Numerical Formulation in Terms of Resistance Elements

Up to this point we have shown how conduction problems can be solved by finite-difference approximations to the differential equations. An equation is formulated for each node and the set of equations solved for the temperatures throughout the body. In formulating the equations we could just as well have used a resistance concept for writing the heat transfer between nodes. Designating our node of interest with the subscript i and the adjoining nodes with subscript j, we have the general-conduction-node situation shown in Fig. 3-10. At steady state the net heat input to node i must be zero or 

No new information is conveyed by using a resistance formulation, but some workers may find it convenient to think in these terms. When a numerical solution is to be performed which takes into account property variations, the resistance formulation is particularly useful. 

For convenience of the reader Table 3-4 lists the resistance elements which correspond to the nodes in Table 3-2. Note that all resistance elements are for unit depth of material and Ax = Ay. The nomenclature for the table is that Rm+ refers to the resistance on the positive x side of node (m,n), refers 

The resistance formulation is also useful for numerical solution of complicated three-dimensional shapes. The volume elements for the three common coordinate systems are shown in Fig. 3-11, and internal nodal resistances for each system are given in Table 3-3. The nomenclature for the (m, rt, k) subscripts is given at the top of the table, and the plus or minus sign on the resistance subscripts designates the resistance in a positive or negative direction from the central node (m, n, k). The elemental volume AV is also indicated for each 

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