We present the Onsager–Stefan–Maxwell thermodiffusion equations, which account for Soret and Dufour effects in multicomponent fluids. Unlike transport laws derived from kinetic theory, this framework preserves structure of isothermal Stefan–Maxwell separating thermodynamic forces that drive diffusion force drives heat flow. The transport-coefficient matrix is symmetric, second law thermodynamic...

This article describes the effect of thermal radiation on the thin film nanofluid flow of a Williamson fluid over an unsteady stretching surface with variable fluid properties. The basic governing equations of continuity, momentum, energy, and concentration are incorporated. The effect of thermal radiation and viscous dissipation terms are included in the energy equation. The energy and concent...

This study focused on free convective MHD Casson fluid flow past a permeable vertical plate with microorganisms and Soret-Dufour mechanisms. The physical model is governed by system of partial differential equations (PDEs). set PDEs were overhaul into nonlinear ordinary equation considering acceptable similarity variable. spectral relaxation method (SRM) was utilized to obtain solution the equa...

The aim of this article is to investigate the effect mass and heat transfer on unsteady squeeze flow viscous fluid under influence variable magnetic field. observed in a rotating channel. equations momentum conservation are coupled with field energy equations. By using some appropriate similarity transformations, partial differential obtained then converted into system ordinary solved by Homoto...