Numerical Simulation of Natural Convection in a Rectangular Cavity with Heated Triangle and Internal Heat Generation

Md. Shirazul Hoque Mollah; Md. Shahidul Alam; Md. Abdul Alim

doi:doi:10.11648/j.ijtam.20190503.12

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Numerical Simulation of Natural Convection in a Rectangular Cavity with Heated Triangle and Internal Heat Generation

Md. Shirazul Hoque Mollah, Md. Shahidul Alam, Md. Abdul Alim

Published in International Journal of Theoretical and Applied Mathematics (Volume 5, Issue 3)

Received: 9 August 2019 Accepted: 18 September 2019 Published: 9 October 2019

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Abstract

Free convection flow and heat transfer in a rectangular cavity with heated triangle and internal heat generation is investigated numerically. 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 equal sections. The middle section of the horizontal bottom wall, bottom side of the triangle and left vertical left wall in the enclosure were kept temperature at T_h. The other two parts of the horizontal bottom wall and the other two sides of the triangle were kept thermal insulation while the right vertical walls and the top wall of the cavity were maintained constant temperature T_c with T_h>T_c. The physical problems are represented mathematically by different sets of governing equations along with corresponding boundary conditions. The dimensionless Parameters in the equations are performed for Heat generation (λ), Rayleigh number (Ra) and Prandtl number (Pr). The streamlines, isotherms, average Nusselt number, velocity profiles and temperature distribution of the fluid in the enclosure are presented graphically. The numerical results indicate that the Heat Generation 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	International Journal of Theoretical and Applied Mathematics (Volume 5, Issue 3)
DOI	10.11648/j.ijtam.20190503.12
Page(s)	44-56
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), 2019. Published by Science Publishing Group

Keywords

Finite Element Method, Heat Generation, Numerical Simulation, Natural Convection, Rectangle Cavity

References

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[12]	M. S. Alam, M. S. Alam, M. A. Alim, and M. S. H. Mollah, "Numerical Simulation of Natural Convection in a Rectangular Cavity with Triangles of Different Orientation in Presence of Magnetic Field," AIP Conference Proceedings 1851, 020037 doi: 10.1063/1.4984666, 2017.
[13]	M. S. Alam, M. S. Alam, M. 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, No. 6, pp 215-225, June 2017.
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APA Style

Md. Shirazul Hoque Mollah, Md. Shahidul Alam, Md. Abdul Alim. (2019). Numerical Simulation of Natural Convection in a Rectangular Cavity with Heated Triangle and Internal Heat Generation. International Journal of Theoretical and Applied Mathematics, 5(3), 44-56. https://doi.org/10.11648/j.ijtam.20190503.12

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ACS Style

Md. Shirazul Hoque Mollah; Md. Shahidul Alam; Md. Abdul Alim. Numerical Simulation of Natural Convection in a Rectangular Cavity with Heated Triangle and Internal Heat Generation. Int. J. Theor. Appl. Math. 2019, 5(3), 44-56. doi: 10.11648/j.ijtam.20190503.12

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AMA Style

Md. Shirazul Hoque Mollah, Md. Shahidul Alam, Md. Abdul Alim. Numerical Simulation of Natural Convection in a Rectangular Cavity with Heated Triangle and Internal Heat Generation. Int J Theor Appl Math. 2019;5(3):44-56. doi: 10.11648/j.ijtam.20190503.12

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@article{10.11648/j.ijtam.20190503.12,
  author = {Md. Shirazul Hoque Mollah and Md. Shahidul Alam and Md. Abdul Alim},
  title = {Numerical Simulation of Natural Convection in a Rectangular Cavity with Heated Triangle and Internal Heat Generation},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {5},
  number = {3},
  pages = {44-56},
  doi = {10.11648/j.ijtam.20190503.12},
  url = {https://doi.org/10.11648/j.ijtam.20190503.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20190503.12},
  abstract = {Free convection flow and heat transfer in a rectangular cavity with heated triangle and internal heat generation is investigated numerically. 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 equal sections. The middle section of the horizontal bottom wall, bottom side of the triangle and left vertical left wall in the enclosure were kept temperature at Th. The other two parts of the horizontal bottom wall and the other two sides of the triangle were kept thermal insulation while the right vertical walls and the top wall of the cavity were maintained constant temperature Tc with Th>Tc. The physical problems are represented mathematically by different sets of governing equations along with corresponding boundary conditions. The dimensionless Parameters in the equations are performed for Heat generation (λ), Rayleigh number (Ra) and Prandtl number (Pr). The streamlines, isotherms, average Nusselt number, velocity profiles and temperature distribution of the fluid in the enclosure are presented graphically. The numerical results indicate that the Heat Generation 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 = {2019}
}

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TY - JOUR
T1 - Numerical Simulation of Natural Convection in a Rectangular Cavity with Heated Triangle and Internal Heat Generation
AU - Md. Shirazul Hoque Mollah
AU - Md. Shahidul Alam
AU - Md. Abdul Alim
Y1 - 2019/10/09
PY - 2019
N1 - https://doi.org/10.11648/j.ijtam.20190503.12
DO - 10.11648/j.ijtam.20190503.12
T2 - International Journal of Theoretical and Applied Mathematics
JF - International Journal of Theoretical and Applied Mathematics
JO - International Journal of Theoretical and Applied Mathematics
SP - 44
EP - 56
PB - Science Publishing Group
SN - 2575-5080
UR - https://doi.org/10.11648/j.ijtam.20190503.12
AB - Free convection flow and heat transfer in a rectangular cavity with heated triangle and internal heat generation is investigated numerically. 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 equal sections. The middle section of the horizontal bottom wall, bottom side of the triangle and left vertical left wall in the enclosure were kept temperature at Th. The other two parts of the horizontal bottom wall and the other two sides of the triangle were kept thermal insulation while the right vertical walls and the top wall of the cavity were maintained constant temperature Tc with Th>Tc. The physical problems are represented mathematically by different sets of governing equations along with corresponding boundary conditions. The dimensionless Parameters in the equations are performed for Heat generation (λ), Rayleigh number (Ra) and Prandtl number (Pr). The streamlines, isotherms, average Nusselt number, velocity profiles and temperature distribution of the fluid in the enclosure are presented graphically. The numerical results indicate that the Heat Generation 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 - 5
IS - 3
ER -

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Author Information

Md. Shirazul Hoque Mollah

Department of Mathematics, Dhaka University of Engineering & Technology, Gazipur, Bangladesh
Md. Shahidul Alam

Department of Mathematics, Dhaka University of Engineering & Technology, Gazipur, Bangladesh
Md. Abdul Alim

Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka, Bangladesh

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APA Style

Md. Shirazul Hoque Mollah, Md. Shahidul Alam, Md. Abdul Alim. (2019). Numerical Simulation of Natural Convection in a Rectangular Cavity with Heated Triangle and Internal Heat Generation. International Journal of Theoretical and Applied Mathematics, 5(3), 44-56. https://doi.org/10.11648/j.ijtam.20190503.12

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ACS Style

Md. Shirazul Hoque Mollah; Md. Shahidul Alam; Md. Abdul Alim. Numerical Simulation of Natural Convection in a Rectangular Cavity with Heated Triangle and Internal Heat Generation. Int. J. Theor. Appl. Math. 2019, 5(3), 44-56. doi: 10.11648/j.ijtam.20190503.12

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AMA Style

Md. Shirazul Hoque Mollah, Md. Shahidul Alam, Md. Abdul Alim. Numerical Simulation of Natural Convection in a Rectangular Cavity with Heated Triangle and Internal Heat Generation. Int J Theor Appl Math. 2019;5(3):44-56. doi: 10.11648/j.ijtam.20190503.12

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@article{10.11648/j.ijtam.20190503.12,
  author = {Md. Shirazul Hoque Mollah and Md. Shahidul Alam and Md. Abdul Alim},
  title = {Numerical Simulation of Natural Convection in a Rectangular Cavity with Heated Triangle and Internal Heat Generation},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {5},
  number = {3},
  pages = {44-56},
  doi = {10.11648/j.ijtam.20190503.12},
  url = {https://doi.org/10.11648/j.ijtam.20190503.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20190503.12},
  abstract = {Free convection flow and heat transfer in a rectangular cavity with heated triangle and internal heat generation is investigated numerically. 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 equal sections. The middle section of the horizontal bottom wall, bottom side of the triangle and left vertical left wall in the enclosure were kept temperature at Th. The other two parts of the horizontal bottom wall and the other two sides of the triangle were kept thermal insulation while the right vertical walls and the top wall of the cavity were maintained constant temperature Tc with Th>Tc. The physical problems are represented mathematically by different sets of governing equations along with corresponding boundary conditions. The dimensionless Parameters in the equations are performed for Heat generation (λ), Rayleigh number (Ra) and Prandtl number (Pr). The streamlines, isotherms, average Nusselt number, velocity profiles and temperature distribution of the fluid in the enclosure are presented graphically. The numerical results indicate that the Heat Generation 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 = {2019}
}

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