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Heat Convection in a Rotating Pipe

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We study an unsteady-state boundary value problem on the motion of a fluid in a rotating cylindrical pipe. The Oberbeck–Boussinesq equations are used to describe the fluid motion. From the mathematical point of view, this is an inverse problem for the pressure gradients along the cylinder axis. Based on a priori estimates, we obtain conditions under which the solution of the steady-state inverse problem is exponentially stable. In Laplace transforms, the solution is found by quadratures. Sufficient conditions for the solution of the unsteady-state problem to reach a steady-state mode over time are given.

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This work was supported by the Krasnoyarsk Mathematical Center of the Ministry of Education and Science of the Russian Federation within the framework of the creation and development of regional scientific and educational centers of mathematics, agreement no. 075-02-2021-1384.

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Correspondence to V. K. Andreev, I. V. Vakhrameev or E. P. Magdenko.

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Translated by V. Potapchouck

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Andreev, V.K., Vakhrameev, I.V. & Magdenko, E.P. Heat Convection in a Rotating Pipe. J. Appl. Ind. Math. 16, 175–188 (2022).

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