Summary
The problem considered is that of the heat transfer occurring at the inlet to a parallel plate channel. Instead of separating variables, the energy equation is solved, after transformation, in the form of a power series. This method supplies information concerning the initial growth of the thermal boundary layer which is not obtainable by previous methods using eigen-function expansions. A sufficient number of coefficients of the series is computed to allow the present solution to be joined to the asymptotic eigen-function solution, thus completing the treatment of the problem for all values of the longitudinal variable.
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Mercer, A.M. The growth of the thermal boundary layer in laminar flow between parallel flat plates. Appl. sci. Res. 8, 357–365 (1959). https://doi.org/10.1007/BF00411761
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DOI: https://doi.org/10.1007/BF00411761