Stuart number effect on 3-d mhd convection in a cubic area

Abstract

In this paper mathematical modeling of magnetohydrodynamics natural convection in three dimensional area at different Stuart numbers has been considered. The magnetic field is considered vertically and results have been shown at different planes of 3-D enclosure. The modeling of natural convection is based on the solution of a filtered unsteady three - dimensional Navier- Stokes equation and the equation for temperature. The problem is solved numerically: the equations of motion and temperature – by a finite-difference method in combination with penta-diagonal matrix using the Adams-Bashfort scheme, the equation for pressure – by spectral Fourier method with combination of matrix factorization. Change the dynamic of natural convection is gained over the time depending on the different values of Stuart numbers. As result of modelling, isothermal surfaces, velocity and temerature contoures, also profiles for different Sturart numbers are obtained. In this paper mathematical modeling of magnetohydrodynamics natural convection in three dimensional area at different Stuart numbers has been considered. The magnetic field is considered vertically and results have been shown at different planes of 3-D enclosure. The modeling of natural convection is based on the solution of a filtered unsteady three - dimensional Navier- Stokes equation and the equation for temperature. The problem is solved numerically: the equations of motion and temperature – by a finite-difference method in combination with penta-diagonal matrix using the Adams-Bashfort scheme, the equation for pressure – by spectral Fourier method with combination of matrix factorization. Change the dynamic of natural convection is gained over the time depending on the different values of Stuart numbers. As result of modelling, isothermal surfaces, velocity and temerature contoures, also profiles for different Sturart numbers are obtained.