Impact of radiation on Casson fluid in a Forchhiemer porous medium under inclined magnetic field

Abstract

The study investigates the radiation effects on the flow behavior of an electrically conductive Casson fluid in the presence of a magnetic field, coupled with a chemical process. The analysis considers velocity slip phenomena over an inclined non-linear stretching surface within a Forchheimer permeable medium. The governing partial differential equations are transformed into nonlinear ordinary differential equations using appropriate similarity transformations. These equations are then solved using the Runge–Kutta-fourth method and shooting methodology in MATLAB. Graphical representations of flow, temperature, and mass concentration are generated for various values of parameters such as magnetic quantity ( $M$ ), Casson fluid quantity ( $\beta$ ), Prandtl number ( $\mathrm{Pr}$ ), Schmidt number ( $\mathrm{Sc}$ ), chemical reaction parameter ( $\mathrm{Kc}$ ), Forchheimer parameter ( $\mathrm{Fs}$ ), and permeability parameter ( $\mathrm{Kp}$ ). Additionally, the study employs Response Surface Methodology (RSM) to analyze the influence of parameters like Casson fluid quantity ( $\beta$ ), inclined magnetic field ( $\omega$ ), and Forchheimer parameter ( $\mathrm{Fs}$ ) on the skin friction parameter ( $C_f$ ). The RSM technique, utilizing a second-order polynomial regression model, optimizes Cf around its peak, demonstrating the significance of main effects and their interactions. The numerical results indicate a significant decrease in flow velocity with increasing magnetic parameter. The statistical analysis reveals that main effects are significant at a 5% level of significance, with a high coefficient of determination ( $R^2$ ) of 99.98%. Notably, 92% of $R^2$ is attributed to main effects, emphasizing their relevance and superiority in influencing $C_f$ .