Finite Element Analysis of MHD Natural Convection in a Rectangular Cavity and Partially Heated Wall

Md. Shahidul Alam; Md. Shirazul Hoque Mollah; Md. Abdul Alim; Md. Kazi Humayun Kabir

doi:doi:10.11648/j.eas.20170203.12

| Peer-Reviewed

Finite Element Analysis of MHD Natural Convection in a Rectangular Cavity and Partially Heated Wall

Md. Shahidul Alam, Md. Shirazul Hoque Mollah, Md. Abdul Alim, Md. Kazi Humayun Kabir

Published in Engineering and Applied Sciences (Volume 2, Issue 3)

Received: 30 May 2017 Accepted: 16 June 2017 Published: 18 July 2017

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

In this paper numerical study is presented of two-dimensional laminar steady-state on megneto-hydrodynamics (MHD) free convection for heat flow patterns within rectangular enclosures. A finite element analysis is performed to investigate the effects of uniform heating and is also used for solving the Navier-Stokes and Energy balance equations. The horizontal bottom wall is divided into three sections. The middle section of the horizontal bottom wall was kept temperature at T_h and the other two parts of the horizontal bottom wall were kept thermal insulation while the left and right vertical walls and the top wall of the cavity were maintained constant temperature Tc with T_h>T_c. Parametric studies of the fluid flow and heat transfer in the enclosure are performed for magnetic parameter Hartmann number (Ha = 0, 50, 100), Rayleigh number (Ra = 10³ – 10⁶) and Prandtl number Pr=0.71. The streamlines, isotherms, average Nusselt number at the hot wall and velocity profiles and temperature distribution of the fluid in the enclosure are presented for the parameters. The numerical results indicated that the Hartmann number and Rayleigh number have strong influence on the streamlines and isotherms. Also the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the enclosure.

Published in	Engineering and Applied Sciences (Volume 2, Issue 3)
DOI	10.11648/j.eas.20170203.12
Page(s)	53-58
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

Free Convection, Magnetic Field, Rectangle Cavity, Numerical Solution

References

[1]	TanmayBasak, S. Roy, PawanKumer Sharma and I. Pop, Analysis of mixed convection flow within a square cavity with uniform and non-uniform heating of bottom wall, International Journal of Thermal Science, Vol. 48, pp. 891-912, 2009.
[2]	J. N. Reddy, An introduction to Finite element method, McGraw-Hill, New York, 1993.
[3]	L. Lyican and Y. Bayazitoglu, An analytical study of natural convective heat transfer within trapezoidal enclosure, ASME Trans. J. Heat transfer, Vol. 102, pp. 640-647, 1980.
[4]	S. Roy and T. Basak, Finite element analysis of natural convection flows in a square cavity with non- uniformly heated wall(s), Int. J. Engrg. Science, Vol. 45, pp. 668-680, 2005.
[5]	R. A. Kuyper and C. J. Hoogendoorn, Laminar natural convection flows in trapezoidal enclosures, Num. Heat transfer, A Vol. 28, pp. 55 – 67, 1995.
[6]	Y. Varol, H. F. Oztop and I. Pop, Numerical analysis of natural convection in an inclined trapezoidal enclosure filled with a porous medium, Int. J. Thermal Science, Vol. 47, No.10, pp. 1316-1331, 2008.
[7]	Y. Varol, H. F. Oztop and I. Pop, natural convection in right-angle porous trapezoidal enclosure with partially cooled from inclined wall. International Communications in Heat and Mass Transfer, Vol. 36, No. 1, pp. 6-15, 2009.
[8]	Hakan F. Oztop, Eiyad Abu-Nada, Yasin Varoland Ali Chamkha, Natural convection in wavy enclosures with volumetric heat sources, Int. J. Thermal Science, Vol. 50, pp. 502-514, 2011
[9]	Kamil Kahveci and Semiha Öztuna, MHD natural convection flow and heat transfer in a laterally heated partitioned enclosure, European Journal of Mechanics - B/Fluids Vol. 28(6), pp. 744-752, 2009.
[10]	Tanmay Basak, S. Roy and I. Pop, Heat flow analysis for natural convection within trapezoidal enclosures based on heatline concept, Int. J. Heat Mass Transfer, Vol. 52, pp. 2471-2483, 2009.
[11]	Md. M. Molla, M. A. Taher, Md. M. K. Chowdhury and Md. A. Hossain, Magnetohydrodynamic Natural Convection Flow on a sphere in Presence of Heat Generation, Nonlinear Analysis: Modelling and Control, Vol. 10, No. 4, pp. 349-363, 2005.
[12]	Nithyadevi, P. Kandaswamy, S. MalligaSundari, “Magnetoconvtion in a square cavity with partially active vertical walls: Time periodic Boundary condition,” Int. J. Heat Mass Tran., 52, 2009, pp. 1945-195.
[13]	M. Mahmoodi, Z. Talea’pour, “Magnetohydrodynamic Free Convection Heat Transfer in a Square Enclosure heated from side and cooled from the ceiling,” Computational Thermal Sciences, vol. 3, 2011, 219-226.
[14]	M. Hasanuzzaman, Hakan F. Öztop, M. M. Rahman, N. A. Rahim, R. Saidur, Y. Varol, “ Magnetohydrodynamic natural convection in trapezoidal cavities,” International Communications in Heat and Mass Transfer 39, 1384–1394, 2012.
[15]	M. M. Rahman, H. F. Oztop, R. Saidur, S. mekhilef and K. Al-Salem “Unsteady mixed convection in a porous media filled lid-driven cavity heated by a semi-circular heaters,” Thermal Science, Vol. 19, No. 5, pp. 1761-1768 Year 2015.
[16]	K. M. Rabbia, S. Sahaa, S. Mojumdera, M. M. Rahmanb, R. Saidurc and T. A. Ibrahimd Numerical investigation of pure mixed convection in a ferrofluid-filled lid-driven cavity for different heater configurations, Alexandria Engineering Journal, Volume 55, Issue 1, Pages 127–139, 2016.
[17]	O. S. K. Hamama, F. S. Sharif, M. N. Hidouri and T. al-Aqqad, Irreversibility investigation on MHD natural convection in a square cavity for different Prandtl numbers, African Journal of Physics Vol. 3 (4), pp. 090-104, 2016.
[18]	Md. Shahidul Alam, Md. S. H. Mollah, A. H. Bhuiyan and M. A. Alim, Numerical Simulation of Natural Convection in a Rectangular Cavity with Corner Heater in Presence of Magnetic Field, Journal of Computer and Mathematical Sciences, Vol. 8(6), 215-225 2017.

Cite This Article

Plain Text BibTeX RIS

APA Style

Md. Shahidul Alam, Md. Shirazul Hoque Mollah, Md. Abdul Alim, Md. Kazi Humayun Kabir. (2017). Finite Element Analysis of MHD Natural Convection in a Rectangular Cavity and Partially Heated Wall. Engineering and Applied Sciences, 2(3), 53-58. https://doi.org/10.11648/j.eas.20170203.12

Copy | Download

ACS Style

Md. Shahidul Alam; Md. Shirazul Hoque Mollah; Md. Abdul Alim; Md. Kazi Humayun Kabir. Finite Element Analysis of MHD Natural Convection in a Rectangular Cavity and Partially Heated Wall. Eng. Appl. Sci. 2017, 2(3), 53-58. doi: 10.11648/j.eas.20170203.12

Copy | Download

AMA Style

Md. Shahidul Alam, Md. Shirazul Hoque Mollah, Md. Abdul Alim, Md. Kazi Humayun Kabir. Finite Element Analysis of MHD Natural Convection in a Rectangular Cavity and Partially Heated Wall. Eng Appl Sci. 2017;2(3):53-58. doi: 10.11648/j.eas.20170203.12

Copy | Download

@article{10.11648/j.eas.20170203.12,
  author = {Md. Shahidul Alam and Md. Shirazul Hoque Mollah and Md. Abdul Alim and Md. Kazi Humayun Kabir},
  title = {Finite Element Analysis of MHD Natural Convection in a Rectangular Cavity and Partially Heated Wall},
  journal = {Engineering and Applied Sciences},
  volume = {2},
  number = {3},
  pages = {53-58},
  doi = {10.11648/j.eas.20170203.12},
  url = {https://doi.org/10.11648/j.eas.20170203.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.eas.20170203.12},
  abstract = {In this paper numerical study is presented of two-dimensional laminar steady-state on megneto-hydrodynamics (MHD) free convection for heat flow patterns within rectangular enclosures. A finite element analysis is performed to investigate the effects of uniform heating and is also used for solving the Navier-Stokes and Energy balance equations. The horizontal bottom wall is divided into three sections. The middle section of the horizontal bottom wall was kept temperature at Th and the other two parts of the horizontal bottom wall were kept thermal insulation while the left and right vertical walls and the top wall of the cavity were maintained constant temperature Tc with Th>Tc. Parametric studies of the fluid flow and heat transfer in the enclosure are performed for magnetic parameter Hartmann number (Ha = 0, 50, 100), Rayleigh number (Ra = 103 – 106) and Prandtl number Pr=0.71. The streamlines, isotherms, average Nusselt number at the hot wall and velocity profiles and temperature distribution of the fluid in the enclosure are presented for the parameters. The numerical results indicated that the Hartmann number and Rayleigh number have strong influence on the streamlines and isotherms. Also the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the enclosure.},
 year = {2017}
}

Copy | Download

TY - JOUR
T1 - Finite Element Analysis of MHD Natural Convection in a Rectangular Cavity and Partially Heated Wall
AU - Md. Shahidul Alam
AU - Md. Shirazul Hoque Mollah
AU - Md. Abdul Alim
AU - Md. Kazi Humayun Kabir
Y1 - 2017/07/18
PY - 2017
N1 - https://doi.org/10.11648/j.eas.20170203.12
DO - 10.11648/j.eas.20170203.12
T2 - Engineering and Applied Sciences
JF - Engineering and Applied Sciences
JO - Engineering and Applied Sciences
SP - 53
EP - 58
PB - Science Publishing Group
SN - 2575-1468
UR - https://doi.org/10.11648/j.eas.20170203.12
AB - In this paper numerical study is presented of two-dimensional laminar steady-state on megneto-hydrodynamics (MHD) free convection for heat flow patterns within rectangular enclosures. A finite element analysis is performed to investigate the effects of uniform heating and is also used for solving the Navier-Stokes and Energy balance equations. The horizontal bottom wall is divided into three sections. The middle section of the horizontal bottom wall was kept temperature at Th and the other two parts of the horizontal bottom wall were kept thermal insulation while the left and right vertical walls and the top wall of the cavity were maintained constant temperature Tc with Th>Tc. Parametric studies of the fluid flow and heat transfer in the enclosure are performed for magnetic parameter Hartmann number (Ha = 0, 50, 100), Rayleigh number (Ra = 103 – 106) and Prandtl number Pr=0.71. The streamlines, isotherms, average Nusselt number at the hot wall and velocity profiles and temperature distribution of the fluid in the enclosure are presented for the parameters. The numerical results indicated that the Hartmann number and Rayleigh number have strong influence on the streamlines and isotherms. Also the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the enclosure.
VL - 2
IS - 3
ER -

Copy | Download

Author Information

Md. Shahidul Alam

Department of Mathematics, Dhaka University of Engineering and Technology, (DUET), Gazipur, Bangladesh
Md. Shirazul Hoque Mollah

Department of Mathematics, Dhaka University of Engineering and Technology, (DUET), Gazipur, Bangladesh
Md. Abdul Alim

Department of Mathematics, Bangladesh University of Engineering and Technology, (BUET), Dhaka, Bangladesh
Md. Kazi Humayun Kabir

Department of Mathematics, Mohammadpur Kendriya College (MKC), Dhaka, Bangladesh

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Md. Shahidul Alam, Md. Shirazul Hoque Mollah, Md. Abdul Alim, Md. Kazi Humayun Kabir. (2017). Finite Element Analysis of MHD Natural Convection in a Rectangular Cavity and Partially Heated Wall. Engineering and Applied Sciences, 2(3), 53-58. https://doi.org/10.11648/j.eas.20170203.12

Copy | Download

ACS Style

Md. Shahidul Alam; Md. Shirazul Hoque Mollah; Md. Abdul Alim; Md. Kazi Humayun Kabir. Finite Element Analysis of MHD Natural Convection in a Rectangular Cavity and Partially Heated Wall. Eng. Appl. Sci. 2017, 2(3), 53-58. doi: 10.11648/j.eas.20170203.12

Copy | Download

AMA Style

Md. Shahidul Alam, Md. Shirazul Hoque Mollah, Md. Abdul Alim, Md. Kazi Humayun Kabir. Finite Element Analysis of MHD Natural Convection in a Rectangular Cavity and Partially Heated Wall. Eng Appl Sci. 2017;2(3):53-58. doi: 10.11648/j.eas.20170203.12

Copy | Download

@article{10.11648/j.eas.20170203.12,
  author = {Md. Shahidul Alam and Md. Shirazul Hoque Mollah and Md. Abdul Alim and Md. Kazi Humayun Kabir},
  title = {Finite Element Analysis of MHD Natural Convection in a Rectangular Cavity and Partially Heated Wall},
  journal = {Engineering and Applied Sciences},
  volume = {2},
  number = {3},
  pages = {53-58},
  doi = {10.11648/j.eas.20170203.12},
  url = {https://doi.org/10.11648/j.eas.20170203.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.eas.20170203.12},
  abstract = {In this paper numerical study is presented of two-dimensional laminar steady-state on megneto-hydrodynamics (MHD) free convection for heat flow patterns within rectangular enclosures. A finite element analysis is performed to investigate the effects of uniform heating and is also used for solving the Navier-Stokes and Energy balance equations. The horizontal bottom wall is divided into three sections. The middle section of the horizontal bottom wall was kept temperature at Th and the other two parts of the horizontal bottom wall were kept thermal insulation while the left and right vertical walls and the top wall of the cavity were maintained constant temperature Tc with Th>Tc. Parametric studies of the fluid flow and heat transfer in the enclosure are performed for magnetic parameter Hartmann number (Ha = 0, 50, 100), Rayleigh number (Ra = 103 – 106) and Prandtl number Pr=0.71. The streamlines, isotherms, average Nusselt number at the hot wall and velocity profiles and temperature distribution of the fluid in the enclosure are presented for the parameters. The numerical results indicated that the Hartmann number and Rayleigh number have strong influence on the streamlines and isotherms. Also the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the enclosure.},
 year = {2017}
}

Copy | Download