Thermal shock generalized model of massive bodies with internal cavities


Аuthors

Kartashov E. M.1, 2*, Tishaeva I. R.3, Solomonova E. V.3

1. MIREA — Russian Technological University (Lomonosov Institute of Fine Chemical Technologies), 78, Vernadsky prospect, Moscow, 119454, Russia
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
3. MIREA ,

*e-mail: professor.kartashov@qmail.com

Abstract

The article deals with mathematical models of thermal shock in terms of dynamic thermoelasticity, and their application to specific conditions of the solid body boundary intense heating and cooling. The presentation is being conducted within the framework of a generalized model, which includes concurrently the three coordinate systems, namely Cartesian coordinates — a massive body bounded by a flat surface; spherical coordinates — a massive body with an internal spherical cavity, and cylindrical coordinates — a massive body with an internal cylindrical cavity. The model includes conjointly the thermal heating and thermal cooling conditions. The article describes the class of problems, which are of utter importance for many practical applications. In these problems, the combination of thermophysical properties of the material, geometric size of parts or structures, and the body thermal reaction, which presents the interest of the researcher, concerns mainly the presurface layers. In these layers the abrupt (or intensive enough) temperature change occurs, and the main quantity of heat is concentrated at the times close to the intensive heating or cooling commence. It is accounted for herewith that the presurface layer thickness is minor compared to the body size. In this case, the solid is being modeled as by the infinite region, partially bounded by a certain surface. The article demonstrates that it is possible to obtain ostensive and more convenient from the viewpoint of practical application analytical representations of the thermal shock theory problems solutions under these conditions. The presence of the boundary surface curvature dictates the initial formulation of the dynamic problem in displacements using the proposed equation of «compatibility» in displacements for dynamic problems in Cartesian, cylindrical and spherical coordinate systems with a radial heat flow and central symmetry. The presented work develops the thermal shock generalized dynamic model, which touches upon various practical applications as one of the said theory trends, which has not received its development to date. It is shown that this kind of research specificity lies, on the one hand, in the relative simplicity of the initial mathematical models, on the other hand, in computational difficulties in finding the desired result, and herewith in the obvious significance of applying the obtained relations in numerous practical situations. The operational method was used to find the exact analytical solution of the generalized dynamic problem. Based on the solution, a numerical experiment was performed, and it was shown that the process of thermoelastic stresses propagation based on the dynamic model was not diffusional, but was associated with the thermoelastic waves propagation. Stresses surges at the thermoelastic wave front, which can serve as an upper estimation of the thermoelastic stresses maximum at the temperature cooling and heating were computed by the operational solution of the dynamic problem.

Keywords:

thermo-siphon, capillary rise, porous coating, thermal resistance, nanoparticles

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