THE VELOCITY OF MOVEMENT OF ISOTHERMS
NEAR THE THERMAL CENTER OF A COOLED BODY

V. V. Vinogradov,a I. L. Tyazhel'nikova,a 
and E. P. Vinogradovab

UDC 536.2

The behavior of isotherms near the thermal center of a 
cooled body has been considered. It is shown that closer to the thermal 
center the velocity of movement of isotherms increases sharply. An 
expression is obtained that describes the behavior of the velocity 
of movement of isotherms near the center of bodies of simple shapes 
(plate, infinite cylinder, rod of square cross section, sphere, and 
cube). Quantitatively the behavior of the velocity depends on the 
thermal diffusivity of the medium and the geometric form of the body 
but is independent of the absolute magnitude of the isotherms, body 
dimensions, and of the cooling inetnsity. The property indicated is 
typical of the processes described by parabolic-type equations.

Keywords: velocity of movement of isotherms, thermal 
center of a cooled body, plate, cylinder, sphere.

aI. P. Bardin Central Scientific-Research Institute 
of Ferrous Metallurgy, 9/23 2nd Bauman Str., Moscow, 105005, Russia; 
bV. A. Trapeznikov Institute of the Problems of Management, 
Russian Academy of Sciences, 65 Profsoyuznaya Str., Moscow, 117806, Russia; 
email: vvvinogradov@mtu-net.ru. 
Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 82, No. 2, pp. 391-397, 
March-April, 2009. Original article submitted January 29, 2008; 
revision submitted June 19, 2008.