  A new formulation of physical thermal models for variable plug flow through a
pipe is proposed. The derived model is based on a commonly used one-dimensional
distributed parameter model, which explicitly takes into account the heat
capacity of the jacket of the pipe. The main result of the present contribution
is the constitution of the equivalence of this model with a serial connection
of 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 the
Laplace domain as well as classical theory of characteristics. The
finite-dimensional approximation of the DPDE-model leads to a
delay-differential equation (DDE)-system, which can be seen as a generalization
of commonly used DDE-models consisting of a first-order low-pass filter subject
to an input delay. The proposed model is compared to several alternative models
in simulations and experimental studies.
