Chapter 4, Problem 4.45P

Upper and lower surfaces of a bus bar are convectively cooled by air at $T_{\infty },$ with $h_u\ne h_l.$ The sides are cooled by maintaining contact with heat sinks at $T_o,$ through a thermal contact resistance of $R_{t,c}^{"}.$ The bar is of thermal conductivity k, and its width is twice its thickness L.

Consider steady-state conditions for which heat is uniformly generated at a volumetric rate due to passage of an electric current. Using the energy balance method, derive finite-difference equations for nodes 1 and 13.