Problem

Two 3-m-long and 0.4-cm-thick cast iron (k = 52 W/m·K, ε = 0.8) steam pipes of outer diame...

Two 3-m-long and 0.4-cm-thick cast iron (k = 52 W/m·K, ε = 0.8) steam pipes of outer diameter 10 cm are connected to each other through two 1-cm-thick flanges of outer diameter 20 cm, as shown in the figure. The steam flows inside the pipe at an average temperature of 250°C with a heat transfer coefficient of 180 W/m2·K. The outer surface of the pipe is exposed to convection with ambient air at 12°C with a heat transfer coefficient of 25 W/m2·K as well as radiation with the surrounding surfaces at an average temperature of Tsurr = 290 K. Assuming steady one-dimensional heat conduction along the flanges and taking the nodal spacing to be 1 cm along the flange (a) obtain the finite difference formulation for all nodes, (b) determine the temperature at the tip of the flange by solving those equations, and (c) determine the rate of heat transfer from the exposed surfaces of the flange