Arod 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 temperature, to, as a function of the prescribed thermal and geometrical parameters. the rod has an exposed length lo, and the tip is well insulated. b) will a rod of length lo=180mm meet the specified operating limit? if not, which design parameters would you change? note the variables and whether increasing or decreasing them would change to.