Numerical simulation is performed to explore the convective heat transfer characteristics of Fe3O4-H2O nanofluid contained in a right-angle triangular cavity considering three types of thermal boundary conditions at the bottom wall. No heat is allowed to escape through the insulated vertical wall, whereas the inclined wall is kept colder than the bottom one. A sloping magnetic field whose strength is unvarying acts upon the cavity. The physical model is converted to the mathematical form through coupled highly nonlinear partial differential equations. These equations are then transformed into the non-dimensional form with the help of a group of transformations of variables. A very robust pde solver COMSOL Multiphysics that uses the finite element method (FEM) of Galerkin type is applied to carry out the numerical calculation. Heat transfer escalation through middling Nusselt number at the lowermost cavity wall is explored for diverse model parameters and thermal circumstances. The outcomes lead us to conclude that a higher degree of heat transfer is accomplished by reducing the dimension of nanoparticles and aggregating the buoyancy force through the Rayleigh number. It is highest when there is a magnetic field leaning angle of 900 and the lowermost wall is heated homogenously.