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In this paper, we have proposed a modified Marker-And-Cell (MAC) method toinvestigate the problem of an unsteady 2-D incompressible flow with heat andmass transfer at low, moderate, and high Reynolds numbers with no-slip and slipboundary conditions. We have used this method to solve the governing equationsalong with the boundary conditions and thereby to compute the flow variables,viz. $u$-velocity, $v$-velocity, $P$, $T$, and $C$. We have used the staggeredgrid approach of this method to discretize the governing equations of theproblem. A modified MAC algorithm was proposed and used to compute thenumerical solutions of the flow variables for Reynolds numbers $Re = 10$, 500,and 50,000 in consonance with low, moderate, and high Reynolds numbers. We havealso used appropriate Prandtl $(Pr)$ and Schmidt $(Sc)$ numbers in consistencewith relevancy of the physical problem considered. We have executed thismodified MAC algorithm with the aid of a computer program developed and run inC compiler. We have also computed numerical solutions of local Nusselt $(Nu)$and Sherwood $(Sh)$ numbers along the horizontal line through the geometriccenter at low, moderate, and high Reynolds numbers for fixed $Pr = 6.62$ and$Sc = 340$ for two grid systems at time $t = 0.0001s$. Our numerical solutionsfor u and v velocities along the vertical and horizontal line through thegeometric center of the square cavity for $Re = 100$ has been compared withbenchmark solutions available in the literature and it has been found that theyare in good agreement. The present numerical results indicate that, as we movealong the horizontal line through the geometric center of the domain, weobserved that, the heat and mass transfer decreases up to the geometric center.It, then, increases symmetrically.

Numerical solutions of an unsteady 2-D incompressible flow with heat and mass transfer at low, moderate, and high Reynolds numbers