Analytical and Numerical Study of Combined Effects of a Magnetic Field and an External Shear Stress on Soret Convection in a Horizontal Porous Enclosure (original) (raw)
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The problem of steady, laminar, natural convective flow of electrically-conducting liquid metals such as gallium and germanium in an inclined rectangular enclosure in the presence of a uniform magnetic field is considered. Transverse gradient of heat is applied on two opposing walls of the inclined enclosure while the other two walls are adiabatic. A magnetic field is applied normal to the non-insulated walls. The problem is formulated in terms of the vorticity – stream function procedure. A numerical solution based on the finite-difference method is obtained. Representative results illustrating the effects of the enclosure inclination angle and the Hartmann number for two different Rayleigh numbers on the contour maps of the streamlines and temperature as well as the profiles of velocity components and temperature at mid-section of the enclosure are reported. In addition, results for the average Nusselt number are presented and discussed for various parametric conditions.
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Accepted for the publication in Applied Mechanics and Materials
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International Journal of Thermal Sciences, 2008
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ScienceDirect, 2017
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Experimental Thermal and Fluid Science, 2006
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Energies, 2020
Natural convection of liquid metal in an annular enclosure under the influence of azimuthal static magnetic field was numerically studied. The liquid metal in the enclosure whose cross-sectional area is square was heated from an inner vertical wall and cooled from an outer vertical wall both isothermally whereas the other two horizontal walls were assumed to be adiabatic. The static azimuthal magnetic field was imposed by a long straight electric coil that was located at the central axis of the annular enclosure. The computations were carried out for the Prandtl number 0.025, the Rayleigh number 104, 5 × 105 and 107, and the Hartmann number 0–100,000 by using an in-house code. It was found that the contour map of the electric potential was similar to that of the Stokes stream function of the velocity regardless of the Hartmann number. Likewise, the contour map of the pressure was similar to the Stokes stream function of the electric current density in the case of the high Hartmann n...
Magnetic field effects on natural convection flow of a non-Newtonian fluid in an L-shaped enclosure
Journal of Thermal Analysis and Calorimetry, 2018
The effect of magnetic field on natural convection heat transfer in an L-shaped enclosure filled with a non-Newtonian fluid is investigated numerically. The governing equations are solved by finite-volume method using the SIMPLE algorithm. The power-law rheological model is used to characterize the non-Newtonian fluid behavior. It is revealed that heat transfer rate decreases for shear-thinning fluids (of power-law index, n \ 1) and increases for shear-thickening fluids (n [ 1) in comparison with the Newtonian ones. Thermal behavior of shear-thinning and shear-thickening fluids is similar to that of Newtonian fluids for the angle of enclosure a \ 60°and a [ 60°, respectively. Keywords Magnetohydrodynamics (MHD) Á Natural convection Á Newtonian fluid Á Non-Newtonian fluid Á Enclosure List of symbols AR Aspect ratio B o Magnetic induction (T) g Gravitational acceleration (m s-2) Ha Hartmann number K Thermal conductivity (W m-1 K-1) L Specific length (m) n Power-law index Nu Local Nusselt number P Pressure (Pa) Pr Prandtl number Ra Rayleigh number Re Reynolds number T Wall temperature (K) u Velocity in x-direction (m s-1) v Velocity in y-direction (m s-1) U Dimensionless velocity in x-direction V Dimensionless velocity in y-direction x Distance along x-coordinate y Distance along y-coordinate Greek letters b Thermal expansion coefficient (k-1) l Dynamic viscosity (kg m-1 s-1) q Density (kg m-3) h Dimensionless temperature