Nonstationary heat transfer in a hollow composite cylinder

Abstract

NONSTATIONARY HEAT TRANSFER IN A HOLLOW COMPOSITE CYLINDERUDC 536.21 V. V. Mel'nikov Solution of a nonstationary heat-transfer problem for bounded end-conjugated hollow dissimilar cylinders is presented. In the volume of the cylinders, time-and coordinate-dependent heat release of known intensity takes place. The problem is solved using finite integral transformations over two coordinates.As opposed to the well-known stationary problem [1], here we treat a nonstationary heat-conduction problem for a hollow composite cylinder with first-, second-, or third-kind heat-transfer conditions at the external boundaries dependent both on time and coordinates. At the junction interface of the composite cylinder, an ideal thermal contact (fourth-kind boundary conditions) is assumed. Next, we assume that in the volume of the constituent cylinders time-and coordinate-dependent heat release takes place. The cylindrical coordinate system used in the present consideration and the dimensions of the composite cylinder are shown in Fig. 1. The problem on determination of the temperature field in the composite cylinder can be represented in the form of two heat conduction equations, conditions posed at the external boundaries and at the interface between the cylinders, and initial conditions. Heat conduction equation:

Temperature field of a three-layer sphere

“…In each layer of the sphere there is heat release which depends on time and the radial coordinate. The solution of the problem is obtained using the method of finite integral transform employed in [4,5] which allows for an easy solution of the problem with different boundary conditions with a minimum change in the initial algorithm.…”