Modeling magnetized second-grade fluid through porous media under local thermal non-equilibrium and catalytic effects

This study investigates the magnetized second-grade fluid flow through a porous medium under the influence of a thermal non-equilibrium model integrated with surface-catalyzed reactions. The local thermal non-equilibrium approach involved separate temperature equations for solid and liquid phases. The concentration profile incorporates homogeneous–heterogeneous reactions influenced by surface catalysis, which enhances reaction rates and reduces activation energy, improving efficiency. The mathematical modelling is done in terms of PDEs and is transformed into ordinary differential equations (ODEs) via similarity transformations, and is computed numerically using MATLAB’s bvp4c solver. Graphs and tables illustrated the consequences of various parameters on velocity, temperature, and concentration distributions. Results revealed that increasing the interface heat transfer parameter affects heat transfer in the liquid phase while enhancing it in the solid phase. Additionally, higher porosity coefficients improve the temperature distribution in the liquid phase. The heat transmission rate for the liquid phase is ( N u f = 1.37116 ) when the porosity coefficient is e o = 1 , while for the solid phase heat transmission rate is ( N u s = 0.879044 ) . The model’s accuracy was validated by comparing limiting cases with existing literature, showing excellent agreement.