Exact Solution of an MHD Natural Convection Flow in Vertical Concentric Annulus with Heat Absorption

Yusuf Samuel Taiwo

doi:doi:10.11648/j.ijfmts.20170305.12

| Peer-Reviewed

Exact Solution of an MHD Natural Convection Flow in Vertical Concentric Annulus with Heat Absorption

Yusuf Samuel Taiwo

Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 3, Issue 5)

Received: 8 March 2017 Accepted: 30 March 2017 Published: 28 November 2017

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

This paper presents an exact solution of a fully developed natural convection flow in a vertical concentric annulus in the presence of transverse magnetic field and heat absorption. The non-dimensional form of the equation governing the flow is first obtained and then the unified analytical solutions for the temperature field, velocity field, and skin-frictions as well as rate of heat transfer are obtained for both isothermal and constant heat flux case on the outer surface of the inner cylinder. The effect of various identified governing parameters on the flow was illustrated with the aid of line graphs. It is found that the magnitude of maximum fluid velocity is greater in the case of isothermal heating compared with the constant heat flux case when the gap between the cylinders is less or equal to radius of the inner cylinder. More also, the various values of the non-dimensional heat absorption parameter (H) and the corresponding values of annular gap where these fields are almost the same are presented in table 1.

Published in	International Journal of Fluid Mechanics & Thermal Sciences (Volume 3, Issue 5)
DOI	10.11648/j.ijfmts.20170305.12
Page(s)	52-61
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), 2024. Published by Science Publishing Group

Keywords

MHD, Natural Convection, Annulus, Heat Absorption, Isothermal, Isoflux

References

[1]	S. Kakac, W. Aung and R. Viskanta eds., Natural Convection: Fundamentals and Applications, Hemisphere Publishing, New York, 1986.
[2]	A, Bejan and A. D. Kraus, Heat transfer handbook, John Wiley & Sons, Inc., Hoboken, New Jersey, 2003.
[3]	J. S. Turner, Buoyancy Effects in Fluids, Cambridge University Press, Cambridge, 1973.
[4]	R. M. Inman: Experimental study of temperature distribution in laminar tube flow of a fluid with internal heat generation, Int. J. Heat Mass Transfer, Vol. 5(11), 1053-1054, 1962.
[5]	P. L. Chambre: The Laminar boundary layer with distributed heat sources or sinks, Appl. Sci. Res. Sec. A. Vol. 6(5), 393-401, 1957.
[6]	J. Modejski: Temperature distribution in channel flow with friction, Int. J. Heat Mass Transfer Vol. 6(1), 49-51, 1963.
[7]	H. L. Toor: The energy equation for viscous flow, Ind. Eng. Chem. Vol. 48(5), 922-926, 1956.
[8]	K. Vajravelu and J. Nayfeh: Hydromagnetic convection at a cone and a wedge. Int. Commun. Heat Mass Transfer, Vol. 19, 701-710, 1992.
[9]	O. Miyatake and T. Fujii: Free convection heat transfer between vertical plates - one plate isothermally heated and other thermally insulated. Heat Transfer Japan Res. Vol.1, 30-38, 1972.
[10]	H. Tanaka, O. Miyatake, T. Fujii and M. Fujii: Natural convection heat transfer between vertical parallel plates- one plate with a uniform heat flux and the other thermally insulated, Heat Transfer Japan Res. Vol. 2, 25-33, 1973.
[11]	B. K. Jha and A. O. Ajibade: Unsteady free convective Couette flow of heat generating/absorbing fluid. Int. J. Energy and Tech. Vol. 2(12), 1-9, 2010.
[12]	B. K. Jha and A. O. Ajibade: Free convection flow of heat generation/absorption fluid between vertical porous plates with periodic heat input. Int. comm. heat and mass transfer Vol. 36, 624-631, 2009.
[13]	S. Das, B. C. Sarkar and R. N. Jana: Radiation effects on free convection MHD Couette flow started exponentially with variable wall temperature in presence of heat generation. Open J. Fluid Dynamics. Vol. 2, 14-27, 2012.
[14]	C. Mandal, S. Das and R. N. Jana: Effect of radiation on transient natural convection flow between two vertical walls. Int. J. Appl. Inf. Systems. Vol. 2(2), 49-56, 2012.
[15]	S. Das, S. K. Guchhait and R. N. Jana: Radiation effects on unsteady MHD free convective Couette flow of heat generation/absorbing fluid. Int. J. Com. Appl. Vol. 39(3), 42-51, 2012.
[16]	A. J. Chamkha: hydromagnetics combined convection flow in a vertical lid-driven cavity with internal heat generation/absorption. Numer. Heat transfer A, Vol. 41, 529-546, 2002.
[17]	S. K. Singh, B. K. Jha and A. K. Singh: Natural convection in vertical concentric annulus under a radial magnetic field. Heat and mass transfer Vol. 32, 399-401, 1997.
[18]	B. Kalita: Unsteady free convection MHD flow and heat transfer between two heated vertical plates with heat source: an exact solution, J. Applied Mathematics & Bioinformatics, Vol. 2(3), 1-15, 2012.
[19]	R. K. Singh and A. K. Singh: Effect of induced magnetic field on natural convection in a vertical concentric annulus. Acta Mech. Sin. Vol. 28(2), 315-323, 2012.
[20]	D. Kumar, A. K. Singh, Effects of heat source/sink and induced magnetic field on natural convective flow in vertical concentric annuli, Alexandria Eng. J. (2016), http://dx.doi.org/10.1016/j.aej.2016.08.019.

Cite This Article

Plain Text BibTeX RIS

APA Style

Yusuf Samuel Taiwo. (2017). Exact Solution of an MHD Natural Convection Flow in Vertical Concentric Annulus with Heat Absorption. International Journal of Fluid Mechanics & Thermal Sciences, 3(5), 52-61. https://doi.org/10.11648/j.ijfmts.20170305.12

Copy | Download

ACS Style

Yusuf Samuel Taiwo. Exact Solution of an MHD Natural Convection Flow in Vertical Concentric Annulus with Heat Absorption. Int. J. Fluid Mech. Therm. Sci. 2017, 3(5), 52-61. doi: 10.11648/j.ijfmts.20170305.12

Copy | Download

AMA Style

Yusuf Samuel Taiwo. Exact Solution of an MHD Natural Convection Flow in Vertical Concentric Annulus with Heat Absorption. Int J Fluid Mech Therm Sci. 2017;3(5):52-61. doi: 10.11648/j.ijfmts.20170305.12

Copy | Download

@article{10.11648/j.ijfmts.20170305.12,
  author = {Yusuf Samuel Taiwo},
  title = {Exact Solution of an MHD Natural Convection Flow in Vertical Concentric Annulus with Heat Absorption},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {3},
  number = {5},
  pages = {52-61},
  doi = {10.11648/j.ijfmts.20170305.12},
  url = {https://doi.org/10.11648/j.ijfmts.20170305.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20170305.12},
  abstract = {This paper presents an exact solution of a fully developed natural convection flow in a vertical concentric annulus in the presence of transverse magnetic field and heat absorption. The non-dimensional form of the equation governing the flow is first obtained and then the unified analytical solutions for the temperature field, velocity field, and skin-frictions as well as rate of heat transfer are obtained for both isothermal and constant heat flux case on the outer surface of the inner cylinder. The effect of various identified governing parameters on the flow was illustrated with the aid of line graphs. It is found that the magnitude of maximum fluid velocity is greater in the case of isothermal heating compared with the constant heat flux case when the gap between the cylinders is less or equal to radius of the inner cylinder. More also, the various values of the non-dimensional heat absorption parameter (H) and the corresponding values of annular gap where these fields are almost the same are presented in table 1.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Exact Solution of an MHD Natural Convection Flow in Vertical Concentric Annulus with Heat Absorption
AU  - Yusuf Samuel Taiwo
Y1  - 2017/11/28
PY  - 2017
N1  - https://doi.org/10.11648/j.ijfmts.20170305.12
DO  - 10.11648/j.ijfmts.20170305.12
T2  - International Journal of Fluid Mechanics & Thermal Sciences
JF  - International Journal of Fluid Mechanics & Thermal Sciences
JO  - International Journal of Fluid Mechanics & Thermal Sciences
SP  - 52
EP  - 61
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20170305.12
AB  - This paper presents an exact solution of a fully developed natural convection flow in a vertical concentric annulus in the presence of transverse magnetic field and heat absorption. The non-dimensional form of the equation governing the flow is first obtained and then the unified analytical solutions for the temperature field, velocity field, and skin-frictions as well as rate of heat transfer are obtained for both isothermal and constant heat flux case on the outer surface of the inner cylinder. The effect of various identified governing parameters on the flow was illustrated with the aid of line graphs. It is found that the magnitude of maximum fluid velocity is greater in the case of isothermal heating compared with the constant heat flux case when the gap between the cylinders is less or equal to radius of the inner cylinder. More also, the various values of the non-dimensional heat absorption parameter (H) and the corresponding values of annular gap where these fields are almost the same are presented in table 1.
VL  - 3
IS  - 5
ER  -

Copy | Download

Author Information

Yusuf Samuel Taiwo

Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Yusuf Samuel Taiwo. (2017). Exact Solution of an MHD Natural Convection Flow in Vertical Concentric Annulus with Heat Absorption. International Journal of Fluid Mechanics & Thermal Sciences, 3(5), 52-61. https://doi.org/10.11648/j.ijfmts.20170305.12

Copy | Download

ACS Style

Yusuf Samuel Taiwo. Exact Solution of an MHD Natural Convection Flow in Vertical Concentric Annulus with Heat Absorption. Int. J. Fluid Mech. Therm. Sci. 2017, 3(5), 52-61. doi: 10.11648/j.ijfmts.20170305.12

Copy | Download

AMA Style

Yusuf Samuel Taiwo. Exact Solution of an MHD Natural Convection Flow in Vertical Concentric Annulus with Heat Absorption. Int J Fluid Mech Therm Sci. 2017;3(5):52-61. doi: 10.11648/j.ijfmts.20170305.12

Copy | Download

@article{10.11648/j.ijfmts.20170305.12,
  author = {Yusuf Samuel Taiwo},
  title = {Exact Solution of an MHD Natural Convection Flow in Vertical Concentric Annulus with Heat Absorption},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {3},
  number = {5},
  pages = {52-61},
  doi = {10.11648/j.ijfmts.20170305.12},
  url = {https://doi.org/10.11648/j.ijfmts.20170305.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20170305.12},
  abstract = {This paper presents an exact solution of a fully developed natural convection flow in a vertical concentric annulus in the presence of transverse magnetic field and heat absorption. The non-dimensional form of the equation governing the flow is first obtained and then the unified analytical solutions for the temperature field, velocity field, and skin-frictions as well as rate of heat transfer are obtained for both isothermal and constant heat flux case on the outer surface of the inner cylinder. The effect of various identified governing parameters on the flow was illustrated with the aid of line graphs. It is found that the magnitude of maximum fluid velocity is greater in the case of isothermal heating compared with the constant heat flux case when the gap between the cylinders is less or equal to radius of the inner cylinder. More also, the various values of the non-dimensional heat absorption parameter (H) and the corresponding values of annular gap where these fields are almost the same are presented in table 1.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Exact Solution of an MHD Natural Convection Flow in Vertical Concentric Annulus with Heat Absorption
AU  - Yusuf Samuel Taiwo
Y1  - 2017/11/28
PY  - 2017
N1  - https://doi.org/10.11648/j.ijfmts.20170305.12
DO  - 10.11648/j.ijfmts.20170305.12
T2  - International Journal of Fluid Mechanics & Thermal Sciences
JF  - International Journal of Fluid Mechanics & Thermal Sciences
JO  - International Journal of Fluid Mechanics & Thermal Sciences
SP  - 52
EP  - 61
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20170305.12
AB  - This paper presents an exact solution of a fully developed natural convection flow in a vertical concentric annulus in the presence of transverse magnetic field and heat absorption. The non-dimensional form of the equation governing the flow is first obtained and then the unified analytical solutions for the temperature field, velocity field, and skin-frictions as well as rate of heat transfer are obtained for both isothermal and constant heat flux case on the outer surface of the inner cylinder. The effect of various identified governing parameters on the flow was illustrated with the aid of line graphs. It is found that the magnitude of maximum fluid velocity is greater in the case of isothermal heating compared with the constant heat flux case when the gap between the cylinders is less or equal to radius of the inner cylinder. More also, the various values of the non-dimensional heat absorption parameter (H) and the corresponding values of annular gap where these fields are almost the same are presented in table 1.
VL  - 3
IS  - 5
ER  -

Copy | Download