The outline of the paper is as follows. Abrief on CFEM formulation for heat transfer problems is reported in Section 2. Section 3 presents the numerical examples, in which the capabilities of CFEM in heat transfer analysis are numerically illustrated. Conclusions and remarks are given in Section 4. | TAÏP CHÍ PHAÙT TRIEÅN KH&CN, TAÄP 18, SOÁ K4- 2015 A consecutive-interpolation finite element method for heat transfer analysis Nguyen Ngoc Minh1 Nguyen Thanh Nha1 Bui Quoc Tinh2 Truong Tich Thien1 1 Ho Chi Minh city University of Technology, VNU-HCM 2 Dept. of Mechanical and Environmental Informatics, Tokyo Institute of Technology, 2-12-1-W8-22, Ookayama, Meguro-ku, Tokyo, 152-8552, Japan (Manuscript Received on August 01st, 2015, Manuscript Revised August 27th, 2015) ABSTRACT: A consecutive-interpolation 4-node quadrilateral finite element (CQ4) is further extended to solve twodimensional heat transfer problems, taking the average nodal gradients as interpolation condition, resulting in highorder continuity solution without smoothing operation and without increasing the number of degrees of freedom. The implementation is straightforward and can be easily integrated into any existing FEM code. Several numerical examples are investigated to verify the accuracy and efficiency of the proposed formulation in two-dimensional heat transfer analysis. Key words: heat transfer, CFEM, conduction, convection, nodal gradients. 1. INTRO DUCTIO N Heat transfer analysis is of great importance to both engineering and daily life, as one may encounter the problem of heat transfer almost in every activities, such as heating, cooling, air convection etc. Since analytical solutions are only available for some restricted problems, in most cases one has to rely on numerical methods to perform analysis. The standard finite element method (FEM) has been successfully used for heat transfer problems. However, despite its simplicity, the FEM still has many inherent shortcomings. The FEM shape function is C0-continuous, thus the nodal gradient fields, ., the temperature gradient in case of heat transfer, is discontinuous across element boundaries. More critically, FEM suffers loss of accuracy when the mesh is heavily distorted [1]. Various alternative methods have .
