Computational modeling of heat transfer in an annular porous medium solar energy absorber with the P1-radiative differential approximation

Abstract

We study the steady, laminar thermal convection flow in a participating, absorbing-emitting fluid-saturated porous medium occupying a cylindrical annulus with significant thermal radiation effects as a simulation of a solar energy absorber system. The dimensionless incompressible, viscous conservation equations for mass, axial momentum, radial momentum, heat conservation and radiative transfer equation are presented with appropriate boundary conditions in an axisymmetric (X, R) coordinate system. The Traugott P1-Differential radiative transfer model is used which reduces the general integro-differential equation for radiation heat transfer to a partial differential equation. The Darcy–Forcheimmer isotropic porous medium drag force model is employed to simulate resistance effects of the solar porous medium with constant permeability in both the radial (R) and axial (X) direction. A numerical finite difference (FTCS) scheme is used to compute the velocity (U,V), temperature (Θ) and dimensionless zero moment of intensity (I0) distributions for the effects of conduction–radiation parameter (N), Darcy parameter (Da), Forchheimer parameter (Fs), Rayleigh buoyancy number (Ra), aspect ratio (A) and Prandtl number (Pr). The computations have shown that increasing aspect ratio increases both axial and radial velocities and elevates the radiative moment of intensity. Increasing Darcy number accelerates both axial and radial flow whereas increasing Forchheimer number decelerates the axial and radial flow. Higher values of optical thickness induce a weak deceleration in the radial flow whereas they increase both axial flow velocity and temperature. Increasing optical thickness also reduces radial radiative moment of intensity at intermediate axial coordinate values but enhances them at low and high axial coordinate values. Extensive validation is conducted with the network thermo-electric simulation program RAD-SPICE. The model finds important applications in solar energy porous wafer absorber systems, crystal growth technologies and also chemical engineering thermal technologies.