Effect of Hall current on MHD natural convection flow from vertical permeable flat plate with uniform surface heat flux

The effect of the Hall current on the magnetohydrodynamic （MHD） natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field.It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field.The boundary layer equations are reduced to a suitable form by employing the free variable formulation （FVF） and the stream function formulation （SFF）.The parabolic equations obtained from FVF are numerically integrated with the help of a straightforward finite difference method.Moreover,the nonsimilar system of equations obtained from SFF is solved by using a local nonsimilarity method,for the whole range of the local transpiration parameter ζ.Consideration is also given to the regions where the local transpiration parameter ζ is small or large enough.However,in these particular regions,solutions are acquired with the aid of a regular perturbation method.The effects of the magnetic field M and the Hall parameter m on the local skin friction coefficient and the local Nusselt number coefficient are graphically shown for smaller values of the Prandtl number P r （= 0.005,0.01,0.05）.Furthermore,the velocity and temperature profiles are also drawn from various values of the local transpiration parameter ζ.

Unsteady Flow of Hybrid Nanofluid with MagnetohydrodynamicsRadiation-Natural Convection Effects in a U-Shaped Wavy Porous Cavity

In this paper,the unsteady magnetohydrodynamic(MHD)-radiation-natural convection of a hybrid nanofluid within a U-shaped wavy porous cavity is investigated.This problem has relevant applications in optimizing thermal management systems in electronic devices,solar energy collectors,and other industrial applications where efficient heat transfer is very important.The study is based on the application of a numerical approach using the Finite Difference Method(FDM)for the resolution of the governing equations,which incorporates the Rosseland approximation for thermal radiation and the Darcy-Brinkman-Forchheimer model for porous media.It was found that the increase of Hartmann number(Ha)causes a reduction of the average Nusselt number(Nu),with a maximum decrease of 25%observed as Ha increases from 0 to 50.In addition,the influence of the wall’s wave amplitude and the heat source length on the heat transfer rate was quantified,and it was revealed that at high wave amplitude,the average Nu increases by up to 15%.These findings suggest that manipulating magnetic field strength and cavity geometry can significantly enhance thermal performance.The novelty of this is related to the exploration of a U-shaped wavy cavity,which is not covered in previous studies,and to the detailed examination of the combined effects of magnetic fields,radiation,and hybrid nanofluids.