Natural convection in enclosure with discrete isothermal heating from below

Abstract

Natural convection in two-dimensional rectangular enclosure is studied numerically using a finite element method. In the present study, top wall is considered adiabatic, two vertical walls are maintained at constant low temperature, the bottom wall is maintained at constant high temperature and the non-heated parts of the bottom wall are considered adiabatic. The aim of this work is to demonstrate the capabilities of this numerical methodology for handling such problems. The pressure-velocity form of the Navier-Stokes equations and energy equation are used to represent the mass, momentum, and energy conservations of the fluid medium in the enclosure. The finite element formulations of the dimensionless governing equations with the associated boundary conditions are solved by a nonlinear coupled solution algorithm using six-noded triangular element discretization scheme for all the field variables. The Grashof number is varied from 103 to 106 and Prandtl number is taken as 0.71. This study has reported the effect of various aspect ratios, ranging from 0.5 to 1, and inclination angles of the enclosure from 0° to 30° on the thermo-fluid characteristics. Results are presented in the form of streamline and isotherm plots as well as the variation of the Nusselt number at the heat source surface under different conditions. Keywords: Natural convection, rectangular enclosure, aspect ratio, finite element method, Nusselt number. DOI: 10.3329/jname.v4i1.912 Journal of Naval Architecture and Marine Engineering 4(2007) 1-13