External velocity and dissipative flow of clay nanoparticles on the lubricity of drilling fluids across a vertical surface in a Darcy-Brinkman porous medium with thermal radiation

Abstract

Drilling fluids are important in the extraction of oils and gases through rocks and soil. Clay nanoparticles are essential for enhancing drilling fluid efficiency. The thermal conductivity, viscosity, and boiling point of drilling fluids increase when clay nanoparticles are incorporated, providing resistance to high temperatures and regulating fluid costs. This article illustrates the convection heat transfer in drilling nanofluid while taking into account the significant presence of clay nanoparticles in the fluid with viscous dissipation, thermal radiation, and heat source/sink. The efficient thermophysical characteristics of clay nanofluid are expressed mathematically using Maxwell-Garnett and Brinkman’s formulas. The partial differential equations (PDEs) with physical boundary conditions that control the flow phenomena are predetermined. The similarity technique is employed to transmute these PDEs into ordinary differential equations (ODEs) and then an efficient boundary value problem fourth-order (bvp4c) solver is utilized to find dual solutions. The Nusselt number and skin friction are calculated and displayed in tabular form as well as graphical form along with the velocity and temperature profiles. Multiple solutions are observed in the shrinking sheet as well as the buoyancy assisting flow. The findings demonstrate that when volume concentration increases, the Nusselt number rises noticeably. In addition, the permeability parameter expands the boundary layer thickness in the lower solution, while the contrary behavior is observed in the upper solution.