A Keller‐Box Based Numerical Simulations and Prediction of Groundwater Flow via Darcy's Law

Abstract

AbstractComprehending and measuring heat transfer (HT) mechanisms in groundwater systems is crucial for tackling diverse issues and maximizing the use of subterranean resources while reducing ecological consequences. Groundwater flow is frequently simulated and predicted using mathematical models, such as Darcy's law, which governs the movement of fluids through porous media. Thus, a theoretical analysis of HT is therefore carried out for a time‐independent 3D power‐law (PL) nanofluid (NF) flow on the stretching rotating porous disc near the stagnation region, subject to convective boundary condition, using the MHD, heat source/sink, and thermal radiation effects. A numerical simulation via the Keller Box method is performed using PDEs as the mathematical model for the suggested problem. Investigations are conducted on how several classes of pertinent characteristics affect temperature, velocity, surface drag forces, and HT rate. It has been observed that the radial velocity of the disc increases with an escalation in the permeability of the porous media whereas the azimuthal velocity, however, tends to decrease. Additionally, the rate at which heat is transferred escalates as the radiation and heat source/sink parameter's strength increases whereas it decays along the Prandtl and Biot numbers. Lastly, the present study's results can be applied to understand the thermal impact on seepage of groundwater, geothermal energy extraction, containment systems for landfills and waste, design of subsurface infrastructure, aquifer thermal energy storage, and impact assessment against climate change.