Developed Brinkman Model into a Porous Collector for Solar Energy Applications with a Single-Phase Flow

Abstract

In this paper, the effects of the fluid-thermal parameters of a porous medium with different values of porosity and permeability on the fluid flow, heat, and concentration parameters were investigated for solar energy applications. The characteristics of the boundary layer, velocity profiles, pressure drop, and thermal and high heat concentration distribution have been analyzed. A developed Brinkman equation for fluid flow and a power law model for thermal conductivity (considering the porosity and permeability factors) were calculated with constant solar heat flux. The numerical model was developed based on the finite element method by the LU algorithm using the MUMPS solver. The Brinkman equations were solved under steady and unsteady states for velocity, pressure, thermal, and concentration distribution effects, respectively. In a porous medium, the normalized temperature of the presented model had an acceptable agreement with the experimental data, with a maximum error of 3%. At constant permeability, by decreasing the porosity, the velocity profile was extended. This was mainly due to the presence of pores in the collector. With an accelerated flow, the maximum velocity of 2.5 m/s occurred at a porosity of 0.2. It was also found that in the porous collector, the Nusselt number increased where the maximum difference between the porous and the nonporous collectors occurred at the beginning of the collector, with a value of 32%, and the minimum difference was 27%. The results also indicate that in the porous collector, solar energy absorbance was higher and the heat transfer was improved. However, an increase in the pressure drop was noted in the porous collectors.

Keywords

• solar collector
• porous medium
• developed brinkman equation
• mass-fluid analysis