Natural Convection in a Partially Heated and Cooled Square Enclosure Containing a Diamond Shaped Heated Block

Kakali Chowdhury; Abdul Alim; Murad Hossen

doi:doi:10.11648/j.ijfmts.20200601.11

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Natural Convection in a Partially Heated and Cooled Square Enclosure Containing a Diamond Shaped Heated Block

Kakali Chowdhury, Abdul Alim, Murad Hossen

Published in International Journal of Fluid Mechanics & Thermal Sciences (Volume 6, Issue 1)

Received: 20 November 2019 Accepted: 11 December 2019 Published: 6 January 2020

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Abstract

Finite element method is used to solve the two dimensional governing mass, momentum and energy equations for steady state, natural convection problem inside a square enclosure. The enclosure consists of adiabatic vertical walls, heated middle part of bottom wall and the cold (top wall and the rest part of bottom wall) walls and a uniformly heated diamond shaped solid body located somewhere inside the enclosure. The aim of this study is to describe the effect of different sizes and positions of diamond shaped heated block on natural convection. The investigations are conducted for different values of Rayleigh number (Ra), block length (l) and location of block center (C_x, C_y) inside the enclosure by using COMSOL multiphysics. Various results such as streamlines, isotherms, heat transfer rate in terms of the average Nusselt number and average fluid temperature inside the enclosure are presented for different parameters. The results indicate that the average Nusselt number at the heated surface and average temperature of the fluid inside the enclosure are strongly dependent on the configuration of the system under different geometrical and physical conditions. The average Nusselt number decreases with the increasing value of block size and increases in the free convection dominated region, it is maximum for Ra=10⁶ and minimum for Ra=10³. Block size also has significant effect on thermal fields. Average temperature increases with the increasing value of heated block.

Published in	International Journal of Fluid Mechanics & Thermal Sciences (Volume 6, Issue 1)
DOI	10.11648/j.ijfmts.20200601.11
Page(s)	1-8
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), 2020. Published by Science Publishing Group

Keywords

Natural Convection, Finite Element Method, Diamond Shaped Block, COMSOL Multiphysics

References

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[2]	Parvin S., Nasrin R. 2011. Analysis of the flow and heat transfer characteristics for MHD free convection in an enclosure with a heated obstacle. Nonlinear Analysis: Modeling and Control, Vol. 16, No. 1, 89-99.
[3]	Chowdhury, R., Khan, M. A. H., Siddiki, M. N. A. A., 2015. Natural Convection in Porous Triangular Enclosure with a Circular Obstacle in Presence of Heat Generation. American Journal of Applied Mathematics, 3 (2): pp. 51-58. Dechaumphai, P., 1999. Finite Element Method in Engineering, 2^nd ed. Chulalongkorn University Press, Bangkok.
[4]	House, J. M., Beckermann, C., Smith, T. F., 1990. Effect of a centered conducting body on natural convection heat transfer in an enclosure, Numerical Heat Transfer A-Appl., 18, pp. 213-225.
[5]	Kandaswamy, P., Lee, J., Hakeem A. K. A., 2007. Natural convection in a square cavity in presence of heated plate. Nonlinear Analysis: Modeling and Control, Vol. 12, No. 2, 203-212.
[6]	Mousa, M. M. 2010. Modeling of laminar buoyancy convection in a square cavity containing an obstacle. Mathematics Subject Classification: 65M60, 76D05, 80A20.
[7]	Rahman, M. M., Alim, M. A., Saha, S., Chowdhury, M. K., 2008. A numerical study of mixed convection in a square cavity with a heat conducting square cylinder at different locations. Journal of Mechanical Engineering, Vol. ME39, No. 2.
[8]	Saleh, H., Roslan, R., Hashim I., 2011. Natural convection heat transfer in a nanofluid-filled trapezoidal enclosure. International Journal of Heat and Mass Transfer. pp. 194-201, Issues 1-3, Vol. 54, Jan-2011.
[9]	Uddin, H., Saha, S., Hasan, M. N., 2008. Natural convection flows in a trapezoidal enclosure with isoflux heating from below. Proceedings of the 12th Annual Paper Meet, Paper ID: 182-EN08.
[10]	Roy, S., Basak, T., 2005. Finite element analysis of natural convection flows in a square cavity with non-uniformly heated wall (s) International Journal of Engineering Science 43 (2005) 668-680.
[11]	Billah, M. M., Rahman, M. M., Saidur, R., Hasanuzzaman, M. 2011. Simulation of MHD mixed convection heat transfer enhancement in a double lid driven obstructed enclosure. International Journal of Mechanical and Materials Engineering (IJMME). Vol. 6, No. 1, 18-30.
[12]	Oztop, H. F., Al-Salem, K, Pop I., 2011. MHD mixed convection in a lid driven cavity with corner heater. International Journal of heat and mass transfer 54, 3494-3504.
[13]	Basak, T., Predeep, P. V. K., Roy, S., Pop, I. 2011. Finite element based heatline approach to study mixed convection in a porous square cavity with various wall thermal boundary conditions. International Journal of heat and mass transfer. 54, 1706-1727.
[14]	Nasrin, R. 2011. Mixed magnetoconvection in a lid driven cavity with a sinusoidal wavy wall and a central heat conducting body. Journal of naval architecture and marine engineering. DOI: 10.3329/jname.v8il.6793.
[15]	Kabir, K. H., Alim, M. A., Andallah L. S. 2013. Effects of viscous dissipation on MHD natural convection flow along a vertical wavy surface. Journal of Theoritical and Applied Physics. Doi: 10.1186/2251-7235-7-31.

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APA Style

Kakali Chowdhury, Abdul Alim, Murad Hossen. (2020). Natural Convection in a Partially Heated and Cooled Square Enclosure Containing a Diamond Shaped Heated Block. International Journal of Fluid Mechanics & Thermal Sciences, 6(1), 1-8. https://doi.org/10.11648/j.ijfmts.20200601.11

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ACS Style

Kakali Chowdhury; Abdul Alim; Murad Hossen. Natural Convection in a Partially Heated and Cooled Square Enclosure Containing a Diamond Shaped Heated Block. Int. J. Fluid Mech. Therm. Sci. 2020, 6(1), 1-8. doi: 10.11648/j.ijfmts.20200601.11

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AMA Style

Kakali Chowdhury, Abdul Alim, Murad Hossen. Natural Convection in a Partially Heated and Cooled Square Enclosure Containing a Diamond Shaped Heated Block. Int J Fluid Mech Therm Sci. 2020;6(1):1-8. doi: 10.11648/j.ijfmts.20200601.11

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@article{10.11648/j.ijfmts.20200601.11,
  author = {Kakali Chowdhury and Abdul Alim and Murad Hossen},
  title = {Natural Convection in a Partially Heated and Cooled Square Enclosure Containing a Diamond Shaped Heated Block},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {6},
  number = {1},
  pages = {1-8},
  doi = {10.11648/j.ijfmts.20200601.11},
  url = {https://doi.org/10.11648/j.ijfmts.20200601.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20200601.11},
  abstract = {Finite element method is used to solve the two dimensional governing mass, momentum and energy equations for steady state, natural convection problem inside a square enclosure. The enclosure consists of adiabatic vertical walls, heated middle part of bottom wall and the cold (top wall and the rest part of bottom wall) walls and a uniformly heated diamond shaped solid body located somewhere inside the enclosure. The aim of this study is to describe the effect of different sizes and positions of diamond shaped heated block on natural convection. The investigations are conducted for different values of Rayleigh number (Ra), block length (l) and location of block center (Cx, Cy) inside the enclosure by using COMSOL multiphysics. Various results such as streamlines, isotherms, heat transfer rate in terms of the average Nusselt number and average fluid temperature inside the enclosure are presented for different parameters. The results indicate that the average Nusselt number at the heated surface and average temperature of the fluid inside the enclosure are strongly dependent on the configuration of the system under different geometrical and physical conditions. The average Nusselt number decreases with the increasing value of block size and increases in the free convection dominated region, it is maximum for Ra=106 and minimum for Ra=103. Block size also has significant effect on thermal fields. Average temperature increases with the increasing value of heated block.},
 year = {2020}
}

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TY  - JOUR
T1  - Natural Convection in a Partially Heated and Cooled Square Enclosure Containing a Diamond Shaped Heated Block
AU  - Kakali Chowdhury
AU  - Abdul Alim
AU  - Murad Hossen
Y1  - 2020/01/06
PY  - 2020
N1  - https://doi.org/10.11648/j.ijfmts.20200601.11
DO  - 10.11648/j.ijfmts.20200601.11
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  - 1
EP  - 8
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20200601.11
AB  - Finite element method is used to solve the two dimensional governing mass, momentum and energy equations for steady state, natural convection problem inside a square enclosure. The enclosure consists of adiabatic vertical walls, heated middle part of bottom wall and the cold (top wall and the rest part of bottom wall) walls and a uniformly heated diamond shaped solid body located somewhere inside the enclosure. The aim of this study is to describe the effect of different sizes and positions of diamond shaped heated block on natural convection. The investigations are conducted for different values of Rayleigh number (Ra), block length (l) and location of block center (Cx, Cy) inside the enclosure by using COMSOL multiphysics. Various results such as streamlines, isotherms, heat transfer rate in terms of the average Nusselt number and average fluid temperature inside the enclosure are presented for different parameters. The results indicate that the average Nusselt number at the heated surface and average temperature of the fluid inside the enclosure are strongly dependent on the configuration of the system under different geometrical and physical conditions. The average Nusselt number decreases with the increasing value of block size and increases in the free convection dominated region, it is maximum for Ra=106 and minimum for Ra=103. Block size also has significant effect on thermal fields. Average temperature increases with the increasing value of heated block.
VL  - 6
IS  - 1
ER  -

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Author Information

Kakali Chowdhury

Department of Electrical & Computer Engineering, Presidency University, Banani, Dhaka, Bangladesh
Abdul Alim

Department of Mathematics, Bangladesh University of Engineering & Technology, Dhaka, Bangladesh
Murad Hossen

Department of Electrical & Computer Engineering, Presidency University, Banani, Dhaka, Bangladesh

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APA Style

Kakali Chowdhury, Abdul Alim, Murad Hossen. (2020). Natural Convection in a Partially Heated and Cooled Square Enclosure Containing a Diamond Shaped Heated Block. International Journal of Fluid Mechanics & Thermal Sciences, 6(1), 1-8. https://doi.org/10.11648/j.ijfmts.20200601.11

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ACS Style

Kakali Chowdhury; Abdul Alim; Murad Hossen. Natural Convection in a Partially Heated and Cooled Square Enclosure Containing a Diamond Shaped Heated Block. Int. J. Fluid Mech. Therm. Sci. 2020, 6(1), 1-8. doi: 10.11648/j.ijfmts.20200601.11

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AMA Style

Kakali Chowdhury, Abdul Alim, Murad Hossen. Natural Convection in a Partially Heated and Cooled Square Enclosure Containing a Diamond Shaped Heated Block. Int J Fluid Mech Therm Sci. 2020;6(1):1-8. doi: 10.11648/j.ijfmts.20200601.11

Copy | Download

@article{10.11648/j.ijfmts.20200601.11,
  author = {Kakali Chowdhury and Abdul Alim and Murad Hossen},
  title = {Natural Convection in a Partially Heated and Cooled Square Enclosure Containing a Diamond Shaped Heated Block},
  journal = {International Journal of Fluid Mechanics & Thermal Sciences},
  volume = {6},
  number = {1},
  pages = {1-8},
  doi = {10.11648/j.ijfmts.20200601.11},
  url = {https://doi.org/10.11648/j.ijfmts.20200601.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfmts.20200601.11},
  abstract = {Finite element method is used to solve the two dimensional governing mass, momentum and energy equations for steady state, natural convection problem inside a square enclosure. The enclosure consists of adiabatic vertical walls, heated middle part of bottom wall and the cold (top wall and the rest part of bottom wall) walls and a uniformly heated diamond shaped solid body located somewhere inside the enclosure. The aim of this study is to describe the effect of different sizes and positions of diamond shaped heated block on natural convection. The investigations are conducted for different values of Rayleigh number (Ra), block length (l) and location of block center (Cx, Cy) inside the enclosure by using COMSOL multiphysics. Various results such as streamlines, isotherms, heat transfer rate in terms of the average Nusselt number and average fluid temperature inside the enclosure are presented for different parameters. The results indicate that the average Nusselt number at the heated surface and average temperature of the fluid inside the enclosure are strongly dependent on the configuration of the system under different geometrical and physical conditions. The average Nusselt number decreases with the increasing value of block size and increases in the free convection dominated region, it is maximum for Ra=106 and minimum for Ra=103. Block size also has significant effect on thermal fields. Average temperature increases with the increasing value of heated block.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Natural Convection in a Partially Heated and Cooled Square Enclosure Containing a Diamond Shaped Heated Block
AU  - Kakali Chowdhury
AU  - Abdul Alim
AU  - Murad Hossen
Y1  - 2020/01/06
PY  - 2020
N1  - https://doi.org/10.11648/j.ijfmts.20200601.11
DO  - 10.11648/j.ijfmts.20200601.11
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  - 1
EP  - 8
PB  - Science Publishing Group
SN  - 2469-8113
UR  - https://doi.org/10.11648/j.ijfmts.20200601.11
AB  - Finite element method is used to solve the two dimensional governing mass, momentum and energy equations for steady state, natural convection problem inside a square enclosure. The enclosure consists of adiabatic vertical walls, heated middle part of bottom wall and the cold (top wall and the rest part of bottom wall) walls and a uniformly heated diamond shaped solid body located somewhere inside the enclosure. The aim of this study is to describe the effect of different sizes and positions of diamond shaped heated block on natural convection. The investigations are conducted for different values of Rayleigh number (Ra), block length (l) and location of block center (Cx, Cy) inside the enclosure by using COMSOL multiphysics. Various results such as streamlines, isotherms, heat transfer rate in terms of the average Nusselt number and average fluid temperature inside the enclosure are presented for different parameters. The results indicate that the average Nusselt number at the heated surface and average temperature of the fluid inside the enclosure are strongly dependent on the configuration of the system under different geometrical and physical conditions. The average Nusselt number decreases with the increasing value of block size and increases in the free convection dominated region, it is maximum for Ra=106 and minimum for Ra=103. Block size also has significant effect on thermal fields. Average temperature increases with the increasing value of heated block.
VL  - 6
IS  - 1
ER  -

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