Numerical investigation of the first bifurcation for natural convection of fluids enclosed in a 2D square cavity with Pr lower than 1.0

This article presents a numerical study of the effect of the Prandtl number on the first bifurcation of natural convection for fluids enclosed in a 2D square cavity subject to a horizontal temperature gradient. The natural convection equations are solved using a second-order Euler–Taylor–Galerkin (ETG) finite element method of fractional steps. Influence of the mesh resolution on the numerical investigation is analyzed first on ten sets of uniform square element meshes while the Rayleigh numbers are 104 and 105 keeping Pr = 0.71. Variations of the averaged Nusselt number and its relative error in the results provided by the benchmark computation of Davis with the grids are used to find the role of mesh resolution. As for Ra = 104 and 105, NuAVER increases first with the increase in the number of grids used. And for each Ra, NuAVER tends to be independent of the number of elements when it is higher than 80 × 80. Grids (101 × 101) are then used in the study to capture the first bifurcation of natural convection. The bisection method and the flow patterns are utilized to estimate the critical Rayleigh number for 11 different fluids for which Pr ⩽ 1.0. It can be deduced from the results presented that RaCr decreases with the increase in Pr. Variation of RaCr with Pr is also fitted to estimate RaCr for any fluids for which Pr ⩽ 1.0 directly. It is also observed that the global flow cores are inclined for each Pr and that the inclination degree increases in anticlockwise direction with Pr.