Differential Equation of Thermal Conductivity and Convective Heat Transfer in a Cylindrical Coordinate System

-The paper considers the derivation of the basic differential equation of thermal conductivity of a stationary medium in a cylindrical coordinate system. The literature mainly considers versions of this equation for one- and two-dimensional axisymmetric temperature fields. In this paper, the most general form of this equation for a three-dimensional field is obtained and the identity of the two equations in different coordinate systems is shown, which confirms the fundamental reliability and applicability of the obtained equation. An example of a one-dimensional angular field and integral equations of thermal conductivity for three types of one-dimensional temperature fields in directions are also given. The applicability of the differential equation in cylindrical coordinates to describe the thermal conductivity of a flat wall is shown. The differential equation of convective heat transfer and the equation of continuity and continuity of the flow in cylindrical coordinates are also given.