A numerical solution of the anisotropic thermal diffusion equation with experimental verification
Abstract
Saul'yev's, alternating direction explicit procedure (ADEP) is extended for mixed partial derivatives and, hence, the solution of the anisotropic diffusion equation. Consistency criteria of the extended ADEP, applied to the anisotropic diffusion equation, is demonstrated. Temperature distribution in a twodimensional anisotropic medium, new to the literature, are presented. An experimental procedure is developed, using liquid crystals as a temperature measuring device, to map the temperature distribution on the surface of a solid. Liquid crystal color variation with temperatures are calibrated to within. 1 C. Using variable heat flux at a boundary for short times in the vicinity of ambient conditions under a vacuum, the heat losses have been reduced to less than 4%. A computer simulation, based upon the numerical procedure developed, is used to calculate temperature distributions at conditions identical to the experimental runs. A sensitivity analysis is presented which converts the uncertainties in the calibrations of the liquid crystal colors variation with temperature, and the thermal diffusivity of quartz, to a band of probable error around each calculated temperature isotherm.
 Publication:

Ph.D. Thesis
 Pub Date:
 July 1976
 Bibcode:
 1976PhDT........56S
 Keywords:

 Anisotropic Media;
 Equations Of State;
 Thermal Diffusion;
 Computerized Simulation;
 Liquid Crystals;
 Numerical Analysis;
 Temperature Distribution;
 Thermodynamics;
 SolidState Physics