Magnetohydrodynamic mixed convective nanofluid flow in a lid-driven porous trapezoidal enclosure with an obstacle

Abstract

Heat transfer enhancement has been a major concern in modern days in designing heat generating obstacle. In the present study, Magnetohydrodynamic mixed convective nanofluid flow in a lid-driven porous trapezoidal enclosure with constant squareheatedandheatgeneratingobstacleisnumericallysimulated.The 𝐶𝑢(Copper)nanoparticlewithdifferentvolumefraction(1%−5%)mixingwith the base fluid 𝐻2𝑂(Water) is considered. The mathematical model of the systemwill be developed by formulating the continuity, momentum and energy equations with the appropriate boundaryconditions. Thedimensional governingequations will then be transformed into dimensionless form. The top wall lid moves left to rightand the bottom wall lid moves right to left with constant velocity. The left, right and bottomwallsaremaintainedatheatedtemperatureandtopwallismaintainedatcold temperature. There are constant square heated obstacle and heat generating square obstacleinsidethe enclosure.ThefiniteelementmethodbasedonGalerkinweighted residualtechniqueisusedtosolvethegoverningequationsinordertoinvestigatethe effect of Darcy number (𝐷𝑎)and Richardson number (𝑅𝑖)on the fluid flow and heat transfer characteristics inside the enclosure. A set of graphical results are presented in terms of streamlines, isotherms, dimensionless temperature, velocity profiles, average Nusselt number and average fluid temperature. The results demonstrate that heat transfer rate increases with increasing of Richardson number.It is observed that Darcy number is a good control parameter for heat transfer influid flow through trapezoidal enclosure. To validate the computational procedure presents the result compared with other published works.