A method of analytical solution of the problem on the heat exchange in a liquid moving in a tube with dissipation of its energy at the first-kind boundary conditions, i.e., under the conditions of heat shock at the walls of the tube, was developed on the basis of the integral method of heat balance. The approach proposed involves the introduction of an additional desired function and additional boundary conditions, which allows one to reduce the solution of the partial differential equation to the integral ordinary differential equation for the additional desired function determined by only the longitudinal space variable. In this method there is no need to perform integration of the differential equation with respect to the transverse coordinate, involving the use of the heat-balance integral, which enables it to be used for solving the problem on the heat exchange in a medium with variable physical properties as well as nonlinear boundary-value problems.
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 90, No. 5, pp. 1298–1306, September–October, 2017.
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Eremin, A.V., Kudinov, I.V., Dovgyallo, A.I. et al. Heat Exchange in a Liquid with Energy Dissipation. J Eng Phys Thermophy 90, 1234–1242 (2017). https://doi.org/10.1007/s10891-017-1679-6
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DOI: https://doi.org/10.1007/s10891-017-1679-6