Rotational Effect on Viscous Fluid Flow through Rectangular Rotating Straight Duct

Nazmul Islam; Lasker Ershad Ali; Ariful Islam

doi:doi:10.11648/j.ajam.20180605.12

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Rotational Effect on Viscous Fluid Flow through Rectangular Rotating Straight Duct

Nazmul Islam, Lasker Ershad Ali, Ariful Islam

Published in American Journal of Applied Mathematics (Volume 6, Issue 5)

Received: 8 October 2018 Accepted: 6 November 2018 Published: 18 December 2018

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Abstract

In this paper, a numerical study has been done for fully developed laminar flow of an incompressible viscous fluid through a rotating straight duct with rectangular cross-section. The duct is rotated at a constant angular velocity around the vertical axis. The flow depends on the pressure driven parameter and the rotational parameter along with aspect ratio. The dimensionless non-linear equations are solved by using Spectral method where Chebyshev polynomial is adopted as a key tool. The calculations are carried out for different rotational parameter with a fixed aspect ratio at a constant pressure gradient parameter. The effect of rotational parameter has been observed for axial and secondary flows from the obtained results, which are shown in two dimensional contours and surface plots for axial flow whereas, two dimensional streamline plot, surface plot and vector plot for secondary flow. The asymmetry structure is seen in the axial flow pattern while the double vortex configuration is seen in the secondary flow structure, for all rotational parameter. However, the double vortex pattern in the secondary flow configuration is slightly compressed against the upper and lower walls of the duct for small rotational parameter, but it is highly compressed against the upper and lower walls for high rotational speed.

Published in	American Journal of Applied Mathematics (Volume 6, Issue 5)
DOI	10.11648/j.ajam.20180605.12
Page(s)	159-166
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), 2018. Published by Science Publishing Group

Keywords

Viscous Fluid, Steady Flow, Rotating Straight Duct, Rectangular Cross-Section and Pressure Gradient

References

[1]	Batchelor, G. K. An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, 1967.
[2]	Rothstein, J. P. and McKinley, G. H., (2001) The axisymmetric contraction/expansion: the role of extensional rheology on vortex growth dynamics and the enhanced pressure drop, Journal of Non-Newtonian Fluid Mechanics, 98: 33-63.
[3]	Subramanya, K. Flow in Open Channels, Tata McGraw-Hill Education, 1982.
[4]	Mills, Z. G., Shah, T., Warey, A. and Balestrino, S., (2014) Onset of unsteady ow in wavy walled channels at low Reynolds number, Physics of Fluids, 26: 084-104.
[5]	Mofatt, H. K., (1964) Viscous and resistive eddies near a sharp corner, Journal of Fluid Mechanics, 18: 1-18.
[6]	Duck, P. W., (1983) Flow through rotating straight pipes of circular cross-section, Physics of Fluids A, 26(3): 614-618.
[7]	Mansour, K., (1985) Laminar flow through a slowly rotating straight pipe, Journal of Fluid Mechanics, 150: 1-21.
[8]	Lei, U. and Hsu, C. H., (1990) Flow through a straight pipe, Physics of Fluids A, 2(1): 63-75.
[9]	Ishigaki, H., (1994) Analogy between laminar flows in curved pipes and rotating pipes, Journal of Fluid Mechanics, 268: 133-145.
[10]	Barua, S. N., (1995) Secondary flow in rotating straight pipe, Proceeding of Royal Society of London A, 227: 133-139.
[11]	Benton, G. S. and Baltimore, M. D., (1956) The effect of the earth’s rotation on laminar flow in pipes, Journal of Applied Mechanics, March Issue: 123-127.
[12]	Islam, N., Shameem, S. M., Rahman, M. A., and Alam, M. M., (2004) Flow through a rotating straight pipe, Journal of Mathematics and Mathematical Science, 19: 21-33.
[13]	Mori, Y. and Nakayama, W., (1965) Study on Forced Convective Heat Transfer in Curved Pipes, International Journal of Heat and Mass Transfer, 8: 67-82.
[14]	Ito, H. and Nanbu, K., (1971) Flow in rotating straight pipes of circular cross-section, ASME Journal of Basic Engineering, September Issue:383-394.
[15]	Wanger, R. E, Velkoff, H. R., (1972) Measurements of secondary flows in a rotating duct. Journal of Engineering for Power, 94(10): 261–270.
[16]	Sharma, R. K. and Nandakumar, K., (1995) Multiple, two–dimensional solution in a rotating straight pipes, Physics of Fluids A, 7(7): 1568-1575.
[17]	Kheshgi, H. S. and Scriven, L. E., (1985) Viscous flow through a rotating square channel, Physics of Fluids A, 28(10): 2968-2985.
[18]	Nandakumar, K., Raszillier, H. and Durst, F., (1991) Flow through rotating rectangular ducts, Physics of Fluids A, 3(5): 770-781.
[19]	Spezial, C. G., (1982) Numerical study of viscous flow in a rotating system, Journal of Fluid Mechanics, 122: 251-271.
[20]	Zhang, J., Liu, Y., Zhang, J. and Yang, J., (2009) Study of force-dependent and time-dependent transition of secondary flow in a rotating straight channel by the lattice Boltzmann method, Physica A: Statistical Mechanics and its applications, 388(4): 288 - 294.
[21]	Lei, U. and Yang, A. C. Y., (2001) Convective Heat Transfer of the Flow through a Rotating Circular Straight Pipe, Journal of Mechanics, 17(2): 79 – 91.
[22]	Roy, P., Anand, N. K. and Banerjee, D., (2013) Numerical simulation of flow and heat transfer in radially rotating microchannels, Microfluidics and Nanofluidics, 15(3): 397 – 413.
[23]	Yadav, D. and Kim, M. C., (2014) The effect of rotation on the onset of transient Soret-driven buoyancy convection in a porous layer saturated by a nanofluid, Microfluidics and Nanofluidics, 17(6): 1085 – 1087.
[24]	Kanikzadeh, M. and Sohankar, A., (2016) Thermal performance evaluation of the rotating U-shaped micro/mini/macrochannels using water and nanofluids, Numerical Heat Transfer, Part A: Applications, 70(6): 650-654.
[25]	Canuto, C., Hussaini, M. Y., Quarteroni, A. and Zang, T. A., Spectral methods in fluid dynamics, Springer-Verlag, Berlin, 1988.
[26]	Boyd, J. P., Chebyshev and Fourier spectral methods, 2nd edition, Dover, Mineola, 2001.

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APA Style

Nazmul Islam, Lasker Ershad Ali, Ariful Islam. (2018). Rotational Effect on Viscous Fluid Flow through Rectangular Rotating Straight Duct. American Journal of Applied Mathematics, 6(5), 159-166. https://doi.org/10.11648/j.ajam.20180605.12

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ACS Style

Nazmul Islam; Lasker Ershad Ali; Ariful Islam. Rotational Effect on Viscous Fluid Flow through Rectangular Rotating Straight Duct. Am. J. Appl. Math. 2018, 6(5), 159-166. doi: 10.11648/j.ajam.20180605.12

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AMA Style

Nazmul Islam, Lasker Ershad Ali, Ariful Islam. Rotational Effect on Viscous Fluid Flow through Rectangular Rotating Straight Duct. Am J Appl Math. 2018;6(5):159-166. doi: 10.11648/j.ajam.20180605.12

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@article{10.11648/j.ajam.20180605.12,
  author = {Nazmul Islam and Lasker Ershad Ali and Ariful Islam},
  title = {Rotational Effect on Viscous Fluid Flow through Rectangular Rotating Straight Duct},
  journal = {American Journal of Applied Mathematics},
  volume = {6},
  number = {5},
  pages = {159-166},
  doi = {10.11648/j.ajam.20180605.12},
  url = {https://doi.org/10.11648/j.ajam.20180605.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20180605.12},
  abstract = {In this paper, a numerical study has been done for fully developed laminar flow of an incompressible viscous fluid through a rotating straight duct with rectangular cross-section. The duct is rotated at a constant angular velocity around the vertical axis. The flow depends on the pressure driven parameter and the rotational parameter along with aspect ratio. The dimensionless non-linear equations are solved by using Spectral method where Chebyshev polynomial is adopted as a key tool. The calculations are carried out for different rotational parameter with a fixed aspect ratio at a constant pressure gradient parameter. The effect of rotational parameter has been observed for axial and secondary flows from the obtained results, which are shown in two dimensional contours and surface plots for axial flow whereas, two dimensional streamline plot, surface plot and vector plot for secondary flow. The asymmetry structure is seen in the axial flow pattern while the double vortex configuration is seen in the secondary flow structure, for all rotational parameter. However, the double vortex pattern in the secondary flow configuration is slightly compressed against the upper and lower walls of the duct for small rotational parameter, but it is highly compressed against the upper and lower walls for high rotational speed.},
 year = {2018}
}

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TY  - JOUR
T1  - Rotational Effect on Viscous Fluid Flow through Rectangular Rotating Straight Duct
AU  - Nazmul Islam
AU  - Lasker Ershad Ali
AU  - Ariful Islam
Y1  - 2018/12/18
PY  - 2018
N1  - https://doi.org/10.11648/j.ajam.20180605.12
DO  - 10.11648/j.ajam.20180605.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 159
EP  - 166
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20180605.12
AB  - In this paper, a numerical study has been done for fully developed laminar flow of an incompressible viscous fluid through a rotating straight duct with rectangular cross-section. The duct is rotated at a constant angular velocity around the vertical axis. The flow depends on the pressure driven parameter and the rotational parameter along with aspect ratio. The dimensionless non-linear equations are solved by using Spectral method where Chebyshev polynomial is adopted as a key tool. The calculations are carried out for different rotational parameter with a fixed aspect ratio at a constant pressure gradient parameter. The effect of rotational parameter has been observed for axial and secondary flows from the obtained results, which are shown in two dimensional contours and surface plots for axial flow whereas, two dimensional streamline plot, surface plot and vector plot for secondary flow. The asymmetry structure is seen in the axial flow pattern while the double vortex configuration is seen in the secondary flow structure, for all rotational parameter. However, the double vortex pattern in the secondary flow configuration is slightly compressed against the upper and lower walls of the duct for small rotational parameter, but it is highly compressed against the upper and lower walls for high rotational speed.
VL  - 6
IS  - 5
ER  -

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Author Information

Nazmul Islam

Mathematics Discipline, Science, Engineering and Technology School, Khulna University, Khulna, Bangladesh
Lasker Ershad Ali

Mathematics Discipline, Science, Engineering and Technology School, Khulna University, Khulna, Bangladesh
Ariful Islam

Department of Chemical Engineering, Newcastle Institute for Energy and Resources, University of Newcastle, Newcastle, Australia

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Plain Text BibTeX RIS

APA Style

Nazmul Islam, Lasker Ershad Ali, Ariful Islam. (2018). Rotational Effect on Viscous Fluid Flow through Rectangular Rotating Straight Duct. American Journal of Applied Mathematics, 6(5), 159-166. https://doi.org/10.11648/j.ajam.20180605.12

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ACS Style

Nazmul Islam; Lasker Ershad Ali; Ariful Islam. Rotational Effect on Viscous Fluid Flow through Rectangular Rotating Straight Duct. Am. J. Appl. Math. 2018, 6(5), 159-166. doi: 10.11648/j.ajam.20180605.12

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AMA Style

Nazmul Islam, Lasker Ershad Ali, Ariful Islam. Rotational Effect on Viscous Fluid Flow through Rectangular Rotating Straight Duct. Am J Appl Math. 2018;6(5):159-166. doi: 10.11648/j.ajam.20180605.12

Copy | Download

@article{10.11648/j.ajam.20180605.12,
  author = {Nazmul Islam and Lasker Ershad Ali and Ariful Islam},
  title = {Rotational Effect on Viscous Fluid Flow through Rectangular Rotating Straight Duct},
  journal = {American Journal of Applied Mathematics},
  volume = {6},
  number = {5},
  pages = {159-166},
  doi = {10.11648/j.ajam.20180605.12},
  url = {https://doi.org/10.11648/j.ajam.20180605.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20180605.12},
  abstract = {In this paper, a numerical study has been done for fully developed laminar flow of an incompressible viscous fluid through a rotating straight duct with rectangular cross-section. The duct is rotated at a constant angular velocity around the vertical axis. The flow depends on the pressure driven parameter and the rotational parameter along with aspect ratio. The dimensionless non-linear equations are solved by using Spectral method where Chebyshev polynomial is adopted as a key tool. The calculations are carried out for different rotational parameter with a fixed aspect ratio at a constant pressure gradient parameter. The effect of rotational parameter has been observed for axial and secondary flows from the obtained results, which are shown in two dimensional contours and surface plots for axial flow whereas, two dimensional streamline plot, surface plot and vector plot for secondary flow. The asymmetry structure is seen in the axial flow pattern while the double vortex configuration is seen in the secondary flow structure, for all rotational parameter. However, the double vortex pattern in the secondary flow configuration is slightly compressed against the upper and lower walls of the duct for small rotational parameter, but it is highly compressed against the upper and lower walls for high rotational speed.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Rotational Effect on Viscous Fluid Flow through Rectangular Rotating Straight Duct
AU  - Nazmul Islam
AU  - Lasker Ershad Ali
AU  - Ariful Islam
Y1  - 2018/12/18
PY  - 2018
N1  - https://doi.org/10.11648/j.ajam.20180605.12
DO  - 10.11648/j.ajam.20180605.12
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 159
EP  - 166
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20180605.12
AB  - In this paper, a numerical study has been done for fully developed laminar flow of an incompressible viscous fluid through a rotating straight duct with rectangular cross-section. The duct is rotated at a constant angular velocity around the vertical axis. The flow depends on the pressure driven parameter and the rotational parameter along with aspect ratio. The dimensionless non-linear equations are solved by using Spectral method where Chebyshev polynomial is adopted as a key tool. The calculations are carried out for different rotational parameter with a fixed aspect ratio at a constant pressure gradient parameter. The effect of rotational parameter has been observed for axial and secondary flows from the obtained results, which are shown in two dimensional contours and surface plots for axial flow whereas, two dimensional streamline plot, surface plot and vector plot for secondary flow. The asymmetry structure is seen in the axial flow pattern while the double vortex configuration is seen in the secondary flow structure, for all rotational parameter. However, the double vortex pattern in the secondary flow configuration is slightly compressed against the upper and lower walls of the duct for small rotational parameter, but it is highly compressed against the upper and lower walls for high rotational speed.
VL  - 6
IS  - 5
ER  -

Copy | Download