Study of Exponential Thermal Boundary Condition on Unsteady Magnetohydrodynamic Convection in a Square Enclosure Filled with Fe3O4- Water Ferrofluid

In this paper, magnetohydrodynamic convection is analyzed numerically for a square enclosure filled with Fe3O4–water ferrofluid. A time-dependent exponential thermal boundary condition is applied at the bottom wall of the cavity. The ferrofluid is modeled as a single-phase fluid. Maxwell-Garnet model is used for modeling the effective thermal conductivity and viscosity of the ferrofluid. The Galerkin-weighted residuals method of finite-element analysis is adopted for the numerical solutions. The solid volume fraction, f is varied from 2.5 to 10% and the Hartmann number Ha from 0 to 20. Investigations are carried out for Rayleigh number Ra =104 and 105 over dimensionless times τ=0.01–1.0. The present study indicates that Ra, Ha and f, have a significant effect on heat transfer. At τ =1, if Ra=104, a higher solid volume fraction maximizes heat transfer whereas at Ra=105, a lower solid volume fraction maximizes heat transfer. Moreover, at τ =1, incrementing Ha diminishes heat transfer at Ra=104 whereas an optimum value of Ha=10 maximizes heat transfer for Ra=105. The exponential thermal boundary conditions have a certain importance on heat transfer. The present results provide necessary information for further investigation of heat transfer in its different applications.