Based on various applications of the natural convection phenomena especially, in physical applications within the framework of nanofluid, the current investigation presents natural convection flow and the features of entropy generation for \(Cu-Ag-A{L}_{2}{O}_{3}/{H}_{2}O\) ternary-hybrid nanofluid (THNF) within an oblique square cavity. The enclosure is equipped with a vertical cold wire placed in the center, the left and right edges of the cavity are at high temperature, and the top and down ones are adiabatic. Furthermore, the cavity is subjected to an inclined magnetic field. The mathematical problem is tackled in the form of dimensionless coupled partial differential equations using the finite volume method (FVM). For the simulations, a MATLAB code has been developed. The main effective parameters are the Rayleigh number \(Ra\) , the Hartmann number \(Ha\) , the volume fraction of the ternary-hybrid nanoparticle (THNP) \(\phi\) , the cavity inclination angle \(\omega\) , and magnetic field angle \(\gamma\) . The results are illustrated in the form of isotherm contours, streamlines, entropy generation (isentropic), velocity fields, the average Nusselt number and the global Bejan number. The outcomes demonstrate that the highest heat transfer occurs in the case of the non-oblique cavity, where the Nusselt number increases by \(320.502\text{\%}\) as the Rayleigh number rises. The minimum entropy generation is indicated at an inclined cavity angle of \({90}^{\circ }\) , accompanied by a reduction of about \(35.11\text{\%}\) in the average Nusselt number as \(Ha\) increases from \(0\) to \(100\) . Furthermore, the utilization of THNF with a volume concentration ratio of \(75:15:15\) enhances the heat transfer rate by \(12.367\text{\%}\) .
