In: Mechanical Engineering
A rod of diameter D = 25 mm and thermal conductivity of 60 W/m·K protrudes from a furnace with a wall temperature of 200ºC. The rod is welded to the furnace wall and is used as a hangar for instrumentation cables. To avoid damaging the cables, the surface temperature of last 100 mm of the rod must be kept below 100ºC. The ambient air temperature is 25ºC and the convection coefficient is 15 W/m2K. (a) Write the finite-difference equation for an internal node with ?x = 2 mm. (b) Write the finite difference equation for the node at the fin tip.