A rod of diameter D=25mm and thermal conductivity k=60W/(m*K) protrudes normally from a furnace wall that is at Tw=200°C and is covered by insulation of thickness Lins=200mm. The rod is welded to the furnace wall and is used as a hanger to support instrumentation cables. To avoid damaging the cables, the temperature of the rod at its exposed surface, To, must be maintained below a specified operating limit of Tmax=100°C. The ambient air temperature is 30°C, and the convection coefficient is 17.0 W/(m2*K). a) Derive an expression for the exposed surface