Modeling unsteady diffusive and advective heat transfer for linear dynamical systems: A transfer function approach

Transient conjugate heat transfer (advection and diffusion) inside a heterogeneous physical system composed of solids and flowing fluids is considered here. Starting from a steady state initial temperature field, a single separable thermal excitation (thermal power or temperature difference) is activated. The heat equation as well as its associated boundary and interface conditions are assumed to be linear with time independent coefficients: there is no time nor temperature dependence of the thermophysical properties and velocity fields of both solids and fluids present in the system. In this case, it is shown that the temperature rise or heat flux response at any point of the system (or their space integrated quantities) is a convolution product between the intensity of the relative thermal excitation and a specific transfer function. In this work, a semi-analytical expression of the transfer function that takes into account the lateral heat losses, conduction and advection in the fluid as well as conduction in the solid walls (conjugate heat transfer) of a flat channel with a volumetric heat source (half heat exchanger) in transient state is derived. The analytical transfer function can be obtained for a simple geometry only. For complex geometries it can be identified experimentally. The analytical expression of the transfer function has been compared with that identified for a half-exchanger to verify the analytical expression of the transfer function and to show that this function can be identified experimentally.