8. Questions for Practice

1. The wall of a building is a multi-layered composite consisting of brick (100 mm layer), a 100 mm layer of glass fiber (28 kg/m\(^3\)), a 10 mm layer of gypsum plaster, and a 6 mm layer of pine panel. If \(h_{\text{inside}}\) is 10 W/(m\(^2\).K) and \(h_{\text{outside}}\) is 70 W/(m\(^2\).K), calculate the total thermal resistance for heat transfer.

Thermal conductivity of materials: Brick, \(k_b=1.3\) W/(m.K); Glass fiber (28kg/m3), \(k_{gl}= 0.038\) W/(m.K); Gypsum, \(k_{gy}=0.17\) W/(m.K): Pine panel, \(k_p=0.12\) W/(m.K).
(Ans: 2.93 m\(^2\).K/W)


2. A 1m long metal plate with thermal conductivity \(k=50\) W/(m.K) is insulated on its sides. The top surface is maintained at 100\( \circ \)C while the bottom surface is convectively cooled by a fluid at 20\( \circ \)C. Under steady state conditions and with no volumetric heat generation, the temperature at the midpoint of the plate is measured to be 85\( \circ \)C. Calculate the value of the convection heat transfer coefficient at the bottom surface. (Ans: 30 W/(m\(^2\).K))


3. A steam pipe of 0.12 m outside diameter is insulated with a 20 mm thick layer of calcium silicate, with \(k=0.089\) W/(m.K). If the inner and outer surfaces of the insulation are at temperatures of \(T_1=800\) K and \(T_2=490\) K, respectively, what is the heat loss per unit length of the pipe? (Ans: 603 W/m)


4. A cylindrical nuclear fuel rod of 0.2 m dia has a thermal conductivity \(k=0.5\) W/(m.K) and generates uniformly 24,000 W/m\(^3\). This rod is encapsulated within another cylinder having an outer radius of 0.2 m and a thermal conductivity of 4 W/(m.K). The outer surface is cooled by a coolant fluid at 100\( \circ \)C, and the convection coefficient between the outer surface and the coolant is 20 W/(m\(^2\).K). Find the temperatures at the interface between the two cylinders and at the outer surface. Ans: (Ti=151.5\( \circ \)C); \(Ts=130.4\( \circ \)C)


5. Steam at T\( \infty \),1 = 320\( \circ \)C flows in a cast iron pipe (k = 80) W/(m.\( \circ \)C)] whose inner and outer diameter are D1 = 5 cm and D2 = 5.5 cm, respectively. The pipe is covered with a 3 cm thick glass wool insulation [k = 0.05 W/(m.\( \circ \)C]. Heat is lost to the surroundings at T\( \infty \),2= 5\( \circ \)C by natural convection and radiation, with a combined heat transfer coefficient of h2 = 18 W/m2\( \circ \)C.. Taking the heat transfer coefficient inside the pipe to be h1 = 60 W/(m2.K), determine the rate of heat loss from the steam per unit length of the pipe. Also determine the temperature drop across the pipe shell and the insulation. (Ans: Q=120.7 W/m; \( \Delta \)Tpipe=0.02\( \circ \)C; \( \Delta \) Tinsulation=284\( \circ \)C)