Abstract
Natural convection of water near its density maximum in the presence of magnetic field in a cavity with temperature dependent properties is studied numerically. The viscosity and thermal conductivity of the water is varied with reference temperature and calculated by cubic polynomial. The finite volume method is used to solve the governing equations. The results are presented graphically in the form of streamlines, isotherms and velocity vectors and are discussed for various combinations of reference temperature parameter, Rayleigh number, density inversion parameter and Hartmann number. It is observed that flow and temperature field are affected significantly by changing the reference temperature parameter for temperature dependent thermal conductivity and both temperature dependent viscosity and thermal conductivity cases. There is no significant effect on fluid flow and temperature distributions for temperature dependent viscosity case when changing the values of reference temperature parameter. The average heat transfer rate considering temperature-dependent viscosity are higher than considering temperature-dependent thermal conductivity and both temperature-dependent viscosity and thermal conductivity. The average Nusselt number decreases with an increase of Hartmann number. It is observed that the density inversion of water leaves strong effects on fluid flow and heat transfer due to the formation of bi-cellular structure. The heat transfer rate behaves non-linearly with density inversion parameter. The direction of external magnetic field also affect the fluid flow and heat transfer. (C) 2007 Elsevier Masson SAS. All rights reserved.