Studying the effects of a longitudinal magnetic field and discrete isoflux heat source size on natural convection inside a tilted sinusoidal corrugated enclosure

AbstractIn the present work, the effects of the longitudinal magnetic field and the heat source size on natural convection heat transfer through a tilted sinusoidal corrugated enclosure for different values of enclosure inclination angles are analyzed and solved numerically by using the finite volume technique based on body fitted control volumes with a collected variable arrangement. A constant heat flux source is discretely embedded at the central part of the bottom wall whereas the remaining parts of the bottom wall and the upper wall are assumed adiabatic, and two vertical sinusoidal corrugated walls are maintained at a constant low temperature. The range of the variable parameters considered in the present analysis is as follows: the enclosure inclination angle is varied from 0° to 135°, the ratio of the size of the heating element to enclosure width varied from 20 to 80% of enclosure reference length, Hartmann number is varied from 0 to 100, and Rayleigh number varied from 103 to 106. Liquid gallium with constant Prandtl number (0.02) is used as a working fluid with constant properties except the density. The obtained results indicated that streamlines are affected strongly by the magnetic field especially for small values of inclination angle (Φ=0°) and Rayleigh number (Ra=103–106). The magnetic field effect decreases with an increase in the enclosure inclination angle (Φ>0°) especially for large values of Rayleigh number. The increase in Hartmann number will cause the temperature lines to become symmetrical in shape for large values of Rayleigh number (Ra=105–106). The results also explain that the temperature lines are very little affected by the inclination angle especially for small values of (ε=0.4) and (Ra=104), but this effect will increase especially for (ε=0.8) and (Ra=106). The Nusselt number increases first with an increase in inclination angle (0°≤Φ≤45°), then is slightly affected for (45°<Φ≤90°), and finally decreases for (90°<Φ≤135°). An empirical correlation is developed by using Nusselt number versus Hartmann and Rayleigh numbers, and enclosure inclination angle. The increase in Hartmann number and the ratio of heating element to enclosure width will decrease the Nusselt number. Furthermore, four mathematical correlations are extracted from the results and presented, which can be used to accurately predict the average Nusselt number in terms of enclosure inclination angle, Hartmann, and Rayleigh numbers

MHD heat transfer in W-shaped inclined cavity containing a porous medium saturated with Ag/Al2O3 hybrid nanofluid in the presence of uniform heat generation/absorption

© 2020 by the Authors. In this paper, a 2D numerical study of natural convection heat transfer in a W-shaped inclined enclosure with a variable aspect ratio was performed. The enclosure contained a porous medium saturated with Ag/Al2O3 hybrid nanofluid in the presence of uniform heat generation or absorption under the effect of a uniform magnetic field. The vertical walls of the enclosure were heated differentially; however, the top and bottom walls were kept insulated. The governing equations were solved with numerical simulation software COMSOL Multiphysics which is based on the finite element method. The results showed that the convection heat transfer was improved with the increase of the aspect ratio; the average Nusselt number reached a maximum for an aspect ratio (AR) = 0.7 and the effect of the inclination was practically negligible for an aspect ratio of AR = 0.7. The maximum heat transfer performance was obtained for an inclination of ω = 15 and the minimum is obtained for ω = 30. The addition of composite nanoparticles ameliorated the convection heat transfer performance. This effect was proportional to the increase of Rayleigh and Darcy numbers, the aspect ratio and the fraction of Ag in the volumetric fraction of nanoparticles

Numerical Analysis on the Two-Dimensional Unsteady Magnetohydrodynamic Compressible Flow through a Porous Medium

In the present study, the unsteady magnetrohydrodynamic (MHD) flow of compressible fluid with variable thermal properties has been numerically investigated. The electrically conducting fluid flows through a porous media channel. The uniform magnetic field is applied perpendicular to the direction of the flow. The wall is assumed to be non-conducting and maintained at two different temperatures. The thermal conductivity and viscosity of the fluid change with temperature. Sixth - Order Accurate Compact Finite Difference scheme together with the Third-order Runge-Kutta method is used to solve a set of non-linear equations. The results of the calculation are expressed in the form of the velocity and temperature at different values of the magnetic field and porosity. The proposed mathematical model and numerical methods have been validated by comparing with the results of previously published studies that the compared results reveal the same trends. The difference is due to the compressibility and property variation effects. The results showed that the magnetic field and variable properties considerably influences the flows that is compressible thereby affecting the heat transfer as well as the wall shear stress