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A new formulation of physical thermal models for variable plug flow through apipe is proposed. The derived model is based on a commonly used one-dimensionaldistributed parameter model, which explicitly takes into account the heatcapacity of the jacket of the pipe. The main result of the present contributionis the constitution of the equivalence of this model with a serial connectionof a pure delay or transport system and another partial differential equation(PDE), subsequently called delay-partial-differential equation (DPDE)-model.The means for obtaining the proposed model comprise operational calculus in theLaplace domain as well as classical theory of characteristics. Thefinite-dimensional approximation of the DPDE-model leads to adelay-differential equation (DDE)-system, which can be seen as a generalizationof commonly used DDE-models consisting of a first-order low-pass filter subjectto an input delay. The proposed model is compared to several alternative modelsin simulations and experimental studies.

On delay-partial-differential and delay-differential thermal models for variable pipe flow