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The Peristaltic Motion inside a Vertical Cylindrical Tube Surrounded Vapour Bubble with Two-Phase Density Flow

Received: 21 March 2017     Accepted: 19 April 2017     Published: 19 October 2017
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Abstract

The paper presents the growth of vapour bubble in a viscous, superheated liquid. The growth of vapour bubble between two-phase density flow in a vertical cylindrical tube under the effect of peristaltic motion of long wavelength and low Reynolds number is studied. The mathematical model is formulated by mass, momentum, and heat equations. The analytical solution is obtained for temperature and velocity distribution under the effect of different physical parameters. The growth process is studied under the affected of density ratio ε and amplitude ratio e. Moreover, the relation between the bubble radius R with the density ratio E, and amplitude ratio eare obtained. Theseresults agreement with some previous theoretical efforts.

Published in Advances in Bioscience and Bioengineering (Volume 5, Issue 4)
DOI 10.11648/j.abb.20170504.14
Page(s) 71-77
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

Peristaltic Flow, Heat Transfer, Grashof Number, Superheated Liquid, Growth of Vapour Bubble

References
[1] K. Ramesh and M. Devakar. Peristaltic Transport of MHD Walter’s fluid through porous medium with heat transfer. Int. J. of Biomathematics, 11, 34 (2014).
[2] K. Das. Effects of Slip and Heat Transfer on MHD Peristaltic Flow in an Inclined Asymmetric Channel. Iran. J. of Math. Scie. and Info. 7, 35 (2012).
[3] A. V. Mernone, J. N. Mazumdar. A Mathematical Study of Peristaltic Transport of a Casson Fluid. Math. and Comp. Mode. 35, 895 (2002).
[4] T. Hayat, Y. Wang, A. M. Siddiqui, K. Hutter, S. Asghar. Peristaltic Transport of a Third-Order Fluid in a Circular Cylindrical Tube. Math. Mode. And Meth. In Appl. Scie. 12, 1691 (2002).
[5] N. Divinis, T. D. Karapantsios, M. Kostoglou, C. S. Panoutsos, V. Bontozoglou, A. C. Michels. Bubbles growing in supersaturated solutions at reduced gravity. AIChE. J. 50, 2369 2(004).
[6] N. Divinis, T. D. Karapantsios, R. De Bruijn, M. Kostoglou, V. Bontozoglou, J-C. Legros. Bubble dynamics during degassing of liquids at microgravity conditions. AIChE.J.,52, 3029, (2006).
[7] N. Divinis, M. Kostoglou, T. D. Karapantsios, V. Bontozoglou. Self-similar growth of a gas bubble induced by localized heating: the effect of temperature-dependent transport properties. Chem. Engi. Scie. 60, 1673,(2005).
[8] N. Divinis, T. Karapantsios, M. Kostoglou, V. Bontozoglou, R. de Bruijn, J. Legros. Lateral motion and interaction of gas bubbles growing over spherical and plate heaters. Microgravity Sci Tech. 18, 204 (2006).
[9] T. D.Karapantsios, M. Kostoglou, N. Divinis, V. Bontozoglou. Nucleation, growth and detachment of neighboring bubbles over miniature heaters. Chem.Engi.Sci. 63, 3438 (2008).
[10] T. D. Karapantsios, M. Kostoglou, S. P. Evgenidis. From single bubbles on solid surfaces to massive bubbly flows during decompression sickness. Proceedings of the Symposium “Life in Space for Life on Earth” (ESA, SP-663), 22 (2008)[Angers, France]. http://esamultimedia.esa.int/multimedia/publications/SP-663/SP-663-toc.pdf.
[11] S. P. Evgenidis, N. A.Kazakis, T. D. Karapantsios. Bubbly flow characteristics during decompression sickness: effect of surfactant and electrolyte on bubble size distribution. Colloids Surf A Physicochem Eng. Asp. 365, 46 (2010).
[12] M. A. Chappell, S, J. Payne. A physiological model of the interaction between tissue bubbles and the formation of blood-borne bubbles under decompression. Phys. Med. Biol. 51, 2321 (2006).
[13] H. D. Van Liew, M. E. Burkard. Density of decompression bubbles and competition for gas among bubbles, tissue, and blood. J. Appl. Physiol.75, 2293 (1993).
[14] O. M. F. R. S. Lord and Rayleigh. Philos. On the pressure developed in a liquid during the collapse of a spherical cavity. Mag. 34, 94 (1917).
[15] M. S. Plesset and S. A. Zwick. A Non steady Heat Diffusion Problem with Spherical Symmetry. J. Appl. Phys. 23, 95 (1952).
[16] M. S. Plesset and S. A. Zwick. On the dynamics of small vapor bubbles in liquid. J. Appl. Phys. 25, 493 (1954).
[17] H. K. Forster and N. Zuber. J. Appl. Phys. 25, 474 (1954).
[18] P. Dergarabedian. The Rate of Growth of Vapour Bubbles in Superheated Water. J. Appl. Mech., 20, 537 (1953).
[19] L. E. Scriven. On the Dynamics of Phase Growth. Chem. Engi. Scie. 10, 1 (1959).
[20] B. B. Mikic, W. M. Rohsenow, P. Griffith. On Bubble Growth Rates, Int. J. Heat Mass Trans., 13, 657 (1970).
[21] M. A. Lang, N. E. Smith. Proceedings of the Advanced Scientific Diving Workshop, February 23–24, 2006, Smithsonian Institution, Washington, DC, 277 (2006).
[22] S. A. Mohammadein and K. G. Mohamed. Growth of a vapour bubble in a viscous, superheated liquid in two-phase flow. Cana. J. of Phys. 93, 1 (2015).
[23] S. A. Mohammadein and Sh. A. Gouda. Temperature distribution in a mixture surrounding a growing vapour bubble. Heat Mass Transfer, 42, 359 (2006).
[24] S. A. Mohammadein and R. A. Gad El-Rab. The growth of vapour bubble in superheated water between two-finite boundaries. Cana. J. of Phys. 79, 1021 (2001).
[25] S. A. Mohammadein and A. K. Abu-Nab. Growth of Vapour Bubble Flow inside a Symmetric Vertical Cylindrical Tube. Fluid Mech. 2(2), 28 (2016).
[26] S. A. Mohammadein and A. K. Abu-Nab. The Growth of Vapour Bubble between two-Phase Peristaltic Bubbly Flow inside a Vertical Cylindrical Tube. Int. J. Thin. Fil. Sci. Tec. 6, 29 (2017).
[27] S. A. Mohammadein and K. G. Mohamed. Growth of a Vapour Bubble in a Superheated Liquid of Variable Surface Tension and Viscosity Between Two-phase Flow. Appl. Math. Inf. Sci. 7, (6), 2311 (2013).
[28] L. Haar, J. S. Callagher, Kell G. S. NBS/NRV, Steam tables, (1984).
Cite This Article
  • APA Style

    S. A. Mohammadein, A. K. Abu-Nab, G. A. Shalaby. (2017). The Peristaltic Motion inside a Vertical Cylindrical Tube Surrounded Vapour Bubble with Two-Phase Density Flow. Advances in Bioscience and Bioengineering, 5(4), 71-77. https://doi.org/10.11648/j.abb.20170504.14

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    ACS Style

    S. A. Mohammadein; A. K. Abu-Nab; G. A. Shalaby. The Peristaltic Motion inside a Vertical Cylindrical Tube Surrounded Vapour Bubble with Two-Phase Density Flow. Adv. BioSci. Bioeng. 2017, 5(4), 71-77. doi: 10.11648/j.abb.20170504.14

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    AMA Style

    S. A. Mohammadein, A. K. Abu-Nab, G. A. Shalaby. The Peristaltic Motion inside a Vertical Cylindrical Tube Surrounded Vapour Bubble with Two-Phase Density Flow. Adv BioSci Bioeng. 2017;5(4):71-77. doi: 10.11648/j.abb.20170504.14

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  • @article{10.11648/j.abb.20170504.14,
      author = {S. A. Mohammadein and A. K. Abu-Nab and G. A. Shalaby},
      title = {The Peristaltic Motion inside a Vertical Cylindrical Tube Surrounded Vapour Bubble with Two-Phase Density Flow},
      journal = {Advances in Bioscience and Bioengineering},
      volume = {5},
      number = {4},
      pages = {71-77},
      doi = {10.11648/j.abb.20170504.14},
      url = {https://doi.org/10.11648/j.abb.20170504.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.abb.20170504.14},
      abstract = {The paper presents the growth of vapour bubble in a viscous, superheated liquid. The growth of vapour bubble between two-phase density flow in a vertical cylindrical tube under the effect of peristaltic motion of long wavelength and low Reynolds number is studied. The mathematical model is formulated by mass, momentum, and heat equations. The analytical solution is obtained for temperature and velocity distribution under the effect of different physical parameters. The growth process is studied under the affected of density ratio ε and amplitude ratio e. Moreover, the relation between the bubble radius R with the density ratio E, and amplitude ratio eare obtained. Theseresults agreement with some previous theoretical efforts.},
     year = {2017}
    }
    

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    T2  - Advances in Bioscience and Bioengineering
    JF  - Advances in Bioscience and Bioengineering
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    AB  - The paper presents the growth of vapour bubble in a viscous, superheated liquid. The growth of vapour bubble between two-phase density flow in a vertical cylindrical tube under the effect of peristaltic motion of long wavelength and low Reynolds number is studied. The mathematical model is formulated by mass, momentum, and heat equations. The analytical solution is obtained for temperature and velocity distribution under the effect of different physical parameters. The growth process is studied under the affected of density ratio ε and amplitude ratio e. Moreover, the relation between the bubble radius R with the density ratio E, and amplitude ratio eare obtained. Theseresults agreement with some previous theoretical efforts.
    VL  - 5
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Author Information
  • Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt

  • Department of Mathematics, Faculty of Science, Menoufia University, Shebin El-Koom, Egypt

  • Department of Mathematics, Faculty of Science, Menoufia University, Shebin El-Koom, Egypt

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