Analyzing Soret and Dufour Effects on MHD Variable Viscosity Casson Nanofluid Flow Past a Stretching Sheet With Heat Source/Sink

This study explores the impact of Soret and Dufour effects on an magnetohydrodynamics (MHD) variable‐viscosity Casson nanofluid over a stretching sheet with heat generation and absorption. The Buongiorno model is employed to incorporate nanoparticle properties such as Brownian motion and thermophoresis. The governing equations are transformed into first‐order ordinary differential equations, and an analytical solution is obtained using the homotopy analysis method with the BVPh2.0 package in Mathematica. Numerical results reveal that velocity profiles increase with the Soret and Dufour effects, variable viscosity, Casson characteristics, and heat generation and absorption but decrease with the Lewis number and Forchheimer coefficient. Temperature profiles rise with the Dufour number, heat generation and absorption, and variable viscosity, while they decline with the Se number, Casson factor, and stretching parameter. Similarly, concentration profiles exhibit opposing trends, increasing with the Forchheimer coefficient, Soret number, and Casson factor while decreasing with the Dufour number, variable viscosity, and heat generation and absorption. The results highlight significant parameter‐driven variations in transport properties. An increase in the Casson parameter reduces the skin friction coefficient by 40.95%, enhances heat transfer by 15.63%, and decreases mass transfer by 6.72%, indicating a shift toward Newtonian‐like behavior. The Darcy number lowers skin friction by 18.44% and boosts heat transfer by 23.03%, confirming improved permeability‐driven fluid motion. The magnetic parameter slightly increases skin friction by 0.40%, while the Prandtl number enhances heat transfer by 18.36%. The variable viscosity parameter plays a critical role, reducing skin friction by 28.92%, decreasing heat transfer by 34.32%, and increasing mass transfer by 24.86%. Additionally, the Eckert number significantly reduces heat transfer due to viscous dissipation, whereas the radiation parameter enhances both heat and mass transfer. These findings provide valuable insights into fluid transport mechanisms, with applications in industrial and biomedical systems requiring optimized thermal and mass transport. A comparative analysis with existing literature validates the robustness of the results.