Numerical analysis of heat transfer in a mixed-convection flow of drilling nanofluid embedded in a Darcy-Brinkman permeable medium with variables viscosity and thermal conductivity

This study investigates anomalous heat transfer in a radiative mixed convection flow of water-based drilling nanofluid (NF) immersed in a Darcy–Brinkman permeable medium. Since the underground fluids are exposed to anomalous temperatures, the extraction of gases and petroleum from rocks and soil requires the drilling fluids to have temperature-dependent viscosity and thermal conductivity. The variable thermal conductivity and viscosity of the drilling fluid provide resistance to high temperatures and pressure. Therefore, the objective of this study was to investigate anomalous heat transfer subject to frictional heating, melting heat, thermal radiation, and magnetic fields. Using the Brinkman–Maxwell–Garnett model, the effective thermophysical properties of drilling NF are considered. The computational performance of drilling NF is investigated using the Adams–Bashforth predictor and corrector approach. The findings suggest that the volume percentage and free convection parameter increases the Nusselt number considerably. The thickness of the boundary layer is increased by a higher permeability parameter, whereas the Darcy number exhibits the opposite tendency. Fluid velocity and skin friction are reduced by the magnetic number, whereas the temperature profile is raised by increases in the radiation parameter and the volume percentage of nanoparticles. The rate of heat transmission becomes significant in the scenario of variable characteristics.