The unsteady heat-transfer problems of combined free and forced convection of a fully developed laminar flow of a heat-generating fluid in a circular tube with constant axial temperature gradient at the wall are investigated. The general solution with arbitrary time-dependent pressure gradient, heat generation, and wall temperature is established by the application of the “generalized Duhamel’s theorem.” Two specific cases are then studied. The results indicate that this type of transient problem has a time-variation of an oscillatory type with decaying amplitude. This time-variation is different from that of forced convection or of combined free and forced convection with constant axial wall temperature.

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