Consider a rectangular metal block (k = 35 W/m · K) of dimensions 100 cm × 75 cm subjected to a sinusoidal temperature variation at its top surface while its bottom surface is insulated. The two sides of the metal block are exposed to a convective environment at 15°C and having a heat transfer coefficient of 50 W/m² · K. The sinusoidal temperature distribution at the top surface is given as 100 sin(πx/L). Using a uniform mesh size of Δx = Δy = 25 cm determine

(a) Finite difference equations

(b) The nodal temperatures.

Transcribed Image Text:

h = 50 W/m² K 1 T = 15°C 6 2 7 11 12 100sin(#x/L) °C 3 8 13 Insulation 4 9 14 10 15 h = 50 W/m².K T = 15°C