Stationary bifurcation and heatline visualisation in a rectangular cavity with anti –parallel wall motions

The effect of aspect ratio (τ) on stationary bifurcations corresponding to mixed convective flow in a four – sided lid – driven rectangular porous cavity is studied numerically. Two different τ values (1.96 and 0.5) are considered, so that the length to breadth or breadth to length ratios are restricted to half in configuration and the corresponding surface area change is exposed to direct heating. A modification of the finite volume based ISTEC – N algorithm is introduced in the present study. These modifications are employed in the under–relaxed discretised equations without any changes in the explicit correction loops on collocated grids. Implementation of the ‘eigs’ function in Matlab software is discussed to detect the stationary bifurcation points while tracking the eigenvalues. The bifurcations are studied using both non-regularized and regularized boundary conditions. These bifurcations points are calculated at fixed values of the Grashof number, Gr, to detect critical Reynolds number, $$\:{Re}_{c}$$ . The influence of τ on the isotherms, heatlines and the average Nusselt number at the hot wall, $$\:\overline{Nu}$$ are elucidated. It is observed that, for both $$\:\tau\:$$ = 1.96 and 0.5, $$\:\overline{Nu}$$ increases with increasing Reynolds number. As Gr increases, $$\:\overline{Nu}$$ declines for $$\tau$$ = 0.5 and increases for $$\tau$$ = 1.96. Furthermore, $$\:{Re}_{c}\:$$ increases on changing $$\tau$$ from 1.96 to 0.5, with increased shift in $$\:{Re}_{c}$$ on the implementation of regularized boundary conditions.