Author(s): Eare Md. Morshed Alam, Sumona Huq, Md. Sharif Uddin and MM Rahman

Abstract: Ferrofluid convective heat transfer in a square cavity with sinusoidal temperature boundary condition at the bottom wall under the influence of magneto hydrodynamics effect was investigated numerically in the present study. Top wall is maintained at comparatively low temperature and Vertical walls are assumed to be adiabatic. The working fluid is Fe₃O₄-water nanofluid. Single phase model is used to estimate the behavior of ferrofluid and the Maxwell-Garnet model is used for modeling the effective thermal conductivity and viscosity for the ferrofluid. The Galerkin weighted residual method of finite element analysis is implemented to discretize the governing equations. The analysis has been carried out for solid volume fraction (φ = 0- 0.1) and the Hartmann number (Ha = 0-20) for two values of Rayleigh number (Ra = 10⁵, 10⁶) with respect to dimensionless time (τ = 0.1, 1.0). The results are presented both in terms of streamlines, isotherms and Local Nusselt number through the active thermal wall for different combinations of the governing parameters. The results indicate that both the flow and the thermal fields strongly depend on the above-mentioned parameters. The computational results also indicate that the Local Nusselt number at the heated wall for different time are depending on the aforementioned parameters. The results in terms of local Nusselt number are also shown in tabular form. The present investigation lays down a solid foundation for the investigation of time-varying sinusoidal boundary conditions in MHD convection.

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