In this study, the authors proposed one-dimensional non-Fourier heat conduction model applied to phase change problem in the presence of variable internal heat generation and this has been performed by finite element Legendre wavelet Galerkin method (FELWGM). We derived the stability analysis of the non-Fourier heat conduction model in our present case. The finite difference technique has been used to change the non-Fourier heat conduction model into an initial value problem of vector-matrix form and then we applied Legendre wavelet Galerkin method for the numerical solution of the present problem. The location of moving interface is analytically obtained under the steady-state condition. The effectiveness of the proposed numerical technique is verified through the experimental value of parameters which indicate promising results. In addition, the effect of Stefan numbers, internal heat generation, and its linear coefficient on the location of moving interface are discussed in detail and represented graphically.

在这项研究中，作者提出了一维非傅立叶热传导模型，适用于存在可变内部生热的相变问题，这已通过有限元勒让德小波伽辽金方法（FELWGM）执行。在我们的案例中，我们导出了非傅立叶热传导模型的稳定性分析。利用有限差分技术将非傅立叶热传导模型转化为向量矩阵形式的初值问题，然后应用Legendre小波Galerkin方法对该问题进行数值求解。运动界面的位置是在稳态条件下解析获得的。通过参数的实验值验证了所提出的数值技术的有效性，这些参数表明结果很有希望。此外，