Temperature field of cylinder with heat-insulated butt ends during heat exchange convection on the generatrix
Authors: E. A. Makarenkov, A. V. Siasiev
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To consider different elements of constructions, which are used in mechanical engineering, the attention can be paid to the fact that components, in the form of a thick-walled hollow cylinder, which cross-section is a doubly connected area, are used in these elements. The high-temperature speed gas or liquid flow, passing through the inner cavity, creates uneven heating, defined both by conditions of the flow and feature of design. The research arising through this complex thermostressed state is important in the design of mechanical engineering things. Taking into account the fact that we often have to deal with short-term impact of high temperatures, it is important to study unsteady temperature fields to determine their greatest unevenness. The latter thing can give rise to the thermostressed state, leading to disturbance of the operating mode. The proposed paper deals with the task of spreading the heat in the circular cylinder with defined radius and height with the specified starting temperature. The bases of the cylinder are heat-insulated, and along the generatrix is forced heat exchange with the environment. A mathematical statement of the internal problem that satisfies the heterogeneous equation of thermal conduction and homogeneous mixed condition on the generatrix of the cylinder is given. The solution of the problem is carried out by factorization using finite integral transforms of the mixed problem of mathematical physics to the cylinder.