A generalized variational formulation for convective heat transfer
Abstract
The scope of this paper is to develop the basic equations for a variational formulation which can be used to solve problems related to convection and/or diffusion dominated flows. The formulation is based on the introduction of a generalized quantity defined as the heat displacement. The governing equation is expressed in terms of this quantity and a variational formulation is developed which leads to a system of equations similar in form to Lagrange's equations of mechanics. These equations can be used for obtaining approximate solutions, though they are of particular interest for application of the finite element method. As an example of the formulation two finite element models are derived for solving convectiondiffusion boundary value problems. The performance of the two models is investigated and numerical results are given for different cases of convection and diffusion with two types of boundary conditions. The applications of the developed formulations are not limited to convectiondiffusion problems but can also be applied to other types of problems such as mass transfer, hydrodynamics and wave propagation.
 Publication:

International Journal for Numerical Methods in Fluids
 Pub Date:
 December 1981
 DOI:
 10.1002/fld.1650010404
 Bibcode:
 1981IJNMF...1..305K
 Keywords:

 Calculus Of Variations;
 Computational Fluid Dynamics;
 Convective Heat Transfer;
 Flow Equations;
 Boundary Conditions;
 Boundary Value Problems;
 EulerLagrange Equation;
 Finite Element Method;
 Hydrodynamics;
 Incompressible Flow;
 Mass Transfer;
 Temperature Effects;
 Thermal Diffusion;
 Wave Propagation;
 Fluid Mechanics and Heat Transfer