Mathematical Model of the Liquid Film Flow on the Flat Surface

N. I. Klyuev

doi:doi:10.11648/j.ajae.20170401.11

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Mathematical Model of the Liquid Film Flow on the Flat Surface

N. I. Klyuev

Published in American Journal of Aerospace Engineering (Volume 4, Issue 1)

Received: 28 December 2016 Accepted: 19 January 2017 Published: 21 February 2017

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Abstract

A liquid film on surface of a body decreases frictional resistance and can be used as a boundary layer control element. This article contains a mathematical model of a film flow over a half-plane, directed at an angle to the horizon. Liquid flow depends on gravity and friction with the external air flow. A model of incompressible viscous liquid near the boundary layer is used as the flow model. Summands of motion equation are averaged over the film thickness by the Leibniz rule. The square low is assumed for distribution of longitudinal velocity in the cross-section of the film with regard to the friction at the film's surface. An approximate solution of the problem is received as power series in powers of small parameter. The results are presented in a form diagrams of the film thickness and the average longitudinal velocity over the length of the plate. The mathematical flow model can be used to define flat film flow performance.

Published in	American Journal of Aerospace Engineering (Volume 4, Issue 1)
DOI	10.11648/j.ajae.20170401.11
Page(s)	1-5
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Film, Liquid, Boundary Layer, Flow, Friction, Small Parameter

References

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[2]	Lu, H., Lu, L., Luo, Y., Qi, R. Investigation on the dynamic characteristics of the counter-current flow for liquid desiccant dehumidification. Energy. V.101, 2016, pp. 229-238.
[3]	Li, M., Lu, Y., Zhang, S., Xiao, Y. A numerical study of effects of counter-current gas flow rate on local hydrodynamic characteristics of falling films over horizontal tubes. Desalination. V.383, 2016, pp. 68-80.
[4]	Klyuev, N. I., Gimadiev, A. G., Kryukov, Y. A. Two-media boundary layer on a flat plate. IJET. V.6, Issue 5, 2014, pp. 2368-2374.
[5]	Klyuev, N. I., Kryukov, Y. A. Influence of fluid film on friction of a flat plate. Russian Aeronautics (Iz. VUZ). V.57, Issue 4, 2014, pp. 372-377.
[6]	Camassa, R., Ogrosky, H. R. On viscous film flows coating the interior of a tube: Thin-film and long-wave models. Journal of Fluid Mechanics, V.772, 2015, pp.569-599.
[7]	Muramatsu, K., Youn, Y., Han, Y., Hasegawa, Y., Shikazono, N. Numerical study on the effect of initial flow velocity on liquid film thickness of accelerated slug flow in a micro. International Journal of Heat and Fluid Flow. V.54, 2015, pp.77-86.
[8]	Han, Y., Kanno, H., Ahn, Y.-J., Shikazono, N. Measurement of liquid film thickness in micro tube annular flow. International Journal of Multiphase Flow. V.73, 2015, pp.264-274.
[9]	Youn, Y. J., Muramatsu, K., Han, Y., Shikazono, N. The effect of initial flow velocity on the liquid film thickness in micro tube accelerated slug flow. International Journal of Multiphase Flow. V.73, 2015, pp.108-117.
[10]	Ju, P., Brooks, C. S., Ishii, M., Liu, Y., Hibiki, T. Film thickness of vertical upward co- current adiabatic flow in pipes. International Journal of Heat and Mass Transfer. V.89, 2015, pp. 985-995.
[11]	Richard, G. L., Ruyer-Quil, C., Vila, J. P. A three-equation model for thin films down an inclined plane. Journal of Fluid Mechanics. V.804, 2016, pp.162-200.
[12]	Akkuş, Y., Dursunkaya, Z. A new approach to thin film evaporation modeling. International Journal of Heat and Mass Transfer. V.101, 2016, pp.742-748.
[13]	Liu, C. L., Liu, J. L., Zhu, H. R., Wu, A. S., He, Y. H., Zhou, Z. X. Film cooling sensitivity of laidback fanshape holes to variations in exit configuration and mainstream turbulence intensity. International Journal of Heat and Mass Transfer. V.89, Issue 12145, 2015, pp.1141-1154.
[14]	Degan, G., Sanya, A., Akowanou, C. Laminar film condensation along a vertical plate embedded in an anisotropic porous medium with oblique principal axes. Heat and Mass Transfer. V.52, Issue10, 2016, pp.2119-2128.
[15]	Kim, S., Lee, Y. G., Jerng, D. W. Laminar film condensation of saturated vapor on an isothermal vertical cylinder. International Journal of Heat and Mass Transfer. V.83, 2015, pp. 545-551.

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APA Style

N. I. Klyuev. (2017). Mathematical Model of the Liquid Film Flow on the Flat Surface. American Journal of Aerospace Engineering, 4(1), 1-5. https://doi.org/10.11648/j.ajae.20170401.11

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ACS Style

N. I. Klyuev. Mathematical Model of the Liquid Film Flow on the Flat Surface. Am. J. Aerosp. Eng. 2017, 4(1), 1-5. doi: 10.11648/j.ajae.20170401.11

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AMA Style

N. I. Klyuev. Mathematical Model of the Liquid Film Flow on the Flat Surface. Am J Aerosp Eng. 2017;4(1):1-5. doi: 10.11648/j.ajae.20170401.11

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@article{10.11648/j.ajae.20170401.11,
  author = {N. I. Klyuev},
  title = {Mathematical Model of the Liquid Film Flow on the Flat Surface},
  journal = {American Journal of Aerospace Engineering},
  volume = {4},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.ajae.20170401.11},
  url = {https://doi.org/10.11648/j.ajae.20170401.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajae.20170401.11},
  abstract = {A liquid film on surface of a body decreases frictional resistance and can be used as a boundary layer control element. This article contains a mathematical model of a film flow over a half-plane, directed at an angle to the horizon. Liquid flow depends on gravity and friction with the external air flow. A model of incompressible viscous liquid near the boundary layer is used as the flow model. Summands of motion equation are averaged over the film thickness by the Leibniz rule. The square low is assumed for distribution of longitudinal velocity in the cross-section of the film with regard to the friction at the film's surface. An approximate solution of the problem is received as power series in powers of small parameter. The results are presented in a form diagrams of the film thickness and the average longitudinal velocity over the length of the plate. The mathematical flow model can be used to define flat film flow performance.},
 year = {2017}
}

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TY  - JOUR
T1  - Mathematical Model of the Liquid Film Flow on the Flat Surface
AU  - N. I. Klyuev
Y1  - 2017/02/21
PY  - 2017
N1  - https://doi.org/10.11648/j.ajae.20170401.11
DO  - 10.11648/j.ajae.20170401.11
T2  - American Journal of Aerospace Engineering
JF  - American Journal of Aerospace Engineering
JO  - American Journal of Aerospace Engineering
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2376-4821
UR  - https://doi.org/10.11648/j.ajae.20170401.11
AB  - A liquid film on surface of a body decreases frictional resistance and can be used as a boundary layer control element. This article contains a mathematical model of a film flow over a half-plane, directed at an angle to the horizon. Liquid flow depends on gravity and friction with the external air flow. A model of incompressible viscous liquid near the boundary layer is used as the flow model. Summands of motion equation are averaged over the film thickness by the Leibniz rule. The square low is assumed for distribution of longitudinal velocity in the cross-section of the film with regard to the friction at the film's surface. An approximate solution of the problem is received as power series in powers of small parameter. The results are presented in a form diagrams of the film thickness and the average longitudinal velocity over the length of the plate. The mathematical flow model can be used to define flat film flow performance.
VL  - 4
IS  - 1
ER  -

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Author Information

N. I. Klyuev

Department of Mathematical Modeling in Mechanics, Samara State University, Samara, Russia

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APA Style

N. I. Klyuev. (2017). Mathematical Model of the Liquid Film Flow on the Flat Surface. American Journal of Aerospace Engineering, 4(1), 1-5. https://doi.org/10.11648/j.ajae.20170401.11

Copy | Download

ACS Style

N. I. Klyuev. Mathematical Model of the Liquid Film Flow on the Flat Surface. Am. J. Aerosp. Eng. 2017, 4(1), 1-5. doi: 10.11648/j.ajae.20170401.11

Copy | Download

AMA Style

N. I. Klyuev. Mathematical Model of the Liquid Film Flow on the Flat Surface. Am J Aerosp Eng. 2017;4(1):1-5. doi: 10.11648/j.ajae.20170401.11

Copy | Download

@article{10.11648/j.ajae.20170401.11,
  author = {N. I. Klyuev},
  title = {Mathematical Model of the Liquid Film Flow on the Flat Surface},
  journal = {American Journal of Aerospace Engineering},
  volume = {4},
  number = {1},
  pages = {1-5},
  doi = {10.11648/j.ajae.20170401.11},
  url = {https://doi.org/10.11648/j.ajae.20170401.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajae.20170401.11},
  abstract = {A liquid film on surface of a body decreases frictional resistance and can be used as a boundary layer control element. This article contains a mathematical model of a film flow over a half-plane, directed at an angle to the horizon. Liquid flow depends on gravity and friction with the external air flow. A model of incompressible viscous liquid near the boundary layer is used as the flow model. Summands of motion equation are averaged over the film thickness by the Leibniz rule. The square low is assumed for distribution of longitudinal velocity in the cross-section of the film with regard to the friction at the film's surface. An approximate solution of the problem is received as power series in powers of small parameter. The results are presented in a form diagrams of the film thickness and the average longitudinal velocity over the length of the plate. The mathematical flow model can be used to define flat film flow performance.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Mathematical Model of the Liquid Film Flow on the Flat Surface
AU  - N. I. Klyuev
Y1  - 2017/02/21
PY  - 2017
N1  - https://doi.org/10.11648/j.ajae.20170401.11
DO  - 10.11648/j.ajae.20170401.11
T2  - American Journal of Aerospace Engineering
JF  - American Journal of Aerospace Engineering
JO  - American Journal of Aerospace Engineering
SP  - 1
EP  - 5
PB  - Science Publishing Group
SN  - 2376-4821
UR  - https://doi.org/10.11648/j.ajae.20170401.11
AB  - A liquid film on surface of a body decreases frictional resistance and can be used as a boundary layer control element. This article contains a mathematical model of a film flow over a half-plane, directed at an angle to the horizon. Liquid flow depends on gravity and friction with the external air flow. A model of incompressible viscous liquid near the boundary layer is used as the flow model. Summands of motion equation are averaged over the film thickness by the Leibniz rule. The square low is assumed for distribution of longitudinal velocity in the cross-section of the film with regard to the friction at the film's surface. An approximate solution of the problem is received as power series in powers of small parameter. The results are presented in a form diagrams of the film thickness and the average longitudinal velocity over the length of the plate. The mathematical flow model can be used to define flat film flow performance.
VL  - 4
IS  - 1
ER  -

Copy | Download