Transfer Function Coefficients for Time Varying Coupled Heat Transfers in Vertically Heated Hollow Concrete Bricks

This paper describes a two step numerical procedure to determinate empirical transfer function coefficients (TFCs) for vertically heated hollow concrete bricks. For such systems TFCs cannot be generated using the analytical techniques available in the literature such as the z-transfer function method or the space state representation method because of the nonlinear local character of the heat transfer by natural convection and radiation in the air cells of the hollow concrete bricks. The first step of the procedure consists in predicting coupled heat transfer by conduction, convection, and radiation in realistic time varying conditions using a detailed numerical simulation. In the second step, the results of the simulation (the time-varying heat fluxes at the hollow brick surfaces) are used to obtain empirical transfer function coefficients using an identification technique. Transfer function coefficients are generated for three different types of hollow concrete bricks mostly used in practice. It is shown that the empirical transfer function coefficients permit fast and accurate prediction of heat transfer for thermal excitations that differ markedly from those used to generate these coefficients without solving the complex system of equations governing the coupled heat transfer mechanisms.