Numerical investigation of magnetohydrodynamic mixed convective nanofluid flow in a lid-driven porous cavity with an obstacle of different aspects

Abstract

Magnetohydrodynamic mixed convective nanofluid flow in a lid-driven porous cavity with an obstacle of different aspects is investigated numerically. The current geometry is analyzed numerically by finite element method using Galerkin weighted residual approach. The physical problems are represented mathematically by the governing equations along with the corresponding boundary conditions. Two-dimensional steady state Navier-Stokes equations, energy equations 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. In this thesis six problems have been studied. This study as well depending on various flow and geometrical conditions are abstracted below. Firstly, the reports on mixed convection Cu-water nanofluid flow in a lid-driven porous square enclosure with elliptic body and constant flux heat source on bottom wall have been investigated. The left and right walls are cold upward and downward lid-directions. Four different cases have been studied based on the location of the elliptic body. A set of graphysical results are presented interms of streamlines, isotherms, velocity profiles and the variation of the average Nusselt number and average fluid temperature. The results reveal that heat transfer rate increases for increasing Grashof number and Reynolds number. It is observed that Darcy number is a good control parameter for heat transfer in fluid flow through porous medium in enclosure. Secondly, the hydrodynamic mixed convection nanofluid flow in a lid-driven porous square cavity including elliptic shape heated block with corner heater has been studied numerically. The top lid moves at a constant speed with cold temperature. The corner heater is under isothermal boundary conditions with different length in bottom and right vertical walls. Numerical results are obtained for wide range of parameters such as Darcy number, Grashof number, Reynolds number, the rate of heat transfer in terms of Nusselt number, the velocity and temperature profiles, the streamlines and the isotherms over the whole boundary layer are displayed graphically and presented in tabular forms. It is found that both the Darcy number and moving lid ordinations have a significant effect on the flow and thermal fields in the enclosure. Heat transfer also increases with increasing of heater length. The results reveal that heat transfer rate increases as heater length increases for increasing Darcy number, Grashof number and Reynolds number. It is observed that, Darcy number is a good control parameter for heat transfer in fluid flow through porous medium in enclosure. Moreover, Copper-water nanofluid has greater merit to be used for heat transfer enhancement. Thirdly, the numerical study dealing with mixed convection copper-water nanofluids in a lid-driven porous square cavity with internal elliptic block is simulated here. The top moving wall is cold and bottom moving wall is heated. Also linearly heated left and right wall and inside elliptic body is heated. The numerical results indicate the strong influence of the mentioned parameters on the flow structure and heat transfer as well as average Nusselt number. An optimum combination of the governing parameters would result in higher heat transfer. Moreover, it is observed that both the Reynolds number and moving lid ordination have significant effects on the flow and thermal fields in the enclosure. Fourthly, the mixed convection in a double lid-driven porous square enclosure filled with copper-water nanofluid with heat generating elliptic block has been numerically simulated. The top lid moves at a constant speed with cold temperature while the bottom lid moves at constant speed with heated temperature. A set of graphical results are presented in terms of streamlines, isotherms, mid height velocity profiles and average Nusselt numbers. It is observed that Darcy number is good control parameter for heat transfer in fluid flow through porous medium in enclosure. Moreover, Copper-water nanofluid has greater merit to be used for heat transfer enhancement. Fifthly, in the present study, mixed convection heat transfer of nanofluid in a lid-driven square cavity with three heating blocks is numerically simulated. The calculations are carried out in two parts. First, the effect of vertical displacement of three triangular heating blocks is investigated. In second part, the calculations are performed for the horizontal displacement of three triangular heating blocks. The results of this study illustrate that by reducing Darcy number and increasing the volume fraction of nanoparticles, the average Nusselt number increases. It is also found that there is an optimal position of square heating blocks where the heat transfer rate is maximized. Finally, numerical simulation on mixed convection heat transfer of nanofluid in a two-dimensional lid-driven porous square cavity with several pairs of heat source-sinks are carried out. 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.