Isoparametric line and transition finite elements with temperature and temperature gradients as primary variables for two dimensional heat conduction

This paper presents isoparametric line and transition finite element formulation for two dimensional heat conduction. The element properties are derived using weak formulation of the Fourier heat conduction equation and the element approximation where nodal temperatures and the nodal temperature gradients are retained as primary variables. The formulation permits linear temperature distribution through the element thickness. Distributed heat flux as well as convective boundaries are permitted on all four faces of the elements. Furthermore, the elements can have internal heat generation as well as orthotropic material properties. The superiority of the formulation in terms of efficiency and accuracy is demonstrated. Numerical examples are presented to illustrate their applications, and a comparison is made with theoretical results.