It is proposed to air-cool the cylinders of a combustion chamber by joining an aluminum casing with annular fins (k = 240 W/m · K) to the cylinder wall (k = 50 W/m · K).

The air is at 320K and the corresponding convection coefficient is 100 W/m2 · K. Although heating at the inner surface is periodic, it is reasonable to assume steady-state conditions with a time-averaged heat flux of qi'= 105 W/m2. Assuming negligible contact resistance between the wall and the casing, determine the wall inner temperature Ti, the interface temperature T1, and the fin base temperature Tb' Determine these temperatures if the interface contact resistance is Rt,c = 10-4 m2 · K/W.