A two-dimensional bar has the geometry shown in Fig. P5–141 with specified temperature T_A on the upper surface and T_B on the lower surfaces, and insulation on the sides. The thermal conductivity of the upper part of the bar is k_A while that of the lower part is kB. For a grid defined by Δx = Δy = l, write the simplest form of the matrix equation, AT = C, used to find the steady-state temperature field in the cross section of the bar. Identify on the figure the grid nodes where you write the energy balance.

Transcribed Image Text:

Insulation Тв TA ТВ КА kB ТА ТА ТВ ТВ