Consider steady two-dimensional heat transfer in a long solid bar of square cross section in which heat is generated uniformly at a rate of ė = 0.19 × 10⁵ Btu/h·ft³. The cross section of the bar is 0.5 ft × 0.5 ft in size, and its thermal conductivity is k = 16 Btu/h·ft·°F. All four sides of the bar are subjected to convection with the ambient air at T_∞ = 70°F with a heat transfer coefficient of h = 7.9 Btu/h·ft²·°F. Using the finite difference method with a mesh size of Δx = Δy = 0.25 ft, determine

(a) The temperatures at the nine nodes

(b) The rate of heat loss from the bar through a 1-ft-long section.

Transcribed Image Text:

h, T 00 1 4 7 ė h, To 2 5 8 h, To 6 3 h, T 9