Abstract. A horizontal rod of limited length is considered. The radius of the rod changes linearly along its length. The cross-sectional area of the left end is larger than the right one. The side surface of the rod under study is completely thermally insulated. The heat flow is applied to the cross-sectional area of the left end. Heat exchange with the environment occurs through the cross-sectional area of the right end of the rod. In the work, the field of temperature distribution, displacement, three components of deformation and stress are determined, provided that both ends of the rod are rigidly fixed. And also, the value of the elongation of the rod is determined when one end of the rod is fixed and when the other is free. In the case of fixing the two ends of the rod, the value of the resulting axial compressive force is also calculated. In the study of the rod, the fundamental laws of conservation of energy were used.

Keywords: Elongation, axial force, cross sections, temperature, displacement, deformation, stress.