Analysis of magnetohydrodynamic mixed convection nanofluid flow in a lid-driven porous rectangular cavity with three square heating blocks

Abstract

Analyses of magnetohydrodynamic mixed convection nanofluid flow in a lid-driven porous rectangular cavity with three square heating blocks are carried out. The current geometry are analyzed numerically by finite element method using Galerkins weighted residual approach. The physical problem is represented mathematically by the governing equation along with the corresponding boundary conditions. Two-dimensional steady state Navier-Stokes equations, energy equation and continuity equation are modified to account for the presence of thermal buoyancy and heat generation effects. With proper choice of the dimensionless variables, the equations are transformed to non-dimensional form. Comparisons with previously published works are performed and the results are found to be an excellent agreement. The left and right walls are cold upward and downward lid-directions respectively. Three different cases have been studied based on the location of the square blocks. A set of graphical result is presented in terms of streamlines, isotherms, velocity profiles and the variation of the average Nusselt number and average fluid temperature. It is observed that Darcy number is a good control parameter for heat transfer in fluid flow through porous medium in enclosure. The simulation results indicate that there is an optimal volume fraction of the nanoparticles for each Rayleigh number and Darcy number at which the maximum heat transfer rate occurs. Numerical calculation is carried out for different parameters namely, Darcy Number (1e^(-5)≤Da≤1e^(-2)), Hartmann Number (0≤Ha≤150), Solid volume fraction (0≤φ≤0.1), Richardson Number (0.1≤Ri≤10). Various characteristics such as streamlines, isotherms and heat transfer rate in terms of the average Nusselt Number and average fluid temperature are presented for the aforesaid parameters.