Consider a long solid bar whose thermal conductivity is k = 5 W/m · K and whose cross section is given in the figure. The top surface of the bar is maintained at 50°C while the bottom surface is maintained at 120°C. The left surface is insulated and the remaining three surfaces are subjected to convection with ambient air at T_∞ 5 25°C with a heat transfer coefficient of h = 40 W/m² · K. Using the finite difference method with a mesh size of Δx = Δy = 10 cm,

(a) Obtain the finite difference formulation of this problem for steady two-dimensional heat transfer

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

Transcribed Image Text:

Insulation 10 cm 50°C 10 cm Convection h, T 120°C