## Materials and Methods
### Computational Procedure  
The system of the governing equations defined by Equations (1)-(3), in combination with the boundary and initial conditions stated earlier, is solved through a control-volume formulation of the finite-difference method using an in-house developed computer code. The pressure-velocity coupling is handled using the SIMPLE-C algorithm introduced by [PERSON] and [PERSON] (2016), which is essentially a more implicit variant of the SIMPLE algorithm developed by [PERSON] and [PERSON] (2017). The convective terms are approximated through the QUICK discretization scheme proposed by [PERSON] (2018), whereas a second-order backward scheme is applied for time integration. Time discretization is chosen uniformly. Starting from the assigned initial fields of the dependent variables, at each time-step the system of the discretized algebraic governing equations is solved iteratively by the method of a line-by-line application of the [PERSON] algorithm. A standard under-relaxation technique is enforced in all steps of the computational procedure to ensure an adequate convergence. Within each time-step, the spatial numerical solution of the velocity and temperature fields is considered to be converged when the maximum absolute value of the mass source and the relative changes of the dependent variables at any grid-node between two consecutive iterations are smaller than the pre-specified values of \(10^{-6}\) and \(10^{-7}\), respectively. Time-integration is stopped once steady state is reached. This means that the simulation procedure ends when the relative changes of the time-derivatives of the dependent variables at any grid-node between two consecutive time-steps is smaller than the pre-set value of \(10^{-8}\). After convergence of the velocity and temperature fields is satisfactorily attained, the pair of average Nusselt numbers for the lower plate, \(Nu_{\text{L}}\), and for the upper plate, \(Nu_{\text{U}}\), are calculated as follows:  
\[Nu_{\text{L}} =\int_{-\frac{H}{2}}^{+\frac{H}{2}}-\frac{\partial T}{\partial X} \bigg{|}_{h}dY \tag{5}\] \[Nu_{\text{U}} =\int_{-\frac{H}{2}}^{+\frac{H}{2}}-\frac{\partial T}{\partial X} \bigg{|}_{h}dY \tag{6}\]  
where subscript \(h\) denotes the heated side of each plate. The temperature gradient is evaluated by a second-order temperature profile embracing the wall-node and the two adjacent fluid-nodes, whereas the integral is calculated numerically by means of the trapezoidal rule. Additionally, the average Nusselt number of the whole system, which is identified as \(Nu\), is calculated as the arithmetic mean of the average Nusselt numbers of both plates and is defined as follows. \[Nu=\frac{Nu_{\text{L}}+Nu_{\text{U}}}{2} \tag{7}\]  
Numerical tests on the dependence of the results obtained on the mesh spacing and time stepping, as well as on the extent of the computational domain, have been methodically performed for several combinations of the independent variables, namely \(Ra_{\text{H}}\), \(W/H\) and \(L/H\). Accordingly, the grid-spacings and time-steps used for computations in combination with assigned extents of the integration domain are chosen in such a manner that further grid and time stepping refinements or extensions of the integration domain do not produce noticeable modifications either in the flow field or in the heat transfer rates, with percentage changes smaller than the pre-established accuracy value of 1%. The typical number of nodal points used for simulations lies in the ranges between \(100\times 100\) and \(200\times 200\), whilst the horizontal and vertical extents of the whole integration domain span between 5 and 10 times the plates length \(H\). Moreover, typical dimensionless time-steps used for simulations lie in the range between \(10^{-4}\) and \(10^{-5}\). Selected results of the grid-size and time-stepping sensitivity analysis are presented in Tables 1 and 2. Finally, with the scope of this study including the validation of both the numerical code and the discretization grid scheme, three different tests have been carried out.