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<p>This study presents a computationally efficient semi-analytical framework for analyzing steady incompressible Maxwell fluid flow with thermal radiation in an axisymmetric semi-porous channel. The governing nonlinear partial differential equations are reduced to coupled ordinary differential equations through similarity transformations. The resulting system is solved using two hybrid transform-assisted Homotopy Perturbation algorithms, namely the Shehu Transform Homotopy Perturbation Method (Shehu-HPM) and the Sumudu Transform Homotopy Perturbation Method (Sumudu-HPM). A structured computational comparison is performed to examine the solution consistency of the proposed transform-based approaches. Parametric analysis reveals that increasing the Reynolds number enhances the axial velocity due to stronger inertial effects, while larger radiation parameters reduce the velocity magnitude by thickening the thermal boundary layer. Higher Prandtl numbers restrict thermal diffusion and produce sharper temperature gradients near the heated surface, whereas larger Maxwell parameters suppress velocity due to viscoelastic relaxation effects. The accuracy of the obtained solutions is validated through comparison with previously published results for a limiting case of the governing model, showing excellent agreement. Numerical evaluation of the perturbation series solutions in MATLAB further confirms the consistency between the two formulations. Unlike conventional mesh-dependent Computational Fluid Dynamics (CFD) solvers that require spatial discretization and large algebraic systems, the proposed transform-assisted HPM framework constructs recursive perturbation series without forming global algebraic systems, thereby reducing computational complexity. The results indicate that both Shehu-HPM and Sumudu-HPM produce stable and consistent solutions, demonstrating their potential as scalable semi-analytical tools for nonlinear viscoelastic thermal-fluid modeling in computational and high-performance computing environments. These findings are relevant to engineering applications such as turbine cooling systems, porous channel heat exchangers, and polymer processing involving viscoelastic fluids.</p>

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Comparative computational analysis of shehu-HPM and sumudu-HPM for nonlinear maxwell fluid flow with thermal radiation

  • 期刊论文

  • 发表日期：

    2026年4月29日

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  • Deepak Kumar

摘要

This study presents a computationally efficient semi-analytical framework for analyzing steady incompressible Maxwell fluid flow with thermal radiation in an axisymmetric semi-porous channel. The governing nonlinear partial differential equations are reduced to coupled ordinary differential equations through similarity transformations. The resulting system is solved using two hybrid transform-assisted Homotopy Perturbation algorithms, namely the Shehu Transform Homotopy Perturbation Method (Shehu-HPM) and the Sumudu Transform Homotopy Perturbation Method (Sumudu-HPM). A structured computational comparison is performed to examine the solution consistency of the proposed transform-based approaches. Parametric analysis reveals that increasing the Reynolds number enhances the axial velocity due to stronger inertial effects, while larger radiation parameters reduce the velocity magnitude by thickening the thermal boundary layer. Higher Prandtl numbers restrict thermal diffusion and produce sharper temperature gradients near the heated surface, whereas larger Maxwell parameters suppress velocity due to viscoelastic relaxation effects. The accuracy of the obtained solutions is validated through comparison with previously published results for a limiting case of the governing model, showing excellent agreement. Numerical evaluation of the perturbation series solutions in MATLAB further confirms the consistency between the two formulations. Unlike conventional mesh-dependent Computational Fluid Dynamics (CFD) solvers that require spatial discretization and large algebraic systems, the proposed transform-assisted HPM framework constructs recursive perturbation series without forming global algebraic systems, thereby reducing computational complexity. The results indicate that both Shehu-HPM and Sumudu-HPM produce stable and consistent solutions, demonstrating their potential as scalable semi-analytical tools for nonlinear viscoelastic thermal-fluid modeling in computational and high-performance computing environments. These findings are relevant to engineering applications such as turbine cooling systems, porous channel heat exchangers, and polymer processing involving viscoelastic fluids.