A review on the applications of finite element method to heat transfer and fluid flow

Practical engineering problems in heat transfer and fluid flow involve one or more governing equations, together with some boundary conditions over a domain. The domain is often complex and non-uniform. The ability to use a mesh of finite elements to accurately discretise domain of any size and shape makes the finite element method a powerful tool to numerically analyse problems in these areas. This paper reviews the applications of finite element approaches in heat transfer and fluid flow, and highlights some recent advances in this method. These include improvements in methodology and mesh adaptivity, as well as techniques to improve the efficiency and estimate the error bounds. Some aspects closely related to the finite volume method have also been investigated.