An accident in a nuclear power plant involving a reactor core meltdown would result in instigation of molten corium, which is a mixture of nuclear fuel, claddings and structural components. In this paper, an enthalpy porosity model is proposed to comprehensively analyze the ablation of concrete during the Molten Corium and Concrete Interaction (MCCI) process. The developed numerical model is an extension of the enthalpy-porosity model and is termed as Corium-Concrete Enthalpy Porosity Model (CCEPM). The developed CCEPM Computational Fluid Dynamic (CFD) model can predict natural convection, melting and solidification. The developed model simplifies the complex phenomena of concrete ablation and its melting by incorporating the multi-region approach. The model was implemented in OpenFOAM, by developing a new solver which couples the buoyant-driven natural convection and conjugate heat transfer solvers. The thermal modelling and heat transfer capabilities of the developed solver were verified against experimental data sets. Additionally, the effect of various boundary conditions, concrete thermal conductivity and intensity of decay heat were analyzed to study their impact on concrete ablation. We observed significant low concrete ablation, controlled temperature and velocity field, for the water-cooled boundary condition. Accordingly, the ablation of concrete decreased by 17% just by imposing the water-cooled boundary condition. Similarly, when the thermal conductivity was decreased to 0.43 and 0.13 W/m. K, the ablation of concrete reduced by 38% and 75%, respectively. Furthermore, early cooling of molten corium to decrease decay heat was found to be an effective strategy to mitigate the concrete ablation successfully by 20%.