Unsteady heat transfer between a fluid, with time varying temperature, and a plate: An exact solution

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An analysis using Laplace transformations is made for the transient temperature distribution and surface heat flux when a plate which is convectively cooled from below has a fluid passing over it whose free stream temperature at the plate leading edge varies arbitrarily with time, and when the plate's thermal response is coupled to the fluid via the conjugation conditions at the interface. First the solution for a step function is found and then generalized to handle arbitrary fluid temperature variation with time. A simple to use approximate method is presented for the most general case. For comparison, quasi-steady results are also derived.