CONVECTIVE FLOW AND HEAT TRANSPORT OF CLAY NANOFLUID ACROSS A VERTICAL SURFACE IN A DARCY-BRINKMAN POROUS MEDIUM

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 used for drilling. The efficient thermophysical characteristics of clay nanofluid are expressed mathematically using Maxwell-Garnett and Brinkman's formulas. The linear PDEs with physical boundary conditions that control the flow phenomena are predetermined. The similarity technique is employed to transmute these PDEs into ODEs and then an efficient 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 case of shrinkable sheets as well as in the case of 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.