Application of New Finite Volume Method (FVM) on Transient Heat Transferring

Abstract

The new arithmetic of Finite Volume Method (FVM) is created according to the conservation principle in evey control volume, which has great effect on the calculation accuracy of equation. In order to prove the method, the temperature field of transient heat transfer is taken as example in paper to deduced equation, and the result shows that it is same to the result of FEM which is created by variational principle with high precision, except the coefficient of time change. So the new arithmetic of FVM explains successfully the actual physical meaning of triangular element in the variation formula, and can simplify the modeling process while improving the accuracy of finite volume method. In addition, the actual problem of three-dimensional temperature field of thermal calculations is resolved by the new arithmetic of FVM and the FEM, comparing FVM results with the theoretical solution, FEM result shows that the FVM is more similar with the theory than the FEM. As a word, the he new arithmetic of FVM not only can simply the process of establish equation but also can make sure of the calculation accuracy. What’s more, it can extend widely the applied range of the FEM on the problem of temperature field, and has great application value on hard technology.

Sponsor/ National Natural Science Foundation of China (50674091) (50874111)(50844036) (50974050).