Finite element simulation of transient natural convection of low‐Prandtl‐number fluids in heated cavity

Abstract

The aim of the present investigation was to study numerically the transient of thermal convection in a square cavity filled with low‐Prandtl‐number fluids. The flow is driven by the horizontal temperature gradient between the vertical walls maintained at different temperatures. Two‐dimensional equations of conservation and energy are solved using a finite element method and a fractional step time. The discrete equations systems are solved in the lap of each element‐mesh with the aim of verifying the Boussinesq hypothesis locally. To compare our results with the earlier predictions, we have chosen the fluids for Prandtl‐numbers 0.001, 0.005 and 0.01 and with Grashof numbers up to 1 × 10⁷. To predict the steady state solutions with an oscillary transient period, the results are reduced in terms of the time series average Nusselt‐number at the vertical walls, the velocity at the center of the cavity and near right boundary. In addition, the isotherms and the velocity field are produced with the aim of showing the main circulation and particularly the weak circulations at the corners of the cavity.

Citation

Sammouda, H., Belghith, A. and Surry, C. (1999), "Finite element simulation of transient natural convection of low‐Prandtl‐number fluids in heated cavity", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 9 No. 5, pp. 612-624. https://doi.org/10.1108/09615539910276124