Using the method of complex temperature in conjunction with the Laplace transformation, an exact analytical solution is found for the transient, conjugate, forced convection problem consisting of a plate, whose base is insulated, interacting with a fluid, moving in a steady slug fashion, whose temperature, at points far from the plate, varies sinusoidally with time. Simple quasi-steady results are derived for comparison. Also presented is a method for determining the qualitative conditions under which one might expect a quasi-steady analysis to be valid in a general problem.

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