The non-Fourier heat transfer model has gained significant attention in practical engineering applications, particularly under extreme conditions. However, solving the three-dimensional non-Fourier hyperbolic heat conduction equation remains a challenge. A method for solving the three-dimensional Maxwell-Cattaneo-Vernotte hyperbolic heat conduction equation on unstructured grids is proposed, where the total diffusion term is divided into normal diffusion term and cross diffusion term, and the temperature gradient is solved by reconstruction gradient. The convergence and accuracy of this method are verified by calculating the heat transfer process of a three-dimensional hollow cylinder, and the numerical solutions are found to be consistent with existing analytical solutions. Furthermore, the effects of relaxation time on the non-Fourier heat transfer process in three-dimensional hollow cylinder and complex ceramic part are discussed. Importantly, the method presented in this paper is not influenced by the coordinate system or the shape of the calculated region, providing a theoretical reference for solving complex three-dimensional non-Fourier heat transfer problems.

中文翻译：

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非结构网格上求解三维双曲热传导方程的通用数值方法

非傅立叶传热模型在实际工程应用中，特别是在极端条件下，受到了广泛的关注。然而，求解三维非傅里叶双曲热传导方程仍然是一个挑战。提出了一种求解非结构网格上三维Maxwell-Cattaneo-Vernotte双曲热传导方程的方法，将总扩散项分为法向扩散项和交叉扩散项，并通过重构梯度求解温度梯度。通过计算三维空心圆柱体的传热过程验证了该方法的收敛性和准确性，发现数值解与现有解析解一致。此外，还讨论了弛豫时间对三维空心圆柱体和复杂陶瓷零件非傅立叶传热过程的影响。重要的是，本文提出的方法不受坐标系或计算区域形状的影响，为解决复杂的三维非傅立叶传热问题提供了理论参考。