Solution of the unsteadystate heat conduction problem for a twodimensional region with a moving boundary
Abstract
With the use of the convolutiontype functional a variational description is given for the process of unsteadystate heat conduction with the firstkind boundary conditions for a twodimensional region whose boundary moves in time according to the familiar arbitrary law. Based on the GalerkinKantorovich method, a corresponding system of Euler equations is written the solution of which (numerical or analytical) is required to determine the temperature field in each specific case. As an example, the first and second analytic approximations to the solution of the above problem are obtained for the case of the deformation of a prism having initially a circular crosssection.
 Publication:

International Journal of Heat and Mass Transfer
 Pub Date:
 July 1987
 DOI:
 10.1016/00179310(87)901591
 Bibcode:
 1987IJHMT..30.1259T
 Keywords:

 Boundary Layer Flow;
 Computational Fluid Dynamics;
 Conductive Heat Transfer;
 Time Dependence;
 Two Dimensional Flow;
 Unsteady State;
 Approximation;
 Boundary Conditions;
 Euler Equations Of Motion;
 Galerkin Method;
 Temperature Distribution;
 Variational Principles;
 Fluid Mechanics and Heat Transfer