Consider a large plane wall of thickness L = 0.4 m, thermal conductivity k = 2.3 W/m · K, and surface area A = 20 m². The left side of the wall is maintained at a constant temperature of 95°C, while the right side loses heat by convection to the surrounding air at T_∞ = 15°C with a heat transfer coefficient of h = 18 W/m² ·K. Assuming steady one-dimensional heat transfer and taking the nodal spacing to be 10 cm,

(a) Obtain the finite difference formulation for all nodes,

(b) Determine the nodal temperatures by solving those equations, and

(c) Evaluate the rate of heat transfer through the wall.