Thermal transport dynamics of buoyancy-driven bio-convection flow with double diffusion effects of Jeffrey nanofluid

This study investigates Jeffrey the fluid characteristics with buoyancy forces effects across a stretching surface, by incorporating the impacts of thermal diffusion (Soret) and diffusion thermo (Dufour) in thermal and solutal transport phenomena. A theoretical framework is developed to examine the two-dimensional MHD gravity-driven flow incorporating the motility density progressive relaxation feature. The physical interpretation of rheological aspects offers insights into the complex behaviors of non-Newtonian fluids in diverse dynamic systems. The produced flow phenomenon in non-linear ordinary differential equations are derived from the governed PDEs using similarity transformations. The most effective analytical method, known as the homotopy analysis method, is used to solve the nonlinear model equations. This approach facilitates the calculation of both graphical and tabular results. The key features of the solutions are analyzed, and graphical representations are provided to illustrate the influence of various parameter values on the fluid flow and heat transfer behavior. The key physical properties, including heat transfer rate and Nusselt number, are illustrated in tabular form. The buoyancy force and curvature parameters in the fluid flow profile exhibit an inverse relationship. The temperature profile demonstrates an increasing trend with an enhancement in the Dufour number <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>u</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> and heat source parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>δ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>s</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> . This study is deeply embedded in scientific, medical, and engineering applications, including enhanced oil recovery, aircraft cooling systems, heat exchangers, geothermal energy systems, reactive transport in chemical reactors, and nanofluidic devices.