Integral Equation Solution for Internal Flow Subjected to a Variable Heat Transfer Coefficient

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A solution methodology based on integral equations is presented for the problem of heat transfer to laminar duct flow subjected to an axial variation of the external heat transfer coefficient. The technique offers an efficient and accurate calculation procedure which combines standard analytical methods with a simple numerical integration. In order to examine the effect of external finning, results are calculated for the cases of a stepwise periodic and a harmonic variation of the heat transfer coefficient for both fully developed laminar flow and slug flow. The general procedure is applicable to a wide class of problems in heat and mass transfer involving variable boundary condition parameters.