The numerical computations for the magnetohydrodynamic (MHD) mixed convective flow of a non-Newtonian Casson nanofluid (Cu/H$_2$O) within an open-ended cavity formed by earthquake-induced faults are analyzed, aiming to investigate the fluid dynamics and convection processes of geothermal systems. Such cavities, typically found in energy reservoirs, are primarily caused by tensional fault zones formed due to the accumulated energy from the disintegration of radioactive materials. These cavities play a crucial role in energy transmission, particularly in the form of heat. The focus of this paper is on the laminar, steady, and incompressible fluid flow. An inclined magnetic field is applied with an angle of inclination $z=30^{\circ}$. Additionally, a heated material with two vertical corrugated walls is placed at the center of the cavity. The governing nonlinear partial differential equations (PDEs) are transformed into the equations with a non-dimensional form. The Galerkin finite element method (FEM) is implemented to solve the dimensionless equations. The impacts of key variables, including the Reynolds number $Re$, the volume fraction $(0.01\leqslant \phi_{\rm p}\leqslant 0.05)$, the Hartmann number $Ha$, and the Casson parameter $(0.5\leqslant \gamma\leqslant 1.0)$, on the velocity and temperature distributions are studied. The analysis of the fluid flow and the heat transfer rate is conducted. The results indicate that the velocity increases as the volume fraction and the Reynolds number increase. Similarly, the heat transfer rate rises with the Reynolds number and the volume fraction, while decreases with the higher Hartmann number. The Nusselt number increases with the volume fraction and the Reynolds number but decreases with the Hartmann number.