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

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 ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> </mml:math> ), Casson fluid quantity ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>β</mml:mi> </mml:mrow> </mml:math> ), Prandtl number ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Pr</mml:mi> </mml:mrow> </mml:math> ), Schmidt number ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Sc</mml:mi> </mml:mrow> </mml:math> ), chemical reaction parameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Kc</mml:mi> </mml:mrow> </mml:math> ), Forchheimer parameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Fs</mml:mi> </mml:mrow> </mml:math> ), and permeability parameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Kp</mml:mi> </mml:mrow> </mml:math> ). Additionally, the study employs Response Surface Methodology (RSM) to analyze the influence of parameters like Casson fluid quantity ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>β</mml:mi> </mml:mrow> </mml:math> ), inclined magnetic field ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>ω</mml:mi> </mml:mrow> </mml:math> ), and Forchheimer parameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>Fs</mml:mi> </mml:mrow> </mml:math> ) on the skin friction parameter ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ). 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 ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> ) of 99.98%. Notably, 92% of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> is attributed to main effects, emphasizing their relevance and superiority in influencing <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> .