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

S. A. Mohammadein; A. K. Abu-Nab; G. A. Shalaby

doi:doi:10.11648/j.abb.20170504.14

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

S. A. Mohammadein, A. K. Abu-Nab, G. A. Shalaby

Published in Advances in Bioscience and Bioengineering (Volume 5, Issue 4)

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

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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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TY  - JOUR
T1  - The Peristaltic Motion inside a Vertical Cylindrical Tube Surrounded Vapour Bubble with Two-Phase Density Flow
AU  - S. A. Mohammadein
AU  - A. K. Abu-Nab
AU  - G. A. Shalaby
Y1  - 2017/10/19
PY  - 2017
N1  - https://doi.org/10.11648/j.abb.20170504.14
DO  - 10.11648/j.abb.20170504.14
T2  - Advances in Bioscience and Bioengineering
JF  - Advances in Bioscience and Bioengineering
JO  - Advances in Bioscience and Bioengineering
SP  - 71
EP  - 77
PB  - Science Publishing Group
SN  - 2330-4162
UR  - https://doi.org/10.11648/j.abb.20170504.14
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
IS  - 4
ER  -

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Author Information

S. A. Mohammadein

Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt
A. K. Abu-Nab

Department of Mathematics, Faculty of Science, Menoufia University, Shebin El-Koom, Egypt
G. A. Shalaby

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

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Plain Text BibTeX RIS

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - The Peristaltic Motion inside a Vertical Cylindrical Tube Surrounded Vapour Bubble with Two-Phase Density Flow
AU  - S. A. Mohammadein
AU  - A. K. Abu-Nab
AU  - G. A. Shalaby
Y1  - 2017/10/19
PY  - 2017
N1  - https://doi.org/10.11648/j.abb.20170504.14
DO  - 10.11648/j.abb.20170504.14
T2  - Advances in Bioscience and Bioengineering
JF  - Advances in Bioscience and Bioengineering
JO  - Advances in Bioscience and Bioengineering
SP  - 71
EP  - 77
PB  - Science Publishing Group
SN  - 2330-4162
UR  - https://doi.org/10.11648/j.abb.20170504.14
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
IS  - 4
ER  -

Copy | Download