Internally heated penetrative Bénard-Marangoni ferroconvection: Effect of MFD viscosity

Abstract

A representation for the effect of internally heated on penetrative Bénard-Marangoni-ferroconvection (BMF) driven by constant and uniform volumetric heating with magnetic field dependent (M FD) viscosity is studied. The lower surface is rigid-isothermal and the upper free surface is considered to be plane and non-deformable subject to Robin type of thermal boundary condition. A Galerkin-type is based on the weighted residual method (WRM ) has been used to obtain the eigenvalue for gravity and magnetic thermal Rayleigh number. It is noted that the buoyancy, magnetic and surface tension forces influence the onset of BMF. The onset of BMF is delayed with an increase in magnetic field dependent viscosity parameter (Λ), Biot number (Bi) and magnetic susceptibility (χ) with an increase in the region of stability. In addition, the nonlinearity of fluid magnetization (M 3) and magnetic number (M 1) is found to hasten the onset of FTC. Some existing results are reproduced as particular cases from the present study.