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<p>A self-similar framework is developed for unsteady boundary-layer flow and nonlinear radiative heat transfer over a deformable stretching cylinder with uniform transpiration, velocity/thermal slip, and full T<sup>4</sup> Rosseland radiation. The governing PDEs are reduced to coupled similarity ODEs solved by two independent routes, Akbari–Ganji Method (AGM) with Chebyshev collocation and finite-element method (FEM) with quadratic Lagrange elements, cross-validated against a boundary-value reference within 0.5% for skin friction and 1.2% for Nusselt number. AGM achieves 12–16× computational speedup over FEM. Suction (S = 0.7) increases skin friction by a factor of 3.1 relative to blowing and raises Nusselt number by 74%. Nonlinear radiation (<InlineEquation ID="IEq1"><EquationSource Format="TEX">\(\:{R}_{d}\)</EquationSource></InlineEquation> up to 3.0, <InlineEquation ID="IEq2"><EquationSource Format="TEX">\(\:{\theta\:}_{w}\)</EquationSource></InlineEquation> up to 2.0) reduces the convective wall temperature gradient due to enhanced effective radiative conductivity, while the total heat-transfer index, including the radiative contribution, increases within the studied parameter range. Velocity slip (λ = 0.5) reduces skin friction by 41%, while thermal slip produces a modest 5% Nusselt reduction. Unsteadiness (A up to 1.0) amplifies wall shear by 61% and heat transfer by 107%, with strong suction synergy. Within 0.5 ≤ Pr ≤ 50, a fitted empirical relationship between heat transfer and the Prandtl number is observed, with a problem-specific exponent of approximately 0.55; this exponent should not be interpreted as a universal scaling law. Radiation modifies the energy equation and couples with conductive and convective transport, although its influence can be approximated by a multiplicative correction factor within the studied parameter range. Compact correlations achieve R<sup>2</sup> = 0.9996 (MAPE = 0.38%) for skin friction and R<sup>2</sup> = 0.991 (MAPE = 5.36%) for Nusselt number, providing design guidance for high-temperature fiber drawing, hot rolling, and thermal management.</p>

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Unsteady boundary-layer flow and radiative heat transfer over a deformable stretching cylinder with transpiration and slip: cross-validated Akbari-Ganji and finite-element solutions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月18日

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  • Hyder Hassan Abd Balla,
  • Sokhibjan Muminov,
  • Sarvar Iskandarov,
  • Yusufbay Yusupov,
  • Saodatkhon Ibragimova,
  • Otabek Djurabaev,
  • Fohagui Fodoup Cyrille Vinceslas,
  • Kohole Yemeli Wenceslas

摘要

A self-similar framework is developed for unsteady boundary-layer flow and nonlinear radiative heat transfer over a deformable stretching cylinder with uniform transpiration, velocity/thermal slip, and full T4 Rosseland radiation. The governing PDEs are reduced to coupled similarity ODEs solved by two independent routes, Akbari–Ganji Method (AGM) with Chebyshev collocation and finite-element method (FEM) with quadratic Lagrange elements, cross-validated against a boundary-value reference within 0.5% for skin friction and 1.2% for Nusselt number. AGM achieves 12–16× computational speedup over FEM. Suction (S = 0.7) increases skin friction by a factor of 3.1 relative to blowing and raises Nusselt number by 74%. Nonlinear radiation (\(\:{R}_{d}\) up to 3.0, \(\:{\theta\:}_{w}\) up to 2.0) reduces the convective wall temperature gradient due to enhanced effective radiative conductivity, while the total heat-transfer index, including the radiative contribution, increases within the studied parameter range. Velocity slip (λ = 0.5) reduces skin friction by 41%, while thermal slip produces a modest 5% Nusselt reduction. Unsteadiness (A up to 1.0) amplifies wall shear by 61% and heat transfer by 107%, with strong suction synergy. Within 0.5 ≤ Pr ≤ 50, a fitted empirical relationship between heat transfer and the Prandtl number is observed, with a problem-specific exponent of approximately 0.55; this exponent should not be interpreted as a universal scaling law. Radiation modifies the energy equation and couples with conductive and convective transport, although its influence can be approximated by a multiplicative correction factor within the studied parameter range. Compact correlations achieve R2 = 0.9996 (MAPE = 0.38%) for skin friction and R2 = 0.991 (MAPE = 5.36%) for Nusselt number, providing design guidance for high-temperature fiber drawing, hot rolling, and thermal management.