## 3 Results  
Numerical simulations have been carried out for different values of (a) the Rayleigh number \(Ra_{\rm H}\) in the range between \(10^{4}\) and \(10^{6}\); (b) the dimensionless horizontal spacing between the plates \(W/H\) in the range between 0.1 and 1; and (c) the dimensionless vertical alignment of the plates \(L/H\) in the range between 0 (plates fully staggered) and 1 (plates located face to face). In all the simulations executed, the value of the Prandtl number has been set equal to 0.7, which corresponds to air. Based on the collection of computed velocity and temperature fields, the main local and overall heat transfer features will be analyzed first. Subsequently, adequate sets of correlations for the average Nusselt numbers will be constructed and discussed. A selection of typical local results at steady state, displayed in the form of isotherm contour plots, is reported in Figures 3-5 for the following combinations of the independent variables: (a) \(Ra_{\rm H}=10^{5}\), \(W/H=0.25\) and \(L/H=1\), 0.75, 0.5, 0.25 and 0; (b) \(Ra_{\rm H}=10^{5}\), \(L/H=0.5\) and \(W/H=0.25\), 0.5, 0.75 and 1; and (c) \(L/H=0.5\), \(W/H=0.25\) and \(Ra_{\rm H}=10^{4}\), \(10^{5}\), and \(10^{6}\). \begin{table}
\begin{tabular}{c c c} \hline \(Ra_{\rm H}\) & \((W/H)_{\rm opt}\)(Present Study) & \((W/H)_{\rm opt}\)[30] \\ \hline \(10^{6}\) & 0.18 & 0.17 \\ \(10^{5}\) & 0.32 & 0.31 \\ \(10^{4}\) & 0.57 & 0.52 \\ \hline \end{tabular}
\end{table} 
Table 4: Comparison between the numerical data obtained for \((W/H)_{\rm opt}\) and the values derived by [PERSON] [30] for \(Ra_{\rm H}=10^{4}-10^{6}\). Figure 2: Comparison between present numerical data and Bar-Choen and Rohsenow correlation [5] for two vertical parallel plates suspended in free air. It can be observed that when the plates are either located face to face or moderately staggered, the temperature distribution is typical for the channel flow and the thermal performance of both plates is influenced by the well-known chimney effect provided that the separation distance between the plates is neither too small to limit the fluid flow rate due to the marked friction effects and not too large to cause both plates to behave as a single plate. Of course, the chimney effect decreases drastically as the plates are more and more staggered; the effect could vanish when the plates are considerably or fully staggered. In such a case, two distinct boundary layers tend to form along the heated side of each plate. However, while the lower plate tends to actually behave as a single plate, at short separation distances the thermal performance of the upper plate is affected by the concurrence of the two opposite effects which originate from the warm plume spawned by the lower plate. In fact, the hot buoyant flow from the lower plate acts as a forced convection field wherein the upper plate is embedded, which tends to enhance the heat transfer rate at the upper plate surface; on the other hand, the upward-moving warm plume causes a decrease in the temperature difference between the upper plate and the adjacent fluid, which tends to decrease the heat transfer rate at the upper plate  
Figure 4: Isotherm contour plots for \(Ra_{\rm H}=10^{5}\), \(L/H=0.5\) and \(W/H=0.25\), 0.5, 0.75, 1 using a scale from blue \((T=0)\) to red \((T=1)\). Figure 3: Isotherm contour plots for \(Ra_{\rm H}=10^{5}\), \(W/H=0.25\) and \(L/H=1\), 0.75, 0.5, 0.25, 0 using a scale from blue \((T=0)\) to red \((T=1)\). Figure 8: \(Nu\) vs. \(W/H\) for \(L/H=0\) (fully staggered plates) using \(R_{\rm H}\) as the parameter. Figure 7: \(Nu\) vs. \(W/H\) for \(L/H=0.5\) using \(Ra_{\rm H}\) as the parameter.