A thermal performance comparison of quadratic and nonlinear thermal radiation on a Darcy–Forchheimer flow of Prandtl nanofluid over a curved surface with activation energy

Abstract This exploration studies the influence of quadratic and nonlinear thermal radiative heat flux on the two‐dimensional Darcy–Forchheimer flow of Prandtl nanoliquid over a curved extending surface in a porous medium. The mathematical model incorporates both quadratic and nonlinear thermal radiative heat flux separately in the energy equation, while the concentration equation accounts for a chemical reaction term and activation energy effects. Convective heat and mass boundary constraints are applied along the curved geometry. The numerical solution is obtained using the finite difference Labotto‐III and the bvp4c method. Graphs, along with the tabular results, illustrate the consequences of various parameters on temperature and velocity profiles. Results indicate that both temperature and velocity increase with greater surface curvature. For both quadratic heat flux models, the temperature rises as the curvature parameter upsurges. The thermophoresis parameter causes the temperature to decrease in the nonlinear thermal radiative flux case and increase in the quartic thermal radiation case. Additionally, temperature profiles increase with higher thermal Biot and Prandtl numbers in both models. These findings contribute valuable insights for improving system performance in applications such as fluid dynamics, chemical engineering, and thermal management. Model validation is also included to verify the accuracy of the analysis.