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.
Highlights
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
We have successfully extended the consecutive-interpolation finite element method (CFEM) to solve the heat transfer problem in 2D
Straightforward and easy to be implemented into any existing FEM code
Summary
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. The FEM shape function is C0-continuous, the nodal gradient fields, i.e., the temperature gradient in case of heat transfer, is discontinuous across element boundaries. Approach into Q4 element described in an irregular finite element mesh, in which the sets Si, Sj, Sk, Sm contain all the neighboring elements that share the node i, j, k, m, respectively It indicates that the supporting nodes for the point of interest x include all the nodes in the element sets Si, Sj, Sk, Sm. as shown, the support domain in CFEM is in any cases larger than that of the standard FEM, since it includes the nodes of the element in interest and the nodes of the adjacent elements. Comparison of (a) one-dimensional shape functions and (b) their first-order derivatives between CFEM and FEM (b)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
