Consider steady two-dimensional heat transfer in an L-shaped solid body whose cross section is given in the

Question:

Consider steady two-dimensional heat transfer in an L-shaped solid body whose cross section is given in the figure. The thermal conductivity of the body is k = 45 W/m · K, and heat is generated in the body at a rate of ė = 5 × 10⁶ W/m³. The right surface of the body is insulated, and the bottom surface is maintained at a uniform temperature of 120°C. The entire top surface is subjected to convection with ambient air at T_∞ = 30°C with a heat transfer coefficient of h = 55 W/m²·K, and the left surface is subjected to heat flux at a uniform rate of q̇_L = 8000 W/m². The nodal network of the problem consists of 13 equally spaced nodes with Δx = Δy = 1.5 cm. Five of the nodes are at the bottom surface and thus their temperatures are known.

(a) Obtain the finite difference equations at the remaining eight nodes

(b) Determine the nodal temperatures by solving those equations.