Rayleigh–Bénard and Bénard–Marangoni magnetoconvection in variable viscosity finitely conducting liquids

Abstract The thermorheological effect on magneto‐Bénard‐convection is studied numerically in fluids with finite electrical conductivity. A nonlinear thermorheological equation is considered in the problem. The results are compared with the classical approach of constant viscosity, which depicts the fact that the effect of increasing the strength of the magnetic field is to delay the onset of convection. The magnetic field is shown to have a rheostatic influence on convective instabilities. The results obtained by the study have possible applications in the field of astrophysics, sunspots, and in space applications under microgravity.