Consider the two-dimensional grid (∆x = ∆y) representing steady-state conditions with no internal volumetric generation for a system with thermal conductivity k. One of the boundaries is maintained at a constant temperature Ts while the others are adiabatic.

Derive an expression for the heat rate per unit length normal to the page crossing the isothermal boundary (Ts).

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12 11 10 13 14 Insulation Ay * 15 2 Isothermal boundary, T, Ax- 16 Insulation