In the present study the effect of natural convection in a rectangular cavity with three square shape heated block is focused in this numerical is studied. The horizontal bottom wall and three square blocks are temperature Th while the left and right vertical walls and horizontal top wall are temperature Tc with Th>Tc. The governing equations along with appropriate boundary conditions for the present problem are first transformed into a non-dimensional form and the resulting non linear system of partial differential equations are then solved numerically using Galerkin’s finite element method. Parametric studies of the fluid flow and heat transfer in the enclosure are performed for magnetic parameter Hartmann number Ha, Prandtl number Pr and Rayleigh number Ra. The streamlines, isotherms and average Nusselt number at the hot wall and average temperature of the fluid in the enclosure are presented for the parameters. The numerical results indicate that the Hartmann number and Rayleigh number have strong influence on the streamlines and isotherms. On the other hand Prandtl has little effect on the stream line and isotherm plots. Finally, the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the cavity.
| Published in | International Journal of Theoretical and Applied Mathematics (Volume 5, Issue 6) |
| DOI | 10.11648/j.ijtam.20190506.11 |
| Page(s) | 74-82 |
| 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 |
Finite Element Method, Numerical Simulation, Natural Convection and Square Block, Rectangular Cavity
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APA Style
Md. Raihanul Haque, Md. Abdul Alim, Md. Mahmud Alam, Md. Shahidul Alam. (2019). Magneto Hydrodynamics Free Convection in a Rectangular Enclosure with Three Square Heated Block. International Journal of Theoretical and Applied Mathematics, 5(6), 74-82. https://doi.org/10.11648/j.ijtam.20190506.11
ACS Style
Md. Raihanul Haque; Md. Abdul Alim; Md. Mahmud Alam; Md. Shahidul Alam. Magneto Hydrodynamics Free Convection in a Rectangular Enclosure with Three Square Heated Block. Int. J. Theor. Appl. Math. 2019, 5(6), 74-82. doi: 10.11648/j.ijtam.20190506.11
AMA Style
Md. Raihanul Haque, Md. Abdul Alim, Md. Mahmud Alam, Md. Shahidul Alam. Magneto Hydrodynamics Free Convection in a Rectangular Enclosure with Three Square Heated Block. Int J Theor Appl Math. 2019;5(6):74-82. doi: 10.11648/j.ijtam.20190506.11
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Download@article{10.11648/j.ijtam.20190506.11,
author = {Md. Raihanul Haque and Md. Abdul Alim and Md. Mahmud Alam and Md. Shahidul Alam},
title = {Magneto Hydrodynamics Free Convection in a Rectangular Enclosure with Three Square Heated Block},
journal = {International Journal of Theoretical and Applied Mathematics},
volume = {5},
number = {6},
pages = {74-82},
doi = {10.11648/j.ijtam.20190506.11},
url = {https://doi.org/10.11648/j.ijtam.20190506.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20190506.11},
abstract = {In the present study the effect of natural convection in a rectangular cavity with three square shape heated block is focused in this numerical is studied. The horizontal bottom wall and three square blocks are temperature Th while the left and right vertical walls and horizontal top wall are temperature Tc with Th>Tc. The governing equations along with appropriate boundary conditions for the present problem are first transformed into a non-dimensional form and the resulting non linear system of partial differential equations are then solved numerically using Galerkin’s finite element method. Parametric studies of the fluid flow and heat transfer in the enclosure are performed for magnetic parameter Hartmann number Ha, Prandtl number Pr and Rayleigh number Ra. The streamlines, isotherms and average Nusselt number at the hot wall and average temperature of the fluid in the enclosure are presented for the parameters. The numerical results indicate that the Hartmann number and Rayleigh number have strong influence on the streamlines and isotherms. On the other hand Prandtl has little effect on the stream line and isotherm plots. Finally, the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the cavity.},
year = {2019}
}
TY - JOUR T1 - Magneto Hydrodynamics Free Convection in a Rectangular Enclosure with Three Square Heated Block AU - Md. Raihanul Haque AU - Md. Abdul Alim AU - Md. Mahmud Alam AU - Md. Shahidul Alam Y1 - 2019/11/21 PY - 2019 N1 - https://doi.org/10.11648/j.ijtam.20190506.11 DO - 10.11648/j.ijtam.20190506.11 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 - 74 EP - 82 PB - Science Publishing Group SN - 2575-5080 UR - https://doi.org/10.11648/j.ijtam.20190506.11 AB - In the present study the effect of natural convection in a rectangular cavity with three square shape heated block is focused in this numerical is studied. The horizontal bottom wall and three square blocks are temperature Th while the left and right vertical walls and horizontal top wall are temperature Tc with Th>Tc. The governing equations along with appropriate boundary conditions for the present problem are first transformed into a non-dimensional form and the resulting non linear system of partial differential equations are then solved numerically using Galerkin’s finite element method. Parametric studies of the fluid flow and heat transfer in the enclosure are performed for magnetic parameter Hartmann number Ha, Prandtl number Pr and Rayleigh number Ra. The streamlines, isotherms and average Nusselt number at the hot wall and average temperature of the fluid in the enclosure are presented for the parameters. The numerical results indicate that the Hartmann number and Rayleigh number have strong influence on the streamlines and isotherms. On the other hand Prandtl has little effect on the stream line and isotherm plots. Finally, the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the cavity. VL - 5 IS - 6 ER -
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