HEAT TRANSFER IN A SHEAR LAMINAR FLOW BETWEEN ROTATING COAXIAL CYLINDERS

Heat transfer in a laminar flow in a gap between rotating and motionless coaxial cylinders has been studied experimentally. The experiment showed that supply of external heat and heating-up of the setup due to dissipation do not practically influence the distribution of excess pressure in a slot gap. The result obtained points to a self-similar mode of temperature variation in a moving air medium. In the course of the experiments, angular points, on passing which the anomalous variation of temperature occurs, were found on the graphs of temperature dependence on time with a variable rotation speed of the inner cylinder. The lambda-type anomalies originate as the rotation speed of the inner cylinder increases. On the contrary, as the speed decreases, a V-shaped turn takes place. The presence of angular points, where the first time derivative of temperature undergoes the first-kind discontinuity, indicates the existence of jumpwise transitions in the laws that govern heat transfer when the rotation speed of the inner cylinder passes through a critical value. According to measurements, as the rotation speed increases or decreases the transition takes place approximately in the range of the same angular speeds 545– 650 s–1. The Reynolds and Taylor numbers that correspond to the indicated rotation speeds are Re = 245–293 and Ta = 22–26, which is much lower than the critical Reynolds number Recr = 3960 for the laminar-to-turbulent flow transition and the critical Taylor number Tacr = 41.3 for the stability loss with origination of Taylor vortices. The appearance of discontinuities is explained by the change in the kinetics of intermolecular interactions caused by a transition from a molecular to phonon mechanism of transfer.

1. Tyutyuma V. D. Solution of a thermal problem in a shear locally nonequilibrium viscous fluid flow. Doklady Natsional’noi akademii nauk Belarusi = Doklady of the National Academy of Sciences of Belarus, 2014, vol. 58, no. 4, pp. 106–109 (in Russian).

2. Kogan M. N. The Dynamics of the Rarefied Gases. Moscow, Nauka Publ., 1967. 440 p. (in Russian).

3. Tyutyuma V. D. Conceptual features in the construction of the theory of compressible media flows. Journal of Engineering Physics and Thermophysics, 2012, vol. 85, no. 2, pp. 356–358. doi.org/10.1007/s10891-012-0660-7

4. Tyutyuma V. D. Experimental confirmation of the model of locally nonequilibrium viscous fluid flow. Doklady Natsional’noi akademii nauk Belarusi = Doklady of the National Academy of Sciences of Belarus, 2014, vol. 58, no. 6. pp. 107–111 (in Russian).

5. Burtsev S. A., Leontiev A. I. Study of the influence of dissipative effects on the temperature stratification in gas flows (Review). High Temperature, 2014, vol. 52, no. 2, pp. 297–307. doi.org/10.1134/s0018151x13060060

6. Schlichting H. Boundary Layer Theory. 6th ed., Mc Graw-Hill, New York, 1968. 730 p.