ON THE LIMITING FORM OF THE EQUATION OF ANISOTROPIC HEAT CONDUCTION IN A RODA. I. Moshinskii UDC 53.01 The paper considers the problem of the asymptotically substantiated reduction of the three-dimensional, in coordinates, equation describing the process of heat propagation in an anisotropic material to a one-dimensional equation. As a heat-transfer region, a cylindrical rod of an arbitrary cross section was taken. It is assumed that the matrix of thermal diffusivity coefficients depends on the spatial coordinates. In the constructed equivalent heat-conduction equation, a certain effective heat-transfer coefficient is represented and formulas for its calculation have been obtained. Examples of the calculation have been considered. Russian Scientific Center "Applied Chemistry," St. Petersburg, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 76, No. 4, pp. 156-163, July-August, 2003. Original article submitted December 17, 2002.