Analysis on Viscous Incompressible Thermal Flow on a Ventilated Enclosure by Finite Element Method

Abstract

Heat transfer in enclosure in which the influence of free (natural) and forced convection (mixed convection) are of comparable magnitude occurs frequently in engineering situations. The applications include the heat transfer improvement in heat exchanger devices, design of solar collectors, thermal design of building, air conditioning, cooling of electronic circuit boards, lubrication technologies, chemical processing equipment etc. Convection in ventilated enclosures containing obstruction has gained recent research significance as a means of heat transfer enhancement. The mathematical model of the present problem is governed by the couple equations of conservation of mass, momentum and energy. Discretization of the governing equations is achieved using a finite element scheme based on the Galerkin weighted residuals method. Then Newton–Raphson iterative algorithm is used to obtain the solutions of the obtained algebraic equations. Comparisons with previously established on particular cases of the problem are performed and the results show excellent agreement. Firstly, for mixed convection flow the effect of inlet and outlet position of a square ventilated enclosure with a centered heat generating solid body has been investigated. The bottom wall of the enclosure is kept at a uniform constant temperature, while the rest three walls of the enclosure are assumed adiabatic. A transverse uniform magnetic field is imposed in the horizontal direction normal to the right vertical wall. An external flow enters the cavity through an inlet opening whereas it exits via another outlet opening. After that, the effect of pertinent parameters in the considered flow problem in this thesis was analyzed for three different types of internal cavity solid body (heat generating, heat conducting, adiabatic) for a selected BT (bottom inlet and top outlet) configuration. Obtained results from the present study are presented in the form of streamlines, isotherms, average Nusselt number along the bottom heated surface and average fluid temperature in the cavity for each of four configurations as well as three different confined blocks for the pertinent parameters namely Reynolds number, Prandtl number, Hartmann number, solid-fluid thermal conductivity ratio, solid block diameter at the three values of Richardson number, varying from 0.1 to 10. The computational findings of this thesis reveals that both the flow and the thermal fields strongly depend on the parameters Reynolds number Re, Prandtl number Pr, Hartmann number Ha at the three convective regimes (Ri = 0.1, 1, 10). The centered solid body of the enclosure influences the steamlines pattern slightly for the smaller dimension of the block D whereas it has a considerable disparity in temperature distribution inside the enclosure. It is also observed that the solid-fluid thermal conductivity ratio K have insignificant effect on the flow fields and have significant effect on the thermal fields at the three convective regimes.