Dufour and Soret features in entropy optimized Williamson fluid with nonlinear thermal radiation: Modified Darcy law analysis

• Williamson liquid model is studied. • Viscous dissipation, heat generation and Joule heating features are addressed. • Entropy generation rate is discussed. • Convective boundary conditions of heat and mass transfer are addressed. • Mixed convective flow and non-linear thermal radiation is addressed. • Arrhenius activation energy is taken. • Modified Darcy law is studied. Researchers have extensive focus in study of heat transfer. It is due to fact that heat transfer is pivotal in fields of HVAC systems, blood flow simulation, food processing, photovoltaic energy (PVT) processes, pharmaceutical industry, extrusion and injection shaping, fiber spinning, renewable energy processes, metallurgy, 3D printing processes and many others. Among these the heat transfer rate through nonlinear radiation has pivotal role in high-temperature environment applications involving combustion chambers, industrial furnaces, astrophysical flows and cryogenic technology etc. With such consideration the current analysis communicates nonlinear radiative and mixed convective flow of magnetized Williamson liquid. An exponentially stretched sheet induces liquid flow. Thermal expression comprises Ohmic heating, dissipation and nonlinear thermal radiation. Formulation for modified Darcy expression is made. Convective conditions for mass and heat transfer are discussed. Arrhenius activation energy is deliberated. Aspects of Dufour and Soret features are explored. Entropy optimized flow is discussed. Appropriate transformations yield non-linear systems. ND-Solve is utilized to compute solutions. Involved variables for entropy optimized flow, concentration, liquid flow and temperature are graphically examined. Sherwood number, drag force coefficient and thermal transport rate are analyzed through computations. An increase in temperature holds through magnetic field and Dufour number while opposite scenario observed for Prandtl number. A decrease in liquid velocity occurs for porosity and magnetic field. Soret number give rise to concentration distribution whereas reverse observed for mass transport rate. Concentration enhancement is seen through larger Biot number. Buoyancy ratio variable upsurges liquid flow.