An aluminum plate of 25 mm thick (k = 235 W/m·K) is attached on a copper plate with thickness of 10 mm. The copper plate is heated electrically to dissipate a uniform heat flux of 5300 W/m2. The upper surface of the aluminum plate is exposed to convection heat transfer in a condition such that the convection heat transfer coefficient is 67 W/m2·K and the surrounding room temperature is 20°C. Other surfaces of the two attached plates are insulated such that heat only dissipates through the upper surface of the aluminum plate. If the surface of the copper plate that is attached to the aluminum plate has a temperature of 100°C, determine the thermal contact conductance of the aluminum–copper interface.

A 15 cm x 20 cm hot surface at 85°C is to be cooled by attaching 4 cm long aluminum (k = 237 W/m-°C) fins of 2 mm x 2 mm square cross section. The temperature of surrounding medium is 25°C and the heat transfer coefficient on the surfaces can be taken to be 20 W/m²-°C. If it is desired to triple the rate of heat transfer from the bare hot surface, determine the number of fins that needs to be attached. plot the number of fins as a function of the increase in the heat loss by fins relative to no fin case (i.e., overall effectiveness of the fins) in the range of 1.5 to 5. Discuss the results.

Two large stainless steel plates at temperatures of 90°C and 70°C are separated by a stainless steel rod0.3 m long and 2.5 cm in diameter. The thermal conductivity of type 304 stainless steel is k = 16.2W/m K. The rod is welded to each plate. The space between the plates is filled with insulation so thatno heat is lost from the circumference of the rod. Because of a voltage difference between the twoplates, current flows through the rod, resulting in a uniform heat generation rate of 1.5 x 105 W/m3.a) Solve for the temperature distribution in the rod as a function of position x analytically (integratethe equation).b) Determine the maximum temperature in the rod. Where does it occur?c) Solve for the temperature distribution in the rod as a function of position x using the finitedifference method. Assume a ∆x of 0.05 m. How does this compare to the exact solution?

Electrically heated draw batch furnaces are commonly used in the heat treatment industry. Consider a draw batch furnace front made of a 20-mm thick steel plate with a ther- mal conductivity of 25 W/m-K. The furnace is situated in a room with surrounding air temperature of 20 C and an aver- age convection heat transfer coefficient of 10 W/m2-K. If the inside surface of the furnace front is subjected to uniform heat flux of 5 kW/m2 and the outer surface has an emissiv- ity of 0.30, determine the inside surface temperature of the furnace front. I= 20°C Furnace front 4=5kW/m Air, 20 C h= 10 W/m K E=0,30 A= 25 Wim K Page 4.