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сентябрь 2016 (published: 30.09.2016)
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Hydrodynamics and heat transfer in free convection conditions
Vyacheslav B. Tishin
, Alexander G. Novoselov, Fedorov A.A. , Chebotar A.V.
The article deals with a theoretical solution for the problem of determining the velocity profile in laminar fluid flow in a vertical cylindrical-conical device under conditions of free convection caused by the difference in density due to temperature changes in the volume of the device. Two equations describing the local velocity profile along the radius of the device in the upstream and downstream areas of fluid motion were obtained. From the condition of equality for the flow rate in the zones a radius search method defining the border between zones was proposed.
Computing experiment performed on the basis of these equations shows that the laminar flow regime is possible when the temperature difference on the side of the machine and in the center of is<0.01°. This applies to the physical properties of fluids close to water provided that temperature changes along the device radius linearly. The flow regime seems to be turbulent in the real world. To solve the problem of heat exchange between the device wall and the liquid, where yeast cells grow in the conditions of developed turbulence, semi-empirical method was chosen.The method is based on the analogy between the transfer of motion and heat and the turbulent flow three-layer model. For this purpose we used the fourth degree of the of turbulent fluctuations’ attenuation in the boundary layer. Solution of heat exchange problems between the wall unit and the liquid in which yeast cells develop in the conditions of developed turbulence is obtained by a semi-empirical method. The method is based on the analogy between the transfer of momentum and heat, and a three-layer model of turbulent flow, using the law of the fourth degree of attenuation of turbulent fluctuations in the boundary layer. To calculate dynamic velocity an equation where specific heat power depending on biomass buildup rate is taken as definiens is used. A mathematical dependence of motion and heat transfer rate on the rate of biological processes in yeast cells is presented.
The proposed theoretical solutions require further experimental studies to clarify the numerical value of the empirical coefficient and the temperature profile in the cross section of the device.
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Keywords: gravitational convection; cylindrical-conical device; laminar and turbulent regime; velocity profile; heat exchange; dynamic speed; power density.
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