This paper is an extension of two of the authors’ previous papers [1, 2] and considers the dynamic response of the temperature of the heat-transfer surface and the fluid-surface temperature difference in a heat exchanger having internal heat sources. A general solution is presented for a transient resulting from an arbitrary time rate of change of heat generation starting from an arbitrary initial condition. The results are obtained by a direct mathematical attack on the governing differential equations. As a special case, the transient resulting from a linear time rate of change of internal heat generation is given, and this is compared with both experimental and theoretical results corresponding to a step change in heat generation. Satisfactory comparison is obtained. The results for this special case are presented such that the surface temperature and fluid-surface temperature difference may be computed as a function of space and time using four dimensionless, mathematical functions which are given in graphical form. It is shown how the case of the linear time rate of change of internal heat generation may be used to compute the dynamic response of this type of heat exchanger for any transient resulting from excursions in heat-generation rate which may be approximated piece-wise by a series of linear functions of time. Heat exchangers to which these solutions apply include the heterogeneous nuclear reactor.

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