  Numerical simulations for 2-D unsteady, incompressible flow with heat
transfer in a four-sided lid-driven rectangular domain are reported in the
present study. For the four-sided lid-driven rectangular domain, the lower wall
is moved to the left, the upper wall is moved to the right, while the right
wall is moved upwards and the left wall is moved downwards. All four walls move
with equal speed. Different constant temperatures are applied to the left and
right moving walls, and thermal insulation is applied to the upper and bottom
moving walls. The governing equations are discretized using the QUICK scheme of
finite volume methods. The SIMPLE algorithm is adopted to compute the numerical
solutions of the flow variables, $u$-velocity, $v$-velocity, $P$, and $\theta$
as well as local and average Nusselt numbers for $50 \le Re \le 1500$ and
$Pr=6.63$. Due to the force generated by moving fluid, the direction of moving
walls and the Reynolds number affect fluid flow in the rectangular domain in
addition, at different Reynolds numbers along the cold wall of the domain, the
variation in average and local Nusselt numbers reveals that overall heat
transfer increases isotherms showed that as Reynolds numbers increase, the
horizontal temperature gradient near the vertical walls decreases, because of
which heat transfer decreases.decreases.
