A robust quasi-smooth manifold element framework for transient strongly nonlinear heat conduction with temperature-dependent properties and radiative effects

In this paper, a quasi-smooth manifold element (QSME)-based nonlinear solution framework is developed for transient strongly nonlinear heat conduction problems. The basic theory and calculation approach are established, with a high-order approximation employed to improve solution accuracy. In the proposed method, temperature gradients at element nodes are adopted as computational degrees of freedom (DOFs) to effectively address various heat problems, including heat conduction, convective heat transfer, thermal radiation, and their coupled effects. Benchmark examples are first conducted to verify the stability and consistency of the method, confirming its reliability for strongly nonlinear heat conduction analysis. Subsequently, numerical examples involving complex geometries, temperature-dependent material properties, time-dependent boundary conditions, and radiative nonlinearities are presented to demonstrate the effectiveness of the method in accurately capturing temperature fields and improving computational efficiency. The results show that, compared to the finite element method (FEM), the QSME method achieves higher solution accuracy while requiring fewer computational DOFs, highlighting both efficiency and reliability. The proposed QSME method thus provides an accurate and practical numerical tool for engineering applications.