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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 85, 2024 - Issue 1
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Research Articles

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

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Pages 114-136 | Received 15 May 2023, Accepted 28 Jul 2023, Published online: 13 Sep 2023
 

Abstract

Background

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.

Methods

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 parameter Sχ=3.04.5. Stability analysis is performed to assess the robustness and reliability of the solutions.

Findings

Comparisons between the first and second solutions reveal reasonable agreement at specific values of Sχ for surface drag force and Nusselt number, validating the existence of dual solutions. The study further investigates the velocity profiles (f(η),θ(η),φ(η)) in 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.

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