Stream Function-Vorticity Formulation Applied in the Conjugated Heat Problem Using the FEM with Unstructured Mesh

Abstract

Conjugated heat transfer problems have an extensive number of applications because a lot of times it is neces- sary to understand how heat convection in a fluid influences the temperature in solid regions. The stream function-vorticity formulation is a useful alternative to solving the Navier-Stokes equations in two dimensional domain. One of its major difficulties is the lack of boundary conditions for vorticity, and several schemes are proposed to satisfy such a condition. In this paper we propose a finite element scheme for solving the couple problem of the stream function-vorticity formu- lation using linear triangle elements. A possible application of the method is also demonstrated using the calculated velocity field from the formulation in the heat transport equation to study the temperature distribution in a incompressible single-phase fluid medium as a conjugate heat transfer problem. The results obtained were satisfactory when using low Reynolds number.