Heat transportation of 3D chemically reactive flow of Jeffrey nanofluid over a porous frame with variable thermal conductivity

Nanofluids with variable thermal conductivity can potentially bring about a transformative impact in various industries. They offer adaptive and efficient heat transfer solutions that can adjust to changing conditions and specific requirements. The insertion of nanoparticles into the base fluid significantly changes its properties, affecting thermal conductivity and viscosity. The primary objective of this paper is to analyze the heat transfer rate and three-dimensional bio-convective flow of a non-Newtonian Jeffrey nanofluid across a porous surface with variable thermal conductivity. The investigation also considers the impacts of thermophoresis, Brownian motion, and the Lorentz force. The combine impact of thermal radiation and motile microbes also incorporated in the current study. To model these phenomena, we employ the boundary layer approximation to derive a system of partial differential equations (PDEs). These PDEs are subsequently simplified into more manageable ordinary differential equations (ODEs) using the similarity variables. The numerical analysis is performed via the finite difference approach, which consists of a three-stage Lobatto scheme using MATLAB package. Additionally, important engineering parameters under different constraints-like skin friction, Nusselt number, and Sherwood number—are given in a thorough manner using tabular and graphical representations. The results of this study demonstrate significant enhancements in various aspects, including thermophoresis, Brownian motion, and thermal boundary layer thickness are demonstrated through graphically and in the form of tables. As the thermal radiation parameter increases, the temperature profile rises accordingly. This enhancement in the temperature profile is directly attributable to the higher value of the radiation parameter, which results in a physical increase in temperature. These improvements are attributed to a reduction in viscous forces and an increase in the Brownian diffusion coefficient. This research advances the understanding of non-Newtonian thermally radiative flow with variable thermal conductivity, elucidating the complex behavior of such fluids and providing valuable insights for engineering applications.