Write the node equations for the model of heat transfer through the compressor housing section shown in Figure 2-66. Then solve for the node temperatures by using EES, Mathcad, or MATLAB.
Referring to Figure 2-66, which is a scale 1 to 6, the inner radius is assumed to be 21 cm
and the outer radius is then 30 cm. The housing is cast iron so that the thermal
conductivity is 39 W/m?K from Appendix Table B-2 and assuming that the slots have
quiescent fluid at with a thermal conductivity of 1 W/m?K, the node equations may be
written out. Referring to the following sketches some of the nodes are identified, others
need to be to be inferred, and node 1 is shown in some detail.
With this set of equations the temperatures can be determined. Using Mathcad, noting
that the results are tabulated in the final column with node 1 being listed as 0, node 2 as
1, and so on.
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