Abstract
This paper presents a simple geometric transformation for predicting thermal spreading resistance in isotropic and compound rectangular flux channels using the solution for an isotropic or compound circular flux tube. It is shown that the results are valid for a wide range of channel aspect ratios and source to base coverage ratio. Because the circular disk solution requires a single series summation, it is preferable to the rectangular flux channel solution, which requires the evaluation of two single-series and one double-series summation. The effect of edge cooling is also addressed in flux tubes and flux channels. A new analytical solution is obtained for thermal spreading resistance in a rectangular flux channel with edge cooling. This solution contains many limiting cases, including a previously published solution for adiabatic edges. Comparisons are made with the circular flux tube with edge cooling and with adiabatic edges. Simple relationships are developed for edge-cooled systems to assess the importance of edge cooling. This alleviates the issue of computing or recomputing eigenvalues when the edge-cooling conditions change or have no impact. It is shown that this simple approach provides good results for a wide range of dimensionless parameters.
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