Effect of viscosity variation with temperature on convective instability in a hot dusty ferrofluid layer with permeable boundaries

Abstract

As the subject under consideration has numerous industrial, biological, and environmental applications, so the prime objective of this article is to investigate the onset of thermal convection in a dusty ferrofluid layer under the effect of change in viscosity due to temperature in the presence of permeable boundaries. The linear stability analysis is employed to acquire the eigenvalue problem and then the eigenvalue problem is solved for the stationary convection mode using a single-term Galerkin method. The numerical values of critical wave number and critical Rayleigh number are calculated using MATLAB software, and the results are graphically displayed. The investigation shows that the permeability of the boundaries affects the size of the convection cells that form at the beginning of thermal convection. Further, it is found that the parameters related to temperature-dependent viscosity and permeable boundaries have a stabilizing effect on the system, while magnetic and dust particle parameters destabilize the system.