Finite element analysis on heat flow based on heatline concept for MHD free convection within trapezoidal cavity

Abstract

Free convection or natural convection in trapezoidal cavities has received considerable attention because of its importance in several thermal engineering problems, for example, in the design of electronic devices, solar thermal receivers, uncovered flat plate solar collectors having rows of vertical strips geothermal reservoirs etc. In this thesis under the title “Finite Element Analysis on Heat Flow Based on Heatline Concept for MHD Free Convection within Trapezoidal Cavity”, two problems have been studied. The relative direction between the buoyancy force and the externally forced flow is important. In the case where the fluid is externally forced to flow as the buoyancy force, the mode of heat transfer is termed combined forced and natural convection. The studies as well as depending on various flow of uniform and non-uniform heating and geometrical conditions are abstracted below. Initially, Numerical simulation of two-dimensional laminar steady-state on MHD free convection within trapezoidal cavity with uniformly heated bottom wall has been investigated. In this study, natural convection within a trapezoidal enclosure for uniformly heated bottom wall, insulated top wall and isothermal side walls with inclination angles (ф) are considered. Heat flow patterns in the presence of natural convection within trapezoidal enclosures have been analyzed with heatlines concept. The fluid is concerned for the wide range of Rayleigh number (Ra) from 103 to 107 and Prandtl number (Pr) from 0.026, 0.7, 1000 with various tilt angles Ф = 450, 300 and 00(square).. The properties of the fluid were presumed to be constant. The physical problems are represented mathematically by different sets of governing equations along with the corresponding boundary conditions. The non-dimensional governing equations are discretized by using Galerkin weighted residual method of finite element formulation. Results are presented in terms of streamlines, isotherms, average Nusselt number along the bottom wall for uniform heating , average Nusselt number along the side wall for uniform heating, Local Nusselt number along distance for uniform heating of the side wall, Local Nusselt number along distance for uniform heating of the bottom wall, for different combinations of the governing parameters namely Prandtl number Pr, Hartmann number Ha and at the three values of Rayleigh number Ra, varying from 103 to 107. This range of Ra is selected on the basis of calculation covering free convection dominated regimes. The computational results also indicate that the average Nusselt number at the uniform heating of bottom wall and side wall of the cavity is depending on the dimensionless parameters. Comparisons with previously published work are performed and the results are found to be in excellent agreement. Finally, Numerical simulation of two-dimensional laminar steady-state on MHD free convection within trapezoidal cavity with non-uniformly heated bottom wall has also been investigated. The cavity consists of the same condition like previous one i.e., natural convection within a trapezoidal enclosure non-uniformly heated bottom wall, insulated top wall and isothermal side walls with inclination angles (ф) are considered. Heat flow patterns in the presence of natural convection within trapezoidal enclosures have been analyzed with heatlines concept. The fluid is also concerned for the wide range of Rayleigh number (Ra) from 103 to 107 and Prandtl number (Pr) from 0.026, 0.7, 1000 with various tilt angles Ф = 450, 300 and 00(square). Results are also presented in terms of streamlines, isotherms, average Nusselt number along the bottom wall for non-uniform heating , average Nusselt number along the side wall for non-uniform heating, Local Nusselt number along distance for non-uniform heating of the side wall, Local Nusselt number along distance for non- uniform heating of the bottom wall, for different combinations of the governing parameters namely Prandtl number Pr, Hartmann number Ha and at the three values of Rayleigh number Ra, varying from 103 to 107. This range of Ra is selected on the basis of calculation covering free convection dominated regimes. The computational results also indicate that the average Nusselt number at the non-uniform heating of bottom wall and side wall of the cavity is depending on the dimensionless parameters.