Numerical investigation of natural convection in a triangular enclosure with a heated elliptical block

Abstract

This thesis having title “Numerical investigation of natural convection in a triangular enclosure with a heated elliptical block” is focused on comprehensive analysis of heat transfer and fluid flow inside the cavity. The objective of this research is to enhance rate of the heat transfer through introduction of heated elliptical black, to examine the effects of various parameters such as Rayleigh number (Ra) and Prandtl number (Pr) and to examine the overall heat transfer rate and compare the numerical results obtained from this study with relevant published data of cavities having blocks. Natural convection within a triangular enclosure having uniformly heated top wall and cold side walls is studied. The fluid flow is considered for the wide range of Rayleigh number (Ra) from 104 to 106 and Prandtl number (Pr) from 0.71 to 10 having Ellipse Position (EP) = (0.50, 0.30) and Ellipse Size (ES) = (a = 0.10, 0.14, 0.18 and b = 0.05, 0.07, 0.09) 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 using Galerkin weighted residual method of finite element formulation. Results are presented in terms of streamlines, isothermal lines, local Nusselt number (Nul), average Nusselt number (Nuav) along the heated elliptical block having uniform heating, average velocity magnitude (Vav) and average fluid temperature (av). The maximum strength of the velocity magnitude and the greatest average velocity magnitude (Vav) is obtained for ES = (a = 0.10, b = 0.05), Ra = 106 and Pr = 0.71. Also the minimum average fluid temperature (av) is found 0.55 for the same ES and Ra which is mentioned above. It is expected that as the outcome of this study, an optimum combination of the governing parameters would result in higher heat transfer and the numerical results are supposed to indicate strong influence of the above mentioned parameters on the flow structure and heat transfer.