Control of the heat and mass transfer in magnetic fluids 2. Thermal stress distribution in a cylinder cooled in a magnetic fluid

V. V. Gogosov - V. V. Kiryushin - A. Ya. Simonovskii

Abstract
A problem (assumed to be two-dimensional) of thermal stress distribution in an elastic cylinder cooled in a magnetic fluid located in a magnetic field for any given temperature distribution has been solved. The Hookean law has been used. The thermal expansion coefficient is assumed to be temperature independent. The temperature distribution in the cylinder obtained as a result of the solution of the corresponding heat transfer problem heat transfer problem has been used; in the latter, the temperature distribution on the cylinder found experimentally served as the boundary condition. The radial and azimuthal distributions of the stress components p_rr, p_rϕ, p_ϕϕ, p_zz in a cylindrical system with the z-axis coinciding with the cylinder axis have been determined for two different cooling moments, 0.2 and 0.6 sec after the cooling has begun. The three first components have been presented graphically. The angle If is measured wi th respect to the field direction. It has been found that, on the contrary to an ordinary case of uniform cooling, the normal (Pzz) and the tangential (Prlf) stress components do not vanish. The components Prr and Plflf at the nonuniform cooling are greater that at a uniform one. Deformations of a hollow cylinder cooled in the magnetic fluid have been observed and measured experimentally. These deformations are caused by the thermal stresses arising during the nonuniform cooling. Figs. 2, refs 2.