A System of Algebraic Equations

• The nodal equations derived previously are valid for all interior points satisfying the steady state, no generation heat equation. For each node, there is one such equation.

For example: for nodal point m=3, n=4, the equation is

T2,4 + T4,4 + T3,3 + T3,5 - 4T3,4 =0

T3,4=(1/4)(T2,4 + T4,4 + T3,3 + T3,5)

• Nodal relation table for exterior nodes (boundary conditions) can be found in standard heat transfer textbooks. (ex. F.P. Incropera & D.P. DeWitt, “Introduction to Heat Transfer”.)

• Derive one equation for each nodal point (including both interior and exterior points) in the system of interest. The result is a system of N algebraic equations for a total of N nodal points.

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