18-in thick furnace wall insulated with 20 cm thick fire brick whose thermal conductivity of 0.75 Btu/hr-ft- R and 0.5 W/m-K, respectively. Furnace side wall is 500 C while outer side is at 60 C. Calculate the heat transmitted across the wall in Watts per sq meter.

A cylindrical pipe is made up of two materials. The inner material A, which has thermal conductivity of ka, has inner radius ra and outer radius re. On the other hand, the outer material B, which has thermal conductivity of kb, has inner radius re and outer radius rb. Contact resistance between the two materials is known to be hc. The temperature at the inner radius of material A (at ra) is Ta, while the temperature at the outer radius of material B (at ri) is T3. Find an expression for the temperature at the inner radius of material B (at r.) in terms of the given variables.

= A processing plant is convectively heating a solid half-sphere of radius of 12 cm made of pure aluminum (k 237 W/m-K) by placing it on an insulated surface as shown in Fig. 1. It is exposed to hot exhaust gas at 300°C with a convection coefficient of 180 W/m².K. Is the lumped capacitance approximation valid? Figure 1: Half-sphere