Dynamics of Double Pipe Heat Exchangers: Explicit Time Domain Solutions

The dynamics of double pipe heat exchangers are governed by systems of nonhomogeneous hyperbolic partial differential equations when longitudinal dispersion effects are neglected and finite fluid capacitances accounted for. Their non-linear behaviour is described with a theoretical Hammerstein model with delay. The solutions are obtained in original variables by the characteristic, Laplace transform and difference equation methods (CLD) without numerical quadratures neither convolutions and valid for any dependence of heat transfer coefficients and capacitances from input variables. These solutions are also valid for generic non-zero initial conditions and any combination of stepwise variations of inputs, namely temperatures and flow rates of both fluids. The calculations are carried out with the aid of a double grid framework on the physical domain in order to allow for an arbitrary selection of sampling time and spatial coordinates. The results of the calculations are compared with those obtained by finite element method (FEM) and by numerical inversion of the Laplace domain solutions. The solution compare very well with rigorous solutions.