A system of two partial differential equations represent the transient heat transfer behavior of compact heat exchanger surfaces when subjected to a step change in fluid temperature. A solution is presented for this system which includes the effects of longitudinal thermal heat conduction. Also presented are the solutions for the two limiting cases of zero and infinite longitudinal conduction. The numerical results were compared to those of C.P. Howard indicating a significant decrease in computational time and an increase in accuracy of results. The revised curves of maximum slope of fluid temperature versus NTU should be of practical value in the evaluation of heat-transfer data obtained by transient testing of compact heat exchanger surfaces. An unusual combination of mathematical techniques is presented for the solution of a boundary value problem involving partial differential equations. The solution combines the application of Laplace transformation with a numerical technique developed by H. Hurwitz, Jr., and P.F. Sweifel, and adapted by L.A. Schmittroth for the inversion of Laplace transforms. This technique greatly expands the number of cases to which Laplace transforms may be successfully applied. (Author)
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