A numerical study of buoyancy-driven unsteady natural convection boundary layer flow past a vertical cone embedded in a nonDarcian isotropic porous regime with transverse magnetic field applied normal to the surface is considered. The heat and mass flux at the surface of the cone is modeled as a power law according to ( ) = and * ( ) = , respectively, where denotes the coordinate along the slant face of the cone. Both Darcian drag and Forchheimer quadratic porous impedance are incorporated into the two-dimensional viscous flow model. The transient boundary layer equations are then nondimensionalized and solved by the Crank-Nicolson implicit difference method. The velocity, temperature, and concentration fields have been studied for the effect of Grashof number, Darcy number, Forchheimer number, Prandtl number, surface heat flux power-law exponent ( ), surface mass flux power-law exponent ( ), Schmidt number, buoyancy ratio parameter, and semivertical angle of the cone. Present results for selected variables for the purely fluid regime are compared with the published results and are found to be in excellent agreement. The local skin friction, Nusselt number, and Sherwood number are also analyzed graphically. The study finds important applications in geophysical heat transfer, industrial manufacturing processes, and hybrid solar energy systems.

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Two-dimensional unsteady laminar double-diffusive free convective flow of a conducting fluid in a thermally insulated square enclosure except the left wall has been numerically studied in presence of heat generation/absorption. The Marker and Cell (MAC) method is employed for solving nonlinear momentum, energy and concentration equations and the numerical MATLAB code is validated with the previous study. The computed results are depicted graphically and discussed for various values of Rayleigh number (Ra), Hartmann number (Ha), Buoyancy ratio parameter (N), Lewis number (Le) and heat absorption/generation parameter (γ). It is observed that the rate of heat and mass transfer decreases with increasing Rayleigh number.

Purpose This paper aims to focus on linear and non-linear convection in a lid-driven square cavity with isothermal and non-isothermal bottom surface. Design/methodology/approach It is assumed that the top moving wall is adiabatic and the bottom wall is heated in two modes, and the rest of the walls are maintained at uniform cold temperature. The coupled governing non-linear partial differential equations are solved numerically with MAC algorithm for conducting a parametric study with uniform and non-uniform temperature bottom wall. Findings The numerical results are depicted in the form of streamlines, temperature contours and variation of local Nusselt number. The local Nusselt number at the bottom wall of the cavity increases in presence of non-linear temperature parameter as compared with linear temperature parameter and heat transfer reduces with increasing of Ha for uniform and non-uniform heating of bottom wall. Research limitations/implications The numerical investigation is conducted for unsteady, two-dimensional natural convective flow in a square cavity. An extension of the present study with the effect of inclination of cavity, wavy walls and triangular cavity will be the interest of future work. Originality/value This work studies the effect of magnetic field in the presence of linear convection and non-linear convection. This study might be useful to cooling of electronic components, alloy casting, crystal growth and fusion reactors, etc.

In this paper, the unsteady MHD free convective flow through porous medium over an infinite vertical plate under the influence of uniform transverse magnetic field of strength H 0 has been discussed. The flow is induced by a general time dependent movement of vertical plate. The exact solutions for the velocity, temperature and concentration are obtained making use of Laplace transform technique. The effect of various governing flow parameters on the velocity, temperature and concentration are analyzed, and numerical solutions for the skin friction, Nusselt number and Sherwood number are also obtained and discussed.