Natural convection inside a thin plate in a rectangular cabinet containing \(Cu-Al_2 O_3\) water hybrid nanofluids is carried out in the present study. The thin plate is positioned both vertically and horizontally at various locations within the cavity. An isothermal thermal boundary conditions was imposed to the plate. The upper and lower boundaries are maintained under adiabatic thermal boundary conditions, while the lateral boundaries are designated as an isothermal cold wall. Employing the FVM, the dimensionless governing equations alongside the corresponding boundary conditions are solved through numerical techniques. The power law scheme is implemented to address the convective terms effectively. The resultant system of linear equations is resolved utilizing the TDMA algorithm. The characteristics of flow and heat transfer are examined across various parameters, including Rayleigh number \((Ra = 10^6\) and \(10^7)\) , Hartmann number \((Ha = 0-100)\) , concentration of nanoparticles \((\phi = 0.02-0.06)\) , and orientation of the magnetic field \((\gamma =0^o - 135^o)\) . It is observed that the fluid flow pattern exhibits greater intensity at elevated Ra and diminished Ha. The rate of heat transfer (HT) is diminished with an increase in Ha. For both horizontal and vertical plates, the magnetic inclination angle \(\gamma = 90^o\) usually produces the best HT improvement; however, extreme inclinations \(\gamma = 135^o\) cause a number of intricate flow phenomena, which results in an insufficient HT rate. An escalation in the concentration of composite nanoparticles and Ra significantly enhances the Nusselt number. Composite nanofluid gives better HT performance than the single nanofluid. The average increase in Nu for \(Cu-Al_2 O_3\) water hybrid nanofluid is 5.63% when compared to the cavity filled with pure water.
