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

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 4 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, \(\:{θ\:}w\) 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 R 2 = 0.9996 (MAPE = 0.38%) for skin friction and R 2 = 0.991 (MAPE = 5.36%) for Nusselt number, providing design guidance for high-temperature fiber drawing, hot rolling, and thermal management.