Visualization of thermo-magnetic natural convective heat flow in a square enclosure partially filled with a porous medium using bejan heatlines and Hooman energy flux vectors: Hybrid fuel cell simulation

Abstract

The aim of the article is to study the magneto-convective laminar incompressible flow within a differentially heated square enclosure partly filled with porous medium saturated with ionized helium gas in the presence of a transverse magnetic flux, as a model for emerging fuel cell designs. A Darcy model is utilized for porous medium bulk drag effects. Visualization of heat line and energy flux vectors is computed via Bejan's heat line approach and the Hooman energy flux vector method. The horizontal (i.e., bottom and top) wall boundaries are considered adiabatic and impermeable, while the side walls (cold and hot walls) are maintained at different but constant temperatures. The nonlinear coupled conservation equations under prescribed boundary conditions are solved with a finite difference-based vorticity-stream function approach. Appropriate convergence criteria factors are deployed. Furthermore, validation with earlier studies for the purely fluid, non-magnetic case i. e. in the absence of porous medium (Da) and Hartmann number (Ha) effects, is included. A parametric examination of the impact of Rayleigh number (Ra), Darcy number (Da) and Hartmann number (Ha) on temperature contours, heat lines, energy flux vectors and streamline patterns for ionized helium gas (Prandtl number, Pr = 0.71) is conducted. An increment in Hartmann magnetic number decreases the magnitudes of heat lines, suppresses heat transmission in the enclosure and curtails flow circulation. Enhancing the magnetic parameter and Rayleigh number however boosts the average heat transfer rate. Average Nusselt number at the left hot wall is elevated with increasing permeability of the porous medium and Rayleigh number. Mid-section velocities are enhanced in the porous layer but depleted in the non-porous layer of the enclosure with greater Rayleigh number. The simulations find provide some insight into applications in emerging hybrid electromagnetic fuel cells enabling better visualization of the thermal/fluid characteristics via the novel heat flow visualization heat-function and energy flux vectors analogy.