Revisit Prob. 5–61 of two-dimensional heat conduction in a square cross section.

(a) Develop an explicit finite difference formulation for a two-dimensional transient heat conduction case

(b) Find the nodal temperatures after 15 seconds.

Data from problem 61

Consider steady two-dimensional heat conduction in  a square cross section (3 cm × 3 cm, k = 20 W/m · K, α = 6.694 × 10^-6 m²/s) with constant prescribed temperature of 100°C and 300°C at the top and bottom surfaces, respectively. The left surface is exposed to a constant heat flux of 1000 W/m² while the right surface is in contact with a convective environment (h = 45 W/m² · K) at 20°C. Using a uniform mesh size of Δx = Δy, determine

(a) Finite difference equations

(b) The nodal temperatures using Gauss-Seidel iteration method.