CHE463 HEAT TRANSFERASSIGNMENT 2Answer all the questions.

1. The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, kA = 20 W/m2K and kc = 50 W/m2K and known thickness, LA = 0.30 m and LC = 0.15 m. The third material, B which is sandwiched between materials A and C, is of known thickness, LB = 0.15 m, but unknown thermal conductivity kB. Under steady-state operating conditions, measurement reveal an outer surface temperature of Ts,o = 20C, an inner surface temperature of Ts,i = 600C, and an oven air temperature of T = 800C. The inside convection coefficient h is known to be 25 W/m2K. What is the value of kB? (Answer: 1.53 W/mK)2. Consider a 5 m high, 8 m long and 0.22 m thick wall whose representative cross section is as given in Figure 1. The thermal conductivities of various materials used, in W/mC, are kA = kF = 2, kB = 8, kC = 20, kD = 15, and kE = 35. The left and right surfaces of the wall are maintained at uniform temperatures of 300C and 100C, respectively. Assuming heat transfer through the wall to be one dimensional. The representative surface area is

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Figure 1 Composite Wall

a) Sketch the equivalent thermal circuit in variable form, label appropriate resistances, temperatures and heat fluxes.

b) Determine the rate of heat transfer through the wall (Answer: 1.91 x 105 W).c) Calculate the temperature at the point where the sections B, D and E meet (Answer: 263C).

d) Determine the temperature drop across the section F (Answer:143C)3. Steam at 320C flows in a stainless steel pipe (k = 15 W/mK) whose inner and outer diameters are 5 cm and 5.5 cm, respectively. The pipe is covered with 3 cm thick glass wool insulation (k = 0.038 W/mK). Heat is lost to the surroundings at 5C by convection with heat transfer coefficient of 15 W/m2K. Taking the heat transfer coefficient inside the pipe to be 80 W/m2K, determine the rate of heat loss from the steam per unit length of the pipe. Also determine the temperature drops across the pipe shell and the insulation (Answer: 93.9 W/m, 0.095C and 290C)

4. A hollow aluminum sphere, with an electrical heater in the center is used in tests to determine the thermal conductivity of insulating materials. The inner and outer radii of the sphere are 0.15 and 0.18 m, respectively and testing is done under steady state conditions with the inner surface of aluminum maintained at 250C. 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 20C and the convection coefficient at the outer surface of the insulation is 30 W/m2K. If 80 W are dissipated by the heater under steady-state conditions, what is the thermal conductivity of the insulation? (Answer: 0.062 W/mK)