## Nomenclature  
\(\widetilde{\text{B}}_{\text{o}}\) magnetic field strength  
\(\widetilde{\text{Be}}\) Bejan number  
\(\text{b}_{\text{w}}\), \(\text{b}_{\text{s}}\) Insulated wall dimensionless length at the bottom wall  
\(\widetilde{\text{C}}_{\text{P}}\) Specific heat (kJ/kg-K)  
\(\widetilde{\text{Da}}\) Number of Darcy  
\(\widetilde{\text{Gr}}\) Grashof number  
\(\widetilde{g}\) Acceleration of gravity (m/s\({}^{2}\))  
H Enclosure height (m)  
Ha Hartmann number  
\(\widetilde{\text{k}}\) Coefficient of thermal conductivity (W/m\(\cdot\)K)  
\(\widetilde{\text{L}}_{\text{c}}\) Characteristic Length = W (m)  
\(\widetilde{\text{Nu}}\) Local Nusselt number  
\(\widetilde{\text{Nu}}\) Average Nusselt number  
\(\widetilde{\text{P}}\) Dimensionless pressure  
\(\widetilde{\text{P}}\) Pressure (Pa)  
\(\widetilde{\text{Pr}}\) Prandtl number  
\(\widetilde{q}^{ \begin{tabular}{c c} \(\stackrel{{\sim}}{{\mathrm{T}}}\) & Temperature (K) \\ \(\stackrel{{\sim}}{{\mathrm{U}}}\) & X-direction dimensionless velocity component \\ \(\stackrel{{\sim}}{{\mathrm{u}}}\) & X-direction velocity component (m/s) \\ \(\stackrel{{\sim}}{{\mathrm{V}}}\) & Y-direction dimensionless velocity component \\ \(\stackrel{{\sim}}{{\mathrm{v}}}\) & Y-direction velocity component (m/s) \\ W & enclosure Width (m) \\ \(\stackrel{{\sim}}{{\mathrm{X}}}\) & Horizontal direction dimensionless coordinate \\ \(\stackrel{{\sim}}{{\mathrm{X}}}\) & Horizontal direction in cartesian coordinate (m) \\ \(\stackrel{{\sim}}{{\mathrm{Y}}}\) & Vertical direction dimensionless coordinate \\ \(\stackrel{{\sim}}{{\mathrm{Y}}}\) & Vertical direction in cartesian coordinate (m) \\ _Greek Symbols_ & \\ \(\stackrel{{\sim}}{{\alpha}}\) & Thermal diffusivity (m\({}^{2}\) \\ \end{tabular}   
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