The numerical analysis of unsteady combined convective heat transfer properties of kerosene-alumina nanofluid restricted in an L-shaped porous lid-driven cavity has been examined in this research. Fluid flow governing equations and conjugate heat transport along with the corresponding boundary conditions are used to express the physical problem mathematically. Firstly, boundary conditions and governing equations are transformed into non-dimensional forms using a series of appropriate transformations. Later on, the transformed non-dimensional equations are solved by utilizing the Finite Element Method based on the Galerkin residuals. A comparison with earlier available work is shown and turned out to be a great agreement. Numerical solutions are acquired in a wide variety of governing variables. The governing variables in this study are the Darcy number (Da), Reynolds number (Re), Richardson number (Ri), solid volume fraction (δ), time parameter (τ), etc. The numerical findings of flow and thermal fields are represented graphically in respect of isotherms, streamlines, and average Nusselt number at the hot surface of the cavity. The Re and Da are found to have an extensive impact on the isotherms and streamlines in the cavity, and also in determining the average heat transmission rate.