A novel numerical method for solving heat conduction problems

In this work, an efficient numerical method with a high accuracy is proposed for solving the heat conduction problems. In this method, the governing equation of heat conduction in the partial differential equation form is firstly integrated over the small volume around each node point. In the resulting integrals the spatial derivatives of the unknown temperature and heat flux disappear. Then the numerical quadrature is employed to discretize the integrals. Numerical results show that when the same amount of the computer memory and CPU-time is consumed the proposed method can achieve a high accuracy in comparison with the finite volume method (FVM). Furthermore, the proposed method is more accurate than the finite element method (FEM) and boundary element method (BEM) for multi-dimensional heat conduction problems.