Coupled effects of Soret and Dufour on analyzing pollutant concentration and bio-convection under melting conditions

The current research explores the Soret and Dufour effects on the Casson liquid flow across a permeable stretching surface with bioconvection of microorganisms and magnetic field. Additionally, the influence of waste discharge concentration, chemical reaction, thermophoresis and Brownian motion (TBM), quadratic thermal radiation, and melting effect are considered to assess the mass and heat transfer attributes. Casson fluid flow across a stretching sheet has numerous applications in industrial and biomedical fields. Understanding Casson fluid dynamics helps to enhance cooling rates and product homogeneity in metallurgical operations like annealing and continuous casting. Using the similarity variables, the governing partial differential equations (PDEs) are transformed into dimensionless ordinary differential equations (ODEs). Further, the obtained ODEs are numerically solved with Runge Kutta Fehlberg’s fourth-fifth order (RKF-45) approach. The graphs illustrate the effect of numerous parameters on the fluid’s numerous profiles. The upsurge in the magnetic field and porous medium reduces the velocity profile of the liquid. The rise in the thermophoresis, Brownian motion, heat source, and Dufour parameters enhances the liquid’s temperature profile. The upsurge in the melting parameter decreases the temperature profile. The rise in the thermophoresis, pollutant external source, and Soret parameters increases the concentration profile.