Analytical study of heat conduction with phase transition
Abstract
An integral approach is proposed for the approximate solution of transient heat conduction problems involving moving boundary and phase changes such as heat conduction in a melting solid. In the application to heat conduction calculations, the method can be viewed as a refinement of Goodman's (1964) heatbalance integral method which is based on the classical KarmanPohlhausen momentum integral technique in the boundary layer theory. The basic idea of the proposed method lies in the use of the first integration of the heat equation as the expression for the boundary heat flux. A variant of the calculation scheme is presented in which use is made of the first integration equation and a thetamoment equation generated by first multiplying the original heat equation by the temperature and then integrating in the direction of heat diffusion. Idealized yet representative models of melting and ablation are treated.
 Publication:

AIAA, Aerospace Sciences Meeting
 Pub Date:
 January 1976
 Bibcode:
 1976aiaa.meetQ....Z
 Keywords:

 Ablation;
 Aerodynamic Heating;
 Conductive Heat Transfer;
 Phase Transformations;
 Reentry Effects;
 Thermal Analysis;
 Linear Equations;
 Melting Points;
 Numerical Integration;
 Spacecraft Reentry;
 Thermal Boundary Layer;
 Thermodynamics;
 Transient Heating;
 Fluid Mechanics and Heat Transfer