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In this study, the effects of mixed convective, thermally radiating, magnetized flow of a Williamson-Casson fluid (WCF) over an exponentially shrinking surface in a porous material are investigated. The influences of heat generation-absorption, Joule heating, and a unique Cattaneo-Christov (CC) heat flux model are examined, deviating from traditional research approaches. To analyze the fluid flow, nonlinear partial differential equations (PDEs) governing the system are transformed into ordinary differential equations (ODEs) through similarity transformations and nondimensional variables. The resulting ODEs are solved using the BVP4C technique, yielding dual solutions for a range of the parameterStability analysis is performed to assess the robustness and reliability of the solutions. Comparisons between the first and second solutions reveal reasonable agreement at specific values offor surface drag force and Nusselt number, validating the existence of dual solutions. The study further investigates the velocity profilesin the Casson model as the Grashof number  Gr  varies. Fluid velocity decreases, while heat and mass transport velocities increase with higher  Gr  values. The impact of  Gr  on all three velocity profiles of Williamson fluid is explored, showing a decrease in fluid velocity and an increase in temperature transport as  Gr  increases.

numerical heat transfer, part a: applications

Dual solutions of Williamson-Casson fluid over a heated exponentially shrinking surface with stability analysis: A novel Catteneo-Christov heat flux model combination