An analytical model is developed to determine the effect of the temperature of entrained fluid (entrainment temperature) on the local heat transfer to a single, plane, turbulent impinging jet. Solutions of the momentum and energy equations for a single impinging jet are accomplished using similarity and series analyses. Solutions of the energy equation are obtained for the two limiting cases of entrainment temperatures equal to the plate temperature and the initial jet temperature. The analytical solutions are superposed to obtain the solution for all intermediate entrainment temperatures. The constants in the turbulence model are determined by comparing the analytical solutions to experimentally determined local heat transfer rates for single impinging jets issuing into an environment with a controlled entrainment temperature. When the single jet model is applied to jet arrays it predicts that the entrainment in the recirculation region between the jets can significantly affect the heat transfer. Comparison of the model to heat transfer measurements performed for jet arrays shows that the model successfully predicts the local heat transfer in jet arrays.

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