T) W/m 0C, where T is expressed in 0C. The inside & outside surfaces are maintained at 100 0C & 20 0C respectively. What is the heat loss for 2 m long pipe? (Ans: 25229.2 W) 0 0 A surface is at 200 C is exposed to surroundings at 60 C & convects & radiates the heat to the surroundings. Calculate the heat transfer rate from surface to surroundings if the convection coefficient coefficient is 80 W /m 2.K. Consider the black bodies for radiation heat transfer. -8 Take = 5.67 x 10 W/m2.K4. (Ans: 13.34 kW/m2) A glass window 60 cm x 60 cm is 16 mm thick. IfIf its its inside & outside surface surface temperatures 0 0 are 20 C & -20 C respectively. Determine the conduction heat transfer rate through the window. Take thermal conductivity of glass as 0.78 W/m.K (Ans; 702 W) The wall of a building consist of 10 cm of brick (K=0.69 (K=0.69 W/m.K) 1.25 cm of Celotex (K=0.048 W/m.K), 8 cm of glass wool (K=0.038 W/m.K) & 1.25 cm of asbestos cement board (K=0.74 W/m.K). If the outside surface of brick is at 5 0C & inside surface of cement board is at 20 0C. Calculate the heat flow rate per square meter of wall surface. (Ans:-5.94 W/m2) An iron plate 2.5 cm thick (K=62 W/m.C) is in contact with asbestos insulation 1 cm thick (K=0.2 W/m.C) on one side & exposed to hot gas with a heat transfer coefficient of 200 W/m2.C on the other surface. If the outer surface of asbestos is exposed to cool air with a heat transfer coefficient of 40 W/m 2.C, Calculate the overall heat transfer coefficient U & the heat flow rate across the composite wall per square meter of the surface for a T of 2000C between the hot gas & cool air. (Ans: 12.43 W/m2.C, 2.48 kW/m2) A container made of 2 cm thick iron plate (K=62 W/m.C) is insulated with a 1 cm thick asbestos layer (K=0.1W/m.C). If the inner surface of iron plate is exposed to hot gas at 5300C with a heat transfer coefficient coefficient of 100 W/m W /m 2.C & the outer surface of the asbestos is in contact with cool air at 30 0C with a heat transfer coefficient of 20 W/m 2.C. Calculate (i) The heat flow rate across the layers per square meter of the surface area, & (ii) The interface temperature between the layers. (Ans: (i) 3119 W/m 2.C, (ii) 497.8 0C) A double glazed window is made of 2 glass panels of 6 mm thick each with an air gap of 6 mm between them. Assuming that layer is stagnant & only conduction is involved. Determine thermal resistance & the overall heat transfer coefficient if the inside surface is exposed to convection with h = 1.5 W/m W /m 2.K. Compare the values with that of single glass of 12 mm thickness. The conductivity of glass = 1.4 W/m.K. & that for air is 0.025 W/m.K. (Ans: 0.915 m2KW, 1.092 W/m2.K, 0.67 m2K/W) Consider a steel pipe (K=10W/m.C) with an inside radius of of 5 cm & an outside radius of 10 cm. The outer surface is to be insulated with fibre glass insulation (K=0.05 W/m.C) to reduce the heat flow rate through the pipe wall by 50%. Determine the thickness of fibre glass. (Ans: 0.05 cm)
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A metal pipe of 10 cm OD is covered with a 2 cm thick insulation (K = 0.07 W/m.C). The heat loss from the pipe is 100 W per meter of length when the pipe surface is at 100 0C. What is the temperature of the outer surface of the insulation? (Ans: 23.50C) Consider a brass tube (K = 115 W/m.C) with an outside radius of 4 cm & a thickness of 0.5 cm. The inside surface of the tube is kept at uniform temperature, & outside surface is covered with two layers of insulation each 1 cm thick, with thermal conductivities of 0.1 W/m.C & 0.05 W/m.C respectively. Calculate the overall heat transfer coefficient based on the outside surface area of the outer insulation. (Ans: 2.83 W/m2.C) A tube with outer diameter of 2 cm is maintained at uniform temperature & is covered with an insulating layer (K = 0.18 W/m.C) in order to reduce the heat loss. Heat is dissipated from the outer surface of insulation with h = 12 W/m 2.K in to an ambient at constant temperature. Determine the critical thickness of insulation. Calculate the ratio of heat loss from the tube with insulation to heat loss without insulation for (i) The thickness of insulation equal to the critical thickness, & (ii) The thickness of insulation 2.5 cm thicker than the critical thickness. (Ans: 0.5 cm, (i) 1.067 (ii) 0.851) A hollow steel sphere (K = 10 W/m.K) has an inside radius of 10 cm & outside radius of 20 cm. The inside surface is maintained at a uniform temperature of 230 0C, while its outside surface dissipates heat by convection with h = 20 W/m 2.K, in to an ambient air at 30 0C. Calculate the thickness of asbestos insulation (K = 0.5 W/m.K) required to reduce the heat loss by 50%. (Ans: 5.8 cm) UNIT ± II One end of a long rod 3 cm in diameter is inserted in to a furnace with the outer end projecting into the outside air. Once the steady state is reached the temperature of the rod is measured at two points, 15 cm apart & found to be 140 0C & 100 0C, when the atmospheric air is at 30 0C with convection coefficient of 20 W/m 2.K. Calculate the thermal conductivity of the rod material. (Pune University, May 1992) (Ans:293.74W/m.K) 0 It is required to heat the oil to 300 C for frying purpose. A long laddle is used in frying pan. The section of the ladle is 5 mm x 18 mm. The surrounding air is at 30 0C. The thermal conductivity of the material is 205 W/m.K. If the temperature at a distance of 380 mm from the oil should not exceed 40 0C, determine convective heat transfer coefficient. (N.M.U. Dec-2002) (Ans: 30.17W/m2.K) Three rods of copper, aluminum & stainless steel are coated with wax all around & are dipped vertically in a water bath at 85 0C. The length of each rod projecting outside the bath is 300 mm. Diameter of each rod is 20 mm & length is 400 mm. Convective heat transfer coefficient at the surface of each rod is 11 W/m 2.K. Take: K copper rod = 380W/m.K, K aluminum rod = 206 W/m.K, K steel rod = 17 W/m.K Calculate the ratio of lengths of rod upto which wax melting occurs due to transfer of heat? (N.M.U. May-2004) (Ans: 4.727 : 3.481 : 1) One end of copper rod (K=380 W/m.K), 300 mm long is connected to a wall which is maintained at 300 0C. The other end is firmly connected to other wall at 100 0C. The air is blown across the rod so that the heat transfer coefficient of 20 W/m 2.K is maintained. The diameter of the rod 15 mm & the temperature of the air is 40 0C. Determine net heat transfer to air. (Ans: 41 W)
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The temperature of hot gas flowing through pipe is measured by a mercury thermometer inserted in an oil well made of steel (K=40 W/m.K). The thermometer reads the temperature at the end of the well which is lower than the gas temperature due to transfer of heat along the well. Calculate % error in temperature measurement, if thermometer reads 150 0C. The temperature of the pipe wall is 80 0C. The well is 10 cm long, 2 mm thick. Take h = 40 W/m 2.K. (Ans: 11.01%) A thermometer pocket 2.2 cm in diameter, 0.5 mm thick is made of steel (K=27 W/m.K) & it is used to measure the temperature of steam flowing through a pipe. Calculate the minimum length of pocket so that the error is less than 0.5% of applied temperature difference. Take steam at 250 0C & h = 98 W/m 2.K. (Ans: 70.42 mm) 0 The steam at 300 C is passing through a steel tube. A thermometer pocket of steel (K=45W/m.K) of inside diameter 14 mm, & 1 mm thick is used to measure the temperature. Calculate the length of thermometer pocket needed to measure the temperature within 1.8% permissible error. The diameter of steam tube is 95 mm. Take heat transfer coefficient as 93 W/m 2.K & tube wall temperature as 100 0C. (Ans: 91.78 mm) 0 A long rod 6.5 mm in diameter is exposed to an environment at 27 C. The base temperature of the rod is 150 0C. The heat transfer coefficient between the rod & environment is 30 W/m2.K. Calculate the heat loss by the rod. (Ans: 753.5 W/m) A very long copper rod (K=372 W/m.K) 25 mm in diameter has maintained its one end at 1000C. The rod is exposed to a fluid at 40 0C with h = 3.5 W/m 2.K. Calculate the heat lost by the rod. (Ans: 13.44 W) 0 A rectangular copper fin has one end maintained at 200 C, while the remainder of the fin surface is exposed to convective environment at 25 0C with h = 35 W/m 2.K. If the thermal conductivity of copper is 386 W/m.K, determine the heat lost by fin per unit depth. The length of fin is 5 cm & thickness is 4 mm. Assume the fin tip to be insulated. (Ans: 612.41 W) An aluminum rod (K = 200 W/m.K) 2.5 cm in diameter, 15 cm long protrudes from the wall, which is maintained at 260 0C. The rod is exposed to an environment at 16 0C with convection coefficient of 15 W/m 2.K. Calculate the heat lost by the rod. (Ans: 78.5 W) A cylindrical rod 2 cm in diameter & 20 cm long protrudes from a heat source at 300 0C into air at 400C. The heat transfer coefficient is 5 W/m 2.K, on all exposed surface. Neglect the radial variation of temperature & heat lost from the tip. Find the temperature at the fin tip & at the mid point along the rod made of borosilicate glass (K = 1.09 W/m.K) (Ans: 41.230C, 52.70C) One end of 30 cm long steel rod (K = 25 W/m.K) is connected to a wall at 204 0C. The other end is connected to other wall at 93 0C. The air is blown across the rod with h = 17 W/m2.K. The diameter of the rod is 5 cm & air temperature is 30 0C, what is the net rate of heat dissipation to air? (Ans: 190.25 W) The temperature of air in a reservoir is measured with the aid of a mercury in a glass thermometer placed in a protective steel well filled with oil. The thermometer indicates the temperature at the end of the well as 84 0C. The well is 12 cm long, its thickness is 1.5 mm & thermal conductivity of well material is 55.8 W/m.K. Assume heat transfer coefficient between well & air is 23.5 W/m 2.K. Calculate the error in temperature measurement, if the
base of the well is at 40 0C. Also calculate the true temperature.
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(Ans: 160C, 1000C) A thermometer well 22 cm in diameter & 0.5 mm thick is made of steel (K = 27 W/m.K) & it is to be used to measure the temperature of steam flowing through a pipe. Calculate the minimum length of well so that the error is less than 0.5%. of the difference between pipe well & fluid temperature. Take steam temperature as 250 0C & h = 98 W/m 2.K. (Ans: 1.7 cm)
