Consider a 1-D steady state heat conduction in a composite wall made up of two different materials A (k= 45 W/m · K) and B (k = 28 W/m · K). There is a heating element passing through the material A that causes uniform heat generation at a rate of 70,000 W/m³. The total thickness of the wall is 20 cm with equal thickness of material A and material B. Using a uniform nodal spacing of 2.5 cm,

(a) Obtain a finite difference formulation for the case of constant uniform heat flux of 4500 W/m² at the wall inner (left) surface while the outer (right) surface is exposed to combined radiation (ε = 0.9) and convection boundary condition (h = 70 W/m² · K). Assume the surrounding temperature equal to that of the ambient temperature at 10°C and determine

(b) The temperature distribution across the wall thickness using boundary conditions in part (a).