EQUATION OF HEAT EXCHANGE DURING THE FLOW OF NON-NEWTONIAN LIQUIDS IN CHANNELS OF TECHNOLOGICAL EQUIPMENT
DOI:
https://doi.org/10.15421/jchemtech.v29i2.229829Keywords:
heat exchange; flow; liquid; viscoplastic; generalized-shifted; channel; straight; bypass; tankAbstract
In this article we considered the processes of heat exchange in the channels of technological equipment in the cases that are most common in machines and apparatus of the chemical and food industries. In the first case, the external environment is considered to be an infinite heat tank with a given temperature. In the second case, the role of the external environment is performed by the channel with moving heat carrier, while the temperature of the heat carrier is not set and varies along the length of the channel. The heat transfer equation includes convective terms and terms with thermal conductivity.
We formulated the heat exchange equation for the flow of non-Newtonian (viscoplastic and generalized-shifted) fluids. It is determined that: during the flow of generalized-shifted fluid in a flat channel with set wall temperatures it is necessary to define two heat transfer coefficients; in the flat channel, which is immersed in the heat tank - four heat transfer coefficients; in the flat channel, which is surrounded by a bypass channel - eight heat transfer coefficients. When describing heat transfer with a rectangular channel, for all these cases, it is necessary to determine respectively four, eight and sixteen heat transfer coefficients. During the flow of viscoplastic fluid, it is necessary to determine: in the flat channel with the set wall temperatures - four heat transfer coefficients; in the channel, which is immersed in the heat tank - six heat transfer coefficients; in the channel, which is surrounded by a bypass channel - ten heat transfer coefficients. When describing the heat transfer of a flow in a rectangular channel for the same cases, it is necessary to define respectively eight, twelve and twenty heat transfer coefficients.
The heat exchange equations are a system of first-order differential equations in finite differences for the temperature of the liquid in the channel. And this is their main difference from the calculations for the cases of fixed temperatures on the walls of the straight channel and the immersion of the straight channel in the heat tank with a fixed temperature. It is shown that the fluid temperature depends on the longitudinal coordinate along the channel. In this case, the dependence of temperature on the geometric characteristics of the channel is determined by the cross-sectional area of the channel and its perimeter, as well as the ratio of geometric dimensions (width, height and length) of the channel.
When performing engineering calculations, the obtained expressions allow to determine the corresponding coefficients of heat transfer and heat transfer during the flow of non-Newtonian fluids in the channels and with the external environment.
References
Harlamov, S. (2013). [Gidrodinamika i teploobmen: Novyie tendentsii i perspektivyi modelirovaniya vnutrennih techeniy]. LAP LAMBERT Academic Publishing. (in Russian).
Gale, M. (2009). Mixing in Single Screw Extrusion. USA : Smithers Rapra Press.
Ulyev, L. M. (2016). [Laminar flow in coaxial conical channels]. Kharkiv. Ukraine: NTU "KhPI". (in Ukraine).
Anandha, Rao M. (2014) Rheology of Fluid, Semisolid, and Solid Foods: Principles and Applications. New York, USA : Imprint: Springer.
Cantelli, A. (2009). Uniform Flow of Modified Bingham Fluids in Narrow Cross Section]. Journal of Hydraulic Engineering., 135(8), 640–50.
Baptista A., Alves M.A., Coelho P.M. (2014) Heat transfer in fully developed laminar flow of power law fluids. Journal of Heat Transfer., 136(4), 1–8.
Tovazhnyansky, L. L., Biletsky, E.V., Tolchinsky Yu. A. (2013). [Modeling of flows of non-Newtonian fluids in channels of basic geometry]. Kharkiv. Ukraine: NTU "KhPI". (in Ukraine).
Golovanchikov, A. B., Shagarova, A. A. (2015). [Modeling the flow of a viscoplastic reaction mass in a screw reactor with a low viscosity wall layer]. Izvestiya vuzov. Khimiya i khimicheskaya tekhnologiya. 58(12), 69–72. (in Russian).
Ponomareva, M. A. Filina, M. P., Yakutonok, V. A. (2016). [Circulating flow of high viscosity non-Newtonian fluid in a single-screw extruder channel]. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika., 2(40), 97–107.
Kolgruber, K. (2016). [Twin-screw, co-directed extruders. Basics, technology, application], Saint Petersburg. Russian Federation: Profession. (in Russian).
Ryabinin M. V., Trukhanov K. A. (2015). [The method of determining friction losses in a hydraulically smooth round pipe for pseudoplastic fluids]. Modern problems of science and education. 1(1). - http://www.science-education.ru. (in Russian).
Perminov, A. V., . Lyubimova, T. P. (2014). [Stability of a stationary plane-parallel flow of a pseudoplastic fluid in a flat vertical layer]. Vychislitel'naya mekhanika sploshnykh sred. 7(3). 270 – 278.
Mitsoulis, E., Tsamopoulos, J., (2017). Numerical simulations of complex yield-stress fluid flows. Rheologica Acta 56. 231–258.
Frigaard, I. A., Paso, K., de Souza Mendes, P., (2017). Binghams model in the oil and gas industry. Rheologica Acta 56. 259–282.
Biletsky, E. Petrenko, E., Semeniuk, D. (2014). Theoretical aspects of non-newtonian fluids flow simulation in food technologies. Ukrainian Food Journal. 3(2), 271-280.
Biletsky, E. Petrenko, E., Semeniuk, D. (2016). Three-dimensional model of non-Newtonian fluid flow in the rectangular channel. Ukrainian Food Journal. 5(3), 550–560.
Petrenko, E., Biletsky, E., Semeniuk, D. (2019). Modeling of the viscoplastic flow of a bingam fluid with transverse circulation in a rectangular channel of a worm machine. Journal of Chemistry and Technologies. 27(2), 550–560.
Kirsanov, E. A., Matveenko V. N. (2016). [Non-Newtonian Current of Disperse, Polymer, and Liquid Crystal Systems] Moscow. Russian Federation: Technosphere. (in Russian).
Borzenko E., Ryltsev I., Frolov O. Shrager G. (2017) Nonisothermal filling of a planar channel with a power-law fluid. Journal of Physics: Conf. Series. 899. 1-6.
Saramito, P., Wachs A., (2017). Progress in numerical simulation of yield stress fluid flows. Rheologica Acta 56. 211–230.
Frank-Kamenetskii D.A. (2015) Diffusion and Heat Exchange in Chemical Kinetics. Princeton. USA: Princeton University Press.
Кolodiazhnov, V. N., Amzin, C. I. (2005). [Modelling of hydrodynamics and heat transfer for non-Newtonian fluids in channels with annular cross-section], Voronezh, Russian Federation: NGTA. (in Russian).
Boyadjer Chr. (2001). Non liner mass transfer and hydrodynamic stability. In: Physical fundamentals of experimental and mathematical modelling of hydrodynamics and heat mass exchange processes in power installations. 1. 203–212.
Dimitrienko, Yu. I., Shuguan, Li (2018). Finite-element modeling of non-isothermal steady flow of a non-Newtonian fluid in complex areas. Mathematical modeling and numerical methods. 70–95.
Toth, G., Bata, A., Belina, K. (2018). Determination of polymer melts flow-activation energy a function of wide range shear rate. IOP Conf. Series: Journal of Physics. 012040, 1045.
Subbotin, E. V., Trufanova, N. M., Shcherbinin, A. G. (2012). Numerical study of polymer fluid flows in the channel of a screw extruder using one- and two-dimensional models. Vycisl. meh. splos. sred – Computational Continuum Mechanics. 5(4). 452-460.
Vakhrushev, A. A., Lipanov, A. M., Vakhrushev, A. V. (2005). Numerical study of fluid flow with variable viscous properties in curved channels. Chemical physics and mesoscopy. 7(3). 286-30.
Yakhno, A. N., Krivosheev, V. S., Kashuba, D. N., Krivosheev, A. V. (2013). Experimental study of the flow of non-Newtonian fluids in conical annular channels. East -Europe. zhurn. advanced technology. 1(7). 52-55.
Petrenko, E., Biletsky, E., Semeniuk, D. (2020). Determination of heat transfer coefficients during the flow of non-Newtonian fluids in pipes and channels of chemical process equipment. Journal of Chemistry and Technologies. 28(1), 88–99.
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