Numerical analysis of Maxwell fluid flow with quadratic convection under inclined magnetic field employing lie symmetry and Chebyshev spectral techniques

Purpose This paper aims to examine the quadratic convection phenomenon in the presence of a uniformly inclined magnetic field using the Maxwell fluid model. The Cattaneo–Christov heat flux and non-Fickian mass flux models are used to analyze the thermal and mass characteristics. The proposed formulation further incorporates the effects of a heat source/sink and chemical reaction parameters. Design/methodology/approach The governing equations are developed using Lie symmetry transformations. The spectral relaxation (SR) technique, combined with the Chebyshev pseudo-spectral approach, is used to solve the nonlinear differential equations governing the flow problem. The present methodology is developed and implemented using MATLAB. Findings The findings are presented through visualizations such as graphs and tables. Additionally, a numerical comparison is provided to verify the accuracy of the current findings and the proposed approach. Originality/value This study presents the concurrent effects of inclined magnetohydrodynamics, quadratic convection modeling and non-Fickian/Cattaneo-Christov transport models on Maxwell fluids. This innovative framework and its Lie-symmetry-based SR solution have not been comprehensively examined before.