MATHEMATICAL RANDOM GENERATION OF METAL FOAM AND NUMERICAL 3D SIMULATIONS OF HEAT TRANSFER IN A HYBRID SOLAR COLLECTOR

Abstract

This study explores numerically the heat transfer of a hybrid solar collector. The collector is a Cartesian channel partially filled with randomly generated metal foam (MF). The channel is subjected to solar irradiation, and through it the air flows from the side due to natural convection or ventilation. To generate the MF, random Gaussian correlations are used. This technique allows spatial control of density, permeability, and porosity, whose values are also theoretically accessible. To solve the equations of fluid dynamics and heat transfer, a finite volume multigrid scheme is used. An energy equation is framed on the two-temperature model, and a momentum equation is that of the clear fluid case, since the pores' volumes are largely greater than the ver in the porous media. The velocity as well as temperature fields are discussed for different pertinent parameters, and mathematic correlations are given between the Nusselt, porosity, Richardson, and Reynolds numbers. It is found that heat transfer is improved with increasing metal foam blocks and with decreasing porosities for different Reynolds numbers, however it decreases with Richardson number. It is also found that the two-temperature model is more realistic than models with averaged properties, and gives a wide range of perspectives thanks to the possibility of carrying out numerical and experimental investigations on the same MF model: randomly generated and printable in 3D.