The importance of thermo-solutal behavior on the flow of Casson fluids is crucial in different biomedical and polymer processing applications, as control over heat transport phenomena is essential. Specifically, Casson fluids are widely used in modelling of blood flow and polymeric fluid behavior for the coating processes. The consideration of Soret combined with Dufour, along with variable magnetization and heat source, influences the flow phenomena. The flow past through a radial expanding surface embedded within a porous matrix enriches the flow properties. The mathematical model presenting the flow behavior with the inclusion of aforementioned properties forms a nonlinear model and then transformed into a dimensionless form with the utility of similarity rules. One of the novel approaches, such as physics informed neural network (PINN), is employed to analyze the flow profiles. The flow phenomena of the Casson rheological model are reformulated into a residual loss function to be minimized utilizing neural network training. PINN integrates physical laws directly into the loss function without using a mess solution. The observation reveals that with an increasing Casson parameter, the fluid velocity is suppressed, which is crucial in modeling hyperthermia treatment.
Yadav et al. (Wed,) studied this question.