Abstract
A numerical study is presented for mixed convection flow of air (Pr=0.71) within a parallel motion two sided lid-driven parallelogrammic cavity in the presence of magnetic field. The left and right lid-driven sidewalls of the parallelogrammic cavity are maintained at isothermal hot and cold temperatures respectively and slide from bottom to top in upward parallel direction with a uniform lid-driven velocity. A magnetic field of strength (Box) is subjected in the horizontal direction. The horizontal walls of the cavity are considered thermally insulated. The finite volume method has been used to solve the governing Navier–Stokes and energy conservation equations of the fluid medium in the parallelogrammiccavity in order to investigate the effect of magnetic field on the flow and heat transfer for various values of Richardson number, skew angleand Hartmann number. The values of the governing parameters are the Hartmann number (0 ≤ Ha ≤ 75), Richardson number (0.01≤ Ri ≤100) and skew angle (- 60° ≤ Φ ≤ 60°). The present numerical approach is found to beconsistent andthe results is presented in terms ofstreamlines and isotherm contours in addition with the averageNusselt number. It is found that as the Hartmann number increases the circulation of the rotating vortices is reduced and the conduction mode of heat transfer is dominant. Also, it is found that both Richardson number and direction of two sided lid-driven sidewalls affect the heat transfer and fluid flow in the parallelogrammic cavity
Highlights
Magneto-hydrodynamics (MHD) is a branch of continuum mechanics, which deals with the dynamics of electrically conducting fluids in the presence of electromagnetic fields
In the present numerical analysis, the following parametric domains of the dimensionless groups are considered : the Hartmann number is varied as 0 ≤ Ha ≤ 75, the working fluid is air with Prandtl number (Pr) = 0.71, the Richardson number ( Ri ) is varied at 0.01≤ Ri ≤100 while the cavity skew angle, Φ, is varied as - 60° ≤ Φ ≤ 60°
It is clear that the flow within parallelogrammic cavity takes place by a mixture between the natural convection represented by the buoyancy forces due to the temperature difference between two sided liddriven sidewalls and forced convection due to shear force coming from the sliding of two sided liddriven walls in upward direction
Summary
Magneto-hydrodynamics (MHD) is a branch of continuum mechanics, which deals with the dynamics of electrically conducting fluids in the presence of electromagnetic fields. Chamkha [4] investigated the problem of unsteady, laminar, combined forced-free convection flow in a square cavity with the presence of internal heat generation or absorption and a magnetic field Both the top and bottom horizontal walls of the cavity were insulated while the left and right vertical walls were kept at constant and different temperatures. Steady state heat transfer by laminar mixed convection had been studied numerically by solving the equations of mass, momentum and energy to determine the fluid flow and heat transfer characteristics in the cavity as a function of Richardson number, Hartmann number and the cavity aspect ratio. Results were presented in terms of streamlines, isotherms, average Nusselt number at the hot wall and average fluid temperature in the cavity for the magnetic parameter (Ha) and Joule heating parameter (J). It was found that the heat transfer rate increased with the phase deviation up to
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