ThermoclassI



THIAGARAJAR COLLEGE OF ENGINEERING - MADURAI 625 015 DEPARTMENT OF MECHANICAL ENGINEERINGSUBJECT: G62- HEAT AND MASS TRANSFERACADEMIC YEAR: EVEN SEM 2011-12Date of Submission: 31.01.12CLASS WORK SHEET I (UNIT-I)CONDUCTIONAn oven made of Asbestos (K = 0.166 W/ m K) has the following dimensions: Inside = 46 cm x 61 cm x 76 cm and outside = 51cm x 66cm x 81cm. The inside wall temperature is 2040 C and the outside wall temperature is 380 C. Estimate the power input necessary to maintain this steady state condition, ignoring the heat losses through the corners and edges. [SD, Pr. 3.10] (Ans.: 5.387 W)A brick wall (K = 0.7 W/ m K) is 0.3 m thick. If the temperatures of the inner and outer surfaces are maintained at 500 C and 300 C respectively. Calculate the heat loss through one square metre area. Find also the temperature at an interior point of the wall 24 cm distant from the outer wall. [SD, Pr. 3.11] (Ans.: 46.67 W/m2; 340 C )Determine the temperature gradient and temperature difference between two sides of a 50 mm thick brass wall (K = 70 W/ m K), if the rate of heat flow through this wall is 70 W / m2.[SD, Pr. 3.12] (Ans.: 10 C /m )Heat resistant steel tubes of ID 32 mm and OD 42 mm are used in a steam superheater for which the inside and outside temperatures are 5800 C and 4500 C respectively. Estimate the rate of heat flow through the wall of the tube per linear metre. Take K for steel = 14 W/mK.[SD, Pr. 3.13] (Ans.: 42.1 kW/m)A steam pipe 200 mm OD is covered with 25 mm thick layer of insulation material with an average K of 0.08 W/mK. The temperature of the pipe surface is 4000 C and that of the outer surface of insulation is 500 C. Find the loss of heat from a length of 10 m of the pipe line.[SD, Pr. 3.14] (Ans.: 7.884 k W)A hollow sphere of pure iron contains a liquid channel mixture which releases 30 kW of energy. The ID and OD of the sphere are 15 cm and 30 cm respectively. If the outside surface temperature of the sphere is 400 C, determine the temperature at a location 2.5 cm from the outer surface. Take K = 70 W/mK. [SD, Pr. 3.16] (Ans.: 85.50 C )Compute the heat loss per square metre of the surface area of a furnace wall 25 cm thick. The inner and outer surface temperatures are 4000 C and 400 C respectively. The variation of the thermal conductivity in W/mK with temperature in 0 C is given by the following equation: K = 0.002 T – 10-6 T2. [SD, Pr. 3.22] (Ans.: 548.35 W / m2)A wall of a house is constructed from a 11.25 cm layer of common brick (K = 0.7 W/ m K) followed by a 4 cm layer of plaster (K = 0.48 W/ m K) , what thickness of loosely packed rock-wool insulation (K = 0.065 W/ m K) should be added to reduce the heat loss through the wall by 75%? [SD, Pr. 3.32] (Ans.: 4.76 cm)The inner dimensions of a freezer cabinet are 60 cm x 60 cm x 50 cm (height). The cabinet walls consists of two 2 mm thick enameled sheet steel (K = 40 W/mK) walls separated by a 4 cm layer of fibre glass (K = 0.049 W/mK) insulation. The inside temperature is to be maintained at -150 C and outside temperature on a hot summer day is 450 C. Calculate the maximum amount of heat to be thrown out assuming a heat transfer coefficient of 10 W/m2 K, both on the inside and outside cabinet. Also calculate the outer surface temperature of the cabinet. [SD, Pr. 3.34] (Ans.: 510 C)Considering the heating surface of a steam boiler to be plane wall of the thickness 1.2 cm and having K = 50 W/mK, determine the rate of heat flow and surface temperature for the following data: Flue gas temperature = 10000 C; Boiling water temperature = 2000 C; Heat transfer coefficient on flue gas side = 100 W/ m2 K; Heat transfer coefficient on boiler water side = 5000 W/ m2 K. [SD, Pr. 3.36] (Ans.: 76. 628 kW/m2; 2340 C)The heating surface of the boiler plate (described in problem 10) exposed to flue gas, becomes covered with a layer of soot of thickness 1 mm (K = 0.08 W/mK) and the water side surface becomes fouled with a scale thickness 2 mm (K = 0.8 W/mK), calculate the heat flow rate and the surface temperature of different layers. Find also the reduction in heat rate due to fouling of the surfaces. [SD, Pr. 3.37] (Ans.: 31. 447 kW/m2; 685.50 C; 2920 C; 284.50 C; 2060 C; 59%)A circular pipe carries hot transformer oil at a temperature of T0 C. The temperature of the cool air surrounding the pipe is half the oil temperature. If the ratio of outside to inside diameters of the pipe is 1.25, show that the total outward heat flow per unit length of the pipe is, Q / L = K T / ln (1.25). [SD, Pr. 3.38] Determine the heat loss per metre length through a thick walled tube of stainless steel (K = 19 W/m K) with 2 cm ID and 4 cm OD, which is covered with a 3 cm layer of asbestos insulation (K = 0.2 W/m K). The inside and outside temperature of this configuration are 6000 C and 1000 C respectively. [SD, Pr. 3.39] (Ans.: 680 W/m) A steel tube (K = 43.26 W/m K) of 5.08 cm ID and 7.62 cm OD is covered with a 2.54 cm layer of asbestos insulation (K = 0.208 W/m K). The inside surface of the tube receives heat by convection from a hot has at a temperature of 3160 C with a heat transfer coefficient 284 W / m2 K, while the outer surface of the insulation is exposed to the ambient air at 380 C with a heat transfer coefficient of 17 W / m2 K. Estimate (i) the loss to ambient air for 3 length of the tube and (ii) the temperature drops across the tube material and insulation layer. [SD, Pr. 3.40] (Ans.: 1484. 4 W; 193.40 C)A steam pipe is covered with two layers of insulation, the first layer being 3 cm thick and the second 5 cm. The pipe is made of steel (K = 58 W/m K) having an ID of 160 mm and OD of 170 mm. The inside and outside film coefficients are 30 and 5.8 W / m2 K respectively. Calculate the heat loss per metre of pipe, if the steam temperature is 3000 C and the air temperature is 500 C. The thermal conductivity of the two insulating materials is 0.17 and 0.093 W/m K respectively. [SD, Pr. 3.41] (Ans.: 220.5 W/m)A refrigerant at - 400 C flows in copper pipe (K = 400 W/m K) of ID 10 mm and OD 14 mm. A 40 mm thick shell of thermo Cole (K = 0.03 W/m K) is put on the pipe to reduce losses. Estimate the heat leakage to the refrigerant per metre length of pipe, if the ambient air temperature is 400 C. Assume the internal and external heat transfer coefficients to be 500 and 5 W / m2 K respectively. Calculate also the amount of refrigerant evaporated per hour taking its latent heat at -400 C as 1390 kJ/kg. [SD, Pr. 3.44] (Ans.: 7.39 W/m ; 0.019 kg)Evaluate the thickness of rubber insulation necessary in the case of a 10 mm diameter copper conductor to ensure maximum heat transfer to the atmosphere, given the K for rubber = 0.155 W/m K and the surface film coefficient as 8.5 W/m2 K. Estimate the maximum heat transfer rate per metre length of the conductor, if the temperature of the rubber is not to exceed 650 C (due to heat generated with in) while the atmosphere is at 300 C. Discuss the effect of insulation on the bare conductor. [SD, Pr. 3.49] (Ans.: 0.0182 m; 14.86 W/m)A plane wall 10 cm thick generates heat at the rate of 30 kW/m3, when an electric current is passed through it. One face of the wall is insulated and the other face is exposed to 250 C air. If the convective heat transfer coefficient between the air and the exposed surface of the wall is 50 W/m2 K, determine the maximum temperature in the wall. The thermal conductivity of the wall material is 3 W/m K. [SD, Pr. 3.52] (Ans.: Tw = 850 C; To = 1350 C)Nichrome, having a resistivity of 110 ? cm is to be used as a heating element in an electric heater. The wire used is 2 mm in diameter and the other design features include: current flow = 25 A; surrounding air temperature = 200 C: K for Nichrome = 17.5 W/m K; surface heat transfer coefficient = 46.5 W/m2 K. Calculate the rate of heat flow for one metre long heater and also the temperatures at the surface and central line of the Nichrome wire. [SD, Pr. 3.55] (Ans.: Tw = 768.70 C; To = 769.70 C)A current of 200 A is passed through a stainless steel wire 3 mm in diameter. The resistivity of the steel may be taken as 70 ? cm, and the length of the wire is 1 m. The wire is submerged in a liquid at 1100 C and experiences a convective heat transfer coefficient of 4 kW/m2 K. Taking K for the wires as 19 W/mK, calculate the centre temperature of the wire. [SD, Pr. 3.56] (Ans.: Tw = 215.040 C; To = 231.60 C)A 1 m long stell plate ( = 50 W/ m K) is well insulated on its sides, while the top surface at 1000 C and the lower bottom surface is convectively cooled by a fluid at 200 C. Under steady state conditions with no generation, a thermocouple at the mid point of the plate reveals a temperature of 850 C. What is the value of the convection heat transfer coefficient at the bottom surface?[FD, Pr. 3.7, pp144] (Ans.: 30 W/ m2 K)A house has a composite wall of concrete (20 mm) at outside, fibre glass insulation (100 mm) and Plaster board (10 mm ) at the inside. On a cold winder day the convection heat transfer coefficients are h0 = 60 W / m2 K and hi = 30 W/ m2 K. The total wall surface area is 350 m2. The inside and outside air temperatures are 200C and -150C respectively. (a) Determine a symbolic expression for the total thermal resistance of the wall, including inside. (b) Determine the total heat loss through the wall and (c) If the wind were blowing violently, raising h0 to 300 W / m2 K, determine the percentage in the heat loss.[FD, Pr. 3.12, pp145] (Ans.: 34.273 kW; 34.681 kW)Steam at a temperature of 2500 C flows through steel pipe (chrome steel, 5 % Cr) of 60 mm inside diameter and 80 mm outside diameter. The convection coefficient between the steam and the inner surface of the pipe is 500 W/m2 K, while that between the outer surface of the pipe and the surroundings is 25 W/m2 K. The temperature of the surrounding air is 200 C. What is the heat loss per unit length of pipe?[FD, Pr. 3.39, pp152] (Ans.: 1145.7 W/m)A Bakelite ( = 1.4 W/ m K) coating is to be used with a 10 mm diameter conducting rod, whose surface is maintained at 2000 C by passage of an electrical current. The rod is in a fluid at 250 C and the convection coefficient is 140 W/ m2 K. What is the critical radius associated with the coating? What is the heat transfer rate per unit length for the bare rod and for the rod with a coating of Bakelite that corresponds to the critical radius? How much Bakelite should be added to reduce the heat transfer associate with the bare rod by 25%?[FD, Pr. 3.41, pp153] (Ans.: 0.01 m; 909.2 W/m0 C; 8.1 mm)A hollow aluminum sphere, with an electrical heater in the centre, is used in tests to determine the thermal conductivity of insulating materials. The inner and outer radii of the sphere are 0.15 m and 0.18 m respectively and testing is done under steady state conditions with the inner surface of the aluminum maintained at 250 0C. In a particular test, a spherical shell of insulation is cast on the outer surface of the sphere to a thickness of 0.12 m. The system is in a room for which the air temperature is 20 0C and the convection coefficient at the outer surface of the insulation is 30 W/m2 K. If 80 W is dissipated by the heater under steady state conditions, what is the thermal conductivity of the insulation?[FD, Pr. 3.44, pp153] (Ans.: 0.082 W/m K)A plane wall of thickness 0.1 m and thermal conductivity 25 W/m K having uniform volumetric heat generation of 0.3 MW/ m3 is insulated on one side, while the other side is exposed to a fluid at 920 C. The convection heat transfer coefficient between the wall and the fluid is 500 W/m2 K. Determine the maximum temperature in the wall. Redo the problem, if the both surfaces are exposed at the same temperature of 92 0C and h =500 W/m2 K. Calculate the maximum temperature in the plate.[FD, Pr. 3.51, pp155] (Ans.: 1370 C; 212)A copper cable of 30 mm diameter has an electrical resistance of 5 x 10-3 ? per m and is used to carry an electrical current of 250 A. The cable is exposed to ambient air at 200 C and the associated convection coefficient is 25 W /m2 K. What are the surface and centerline temperatures of the copper? [FD, Pr. 3.41, pp153] (Ans.: 152.60 C;152.70 C)Nichrome, having a resistivity of 110 ? ? cm is to be used as a heating element in an electric heater. The wire used is 2 mm in diameter and the other design features include:Current flow = 25 ASurrounding air temperature = 200 CThermal conductivity = 17.5 W / m KSurface heat transfer coefficient = 46.5 W/ m2 KCalculate the rate of heat flow for one metre long heater and also the temperature at the surface and central line of the Nichrome wire.[RCS, Pr. 3.55, pp133] (Ans.:69657980.56 W/m3; 7690 C; 7700 C)A 30 mm outer diameter steam pipe is to be covered with two layers of insulation each having a thickness of 25 mm. The average thermal conductivity of one insulating material is 5 times that of the other. Determine the percentage decrease in heat transfer if better insulating material is put next to the pipe than when it forms the outer layer. Assume that the outside and inside surface temperatures of the composite insulations are fixed. [RCS, Pr. 3.42, pp131] (Ans.: 36.8 %)The thermal conductivity of the plane wall varies = (1+ bT + cT2). If the wall thickness is L and the surface temperatures are T1 and T2, show that the heat flux, q, through the wall is given by,q = A plastic pipe (k = 0.5 W/mK) carries a fluid such that convective heat transfer coefficient is 300 W/m2 K. The average fluid temperature is 1000 C. The pipe has an inner diameter of 3 cm and outer diameter of 4 cm. If the heat transfer rate through the pipe per unit length is 500 W/m, calculate the external pipe temperature.[PKN, Pr.2.3, pp 125] (Ans.: 36.530 C)A steel (k = 15 W/m K) tube with 5 cm inner diameter and 7.6 cm outer diameter is covered with an insulation (k = 0.2 W/mK) of thickness 0.2 cm. A hot gas at 3300 C flows through the tube with hi = 400 W/m2 K. The outer surface of the insulation is exposed to air at 300 C with ho = 60 W/m2 K. Calculate (a) the heat loss from the tube which is 10 m long and (b) the temperature drops resulting from the thermal resistances of the hot gas flow, the steel tube, the insulation layer and the outside air. [PKN, Pr.2.4, pp 126] (Ans.: (a)7251 W; (b) 120 C, 3.30 C, 2530 C, 31.70 C)An electrical resistance wire of radius 1 mm with thermal conductivity 25 W/m K is heated by the flow of electric current which generates heat at the rate of 2 x 109 W/m3. Determine the centerline temperature rise above the surface temperature of the wire, if the surface is maintained at a constant temperature. [PKN, Pr.2.6, pp 126] (Ans.: 200 C)An industrial furnace is made of fireclay brick of thickness 25 cm and thermal conductivity k1 = 1 W/m K. The outside surface is insulated with material (k2 = 0.05 W/m K). Determine the thickness of the insulation layer in order to limit the heat loss from the furnace wall to q = 1000 W/m2, when the inside surface of the wall is at 10300 C and the outside surface at 300 C.[PKN, Pr.2.7, pp 126] (Ans.: 3.75 cm)A hollow steel sphere (k = 10 W/m K) has an inside radius of 10 cm and outside radius of 20 cm. The inside surface is maintained at a uniform temperature of 2300 C and the outside surface dissipates heat by convection with h = 20 W/m2 K into the ambient air at 300 C. Determine the thickness of asbestos insulation (k = 0.5 W/m K) required to reduce the heat loss by 50 %.[PKN, Pr.2.8, pp 126] (Ans.: 5.8 cm)The inner and outer radii of a hollow cylinder are 5 cm and 10 cm respectively. The inside surface is maintained at 3000 C and the outside surface at 1000 C and. The thermal conductivity varies with temperature in the range of 100 < T < 3000 C as k = 0.5 (1 + 10-3 T) where T is in 0 C. Determine the heat flow rate per meter length of cylinder.[PKN, Pr.2.10, pp 127] (Ans.:1.088 kW/m)A copper rod of diameter 5 mm is heated by the flow of current. The surface of the rod is maintained at 1750 C while it is dissipating heat by convection (h = 150 W/m2 K) into the ambient air at 250 C. If the rod is covered with a 1 mm thick coating (k = 0.6 W/m K), will the heat loss from the rod increase or decrease?[PKN, Pr.2.11, pp 127] (Ans.: rc = 4 mm, heat loss increases)A current of 200 amp. is passed through a stainless steel wire 0.25 cm in diameter. The resistivity of steel may be taken as 70 ? cm, and the length of wire is 1 m. If the outer surface temperature of the wire is maintained at 1800 C, calculate the centre temperature. Assume k for stainless steel as 30 W/m K. [PKN, Pr.2.14, pp 127] (Ans.:195.20 C)A hot fluid at an average temperature of 2000 C flows through a plastic pipe of 4 cm OD and 3 cm ID. The thermal conductivity of the plastic is 0.5 W/mK, and the convection at 300 C, and the heat transfer coefficient at the outer surface is 10 W/m2 K. Calculate the heat loss per unit length of the pipe. A boiler furnace has the effective dimensions 4m by 3m by 3m high. The walls are constructed from an inner fire brick wall 25 cm thick (k=0.4 W/mK), a layer of ceramic blanket insulation (k=0.2 W/mK), 8 cm thick and a steel protective layer (k=54 W/mK) 2 mm thick. The inside temperature of the fire brick layer was measured as 600o C and the temperature of the outside of insulation as 60 o C. Determine the rate of heat loss through the vertical walls of the furnace. Also calculate the temperature drop across the steel layer.[23.18W].A high pressure steam pipe of ID 21 cm and thickness 2 cm (k=54 W/mK) carries steam at a temperature of 450 o C. The pipe is covered with a layer of insulation 12 cm thick (k=0.04 W/mK). Considering the resistance of steam to heat flow to be infinitesimally small, calculate the heat loss per metre length of pipe, when the outer surface temperature of insulation is 55 o C. [147.5 W/m]The wall of a house consists of 15 cm cinder blocks (k=1 W/mK) covered by 6 mm pine (k=0.11 W/mK) paneling on the inside. The temperature on the outside surface of the cinder blocks is 1 o C and the inside surface of paneling is 25 o C. Determine the heat flow per square metre of wall area and the temperature at the cinder block-pine interface. [117.07 W/m2,291.6 o C]Determine the heat flow through a 5 m2 section of pine wall 5 cm thick whose inside and outside surface air temperatures are 22 o C and 2 o C respectively. Take the value of the convective heat transfer coefficient on the inside and outside walls to be 12 W/m2 K and 100 W/m2 K respectively. Also determine the new inside and outside wall temperatures. [178.57W, 280.12 K, 276.70 K]A hollow sphere 10 cm ID and 30 cm OD has an inner surface temperature of 300 o C and an outer surface temperature of 100 o C. Determine the temperature one fourth way between the inner and outer surfaces. [15(4k) Watt, 200 o C]Hot water flows through a steel pipe 5 cm ID and 6.5 cm OD. The average temperature of the water is 95 o C and that of the outside ambient air is 15 o C. The convective heat transfer coefficient between the water and the inside surface is 1000 W/m2 K and that between the ambient air and the outside pipe surface is 25 W/m2 K. Take the thermal conductivity of steel to be 50 W/mK. Determine the heat loss per linear metre of pipe. [327.87 W/m]A hollow cylinder 10 cm ID and 20 cm OD has an inner surface temperature of 300 o C and an outer surface temperature of 100 o C. Determine the temperature halfway between the inner and outer surface. [288.6(2 l k) Watt per m, 183 o C]A steel steam pipe 10 cm ID and 6 mm wall thickness is covered with 10 cm of high temperature insulation and 5 cm low temperature insulation. The temperature of steam in the pipe is 300o C and of the air in contact with the low temperature insulation is 25 o C. The value of the convective heat transfer coefficient between the steam and the inner pipe surface to be 85 W/m2 K and the value of the convective heat transfer coefficient between the low temperature insulation and the air to be 40 W/m2 K, determine the heat flow rate and the temperature at the interface of the steel and high temperature insulation and at the interface of the high and low temperature insulation. Also determine the inside and outside surface temperature of the steel pipe. [469.08 W/m,282.4 o C,282.2 o C,251.5 o C,41 o C]A pipe 15 cm OD and 10 cm ID is made of steel with a thermal conductivity that varies according to k=10 + 0.01 T (W/mK), where T is expressed in o C. The inside and outside surface temperatures are 150 o C and 40 o C respectively. What is the heat loss per metre length of the pipe? [7568.09 W/m]A solid sphere with a 50 cm diameter has a uniformly distributed heat source. The convective heat transfer coefficient between the sphere and the environment is 15 W/m2 K and the thermal conductivity is 8 W/mK. If the ambient temperature is 25 o C and the center of the sphere is 65 o C, what is the temperature of the surface of the sphere? ................
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