By use of the Laplace transformation, an exact analytical solution is developed for the case of transient conjugated heat transfer in the thermal entrance region of a parallel plate duct when the unsteadiness is induced by a sudden change in temperature of the ambient fluid outside the duct walls. The solution is presented for the fastest part of the transient, time domain I, and comparison is made with a finite difference solution and also with the approximate, standard quasi-steady approach which is seen to be appreciably in error for a wide range of conjugation parameter values.

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