The flow and heat transfer due to natural convection in a triangular enclosure filled with a fluid saturated porous medium with a circular body in presence of heat generation has been numerically analyzed. The bottom wall of the enclosure is heated at a constant temperature while the left and right inclined wall of the cavity is maintained at cold temperature. The cavity contains a circular body which is insulated. The governing equations are solved numerically subject to suitable boundary conditions by Galerkin’s weighted residuals scheme of finite element method. Results are presented by streamlines, isotherms, mean Nusselt numbers for the variant parameters such as heat generation (λ) and radius of the circular body (R). Prandtl number (Pr) and Rayleigh number (Ra) are considered unchanged. It is found that these parameters have significant effect on the flow and temperature fields inside the cavity.
| Published in | American Journal of Applied Mathematics (Volume 3, Issue 2) |
| DOI | 10.11648/j.ajam.20150302.14 |
| Page(s) | 51-58 |
| 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), 2024. Published by Science Publishing Group |
Natural Convection, Heat Generation, Triangular Cavity, Circular Body, Porous Media
| [1] | D. A. Nield, A. Bejan, Convection in Porous Media, second ed., Springer, NY, 2006. |
| [2] | D. B. Ingham, I. Pop, Transport Phenomena in Porous Media II, Pergamon, 2005. |
| [3] | S. Ostrach, Natural convection in enclosures, Adv. Heat Transfer 8 (1972) 161-227. |
| [4] | M. A. Hossain, M. Wilson, Natural convection flow in a fluid-saturated porous medium enclosed by non-isothermal walls with heat generation, Int. J. Therm. Sci. 41 (2002) 447-454. |
| [5] | S. Parvin and R. Nasrin, Analysis of the Flow and Heat Transfer Characteristics for MHD Free Convection in an Enclosure with a Heated Obstacle, Nonlinear Analysis: Modelling and Control, 16 (2011) 89-99. |
| [6] | H. Asan, L. Namli, Laminar natural convection in a pitched roof of triangular cross-section: Summer day boundary conditions, Energy and Building 33 (2000) 69-73. |
| [7] | V. A. Akinsete, T. A. Coleman, Heat transfer by steady laminar free convection in triangular enclosures, Int. J. Heat Mass Transfer 25 (1982) 991-998. |
| [8] | Y. Varol, H. F. Oztop, A. Varol, Free convection in porous media filled right-angle triangular enclosures, Int. Comm. Heat Mass Transfer 33 (2006) 1190-1197. |
| [9] | A. C. Baytas, I. Pop, Free convection in oblique enclosures filled with a porous medium, Int. J. Heat Mass Transfer 42 (1999) 1047-1057. |
| [10] | Y. Varol, H. F. Oztop, Free convection in a shallow wavy enclosure, Int. Comm. Heat Mass Transfer 33 (2006) 764-771. |
| [11] | Y. Varol, A. Koca, H. F. Oztop, Numerical convection in a triangle enclosure with flush mounted heater on the wall, Int. Comm. Heat Mass Transfer 33 (2006) 951-958. |
| [12] | E. Ridouane, A Campo, M. Hasnaoui, Benefits derivable from connecting the bottom and top walls of attic enclosure with insulated vertical side walls, Numer. Heat Transfer Part A-Applications 49 (2006) 175-193. |
| [13] | K. A. Joudi, I. A. Hussein, A. A. Farhan, Computational model for a prism shaped storage solar collector with a right triangular cross section, Energy Conservation and Management 45 (2004) 391-409. |
| [14] | S. C. Tzeng, J. H. Liou, R. Y. Jou, Numerical simulation-aided parametric analysis of natural convection in a roof of triangular enclosures, Heat Transfer Engrg. 26 (2005) 69-79. |
| [15] | A. Bejan, D. Poulikakos, Natural convection in an attic-shaped space filled with porous material, J. Heat Transfer 104 (1982) 241-247. |
| [16] | Y. Varol, H. F. Oztop, A. Varol, Free convection in porous media filled right-angle triangular enclosures, Int. Comm. Heat Mass Transfer 33 (2006) 1190-1197. |
| [17] | T. Basak, C. Thirumalesha, S. Roy, Finite element simulations of natural convection in a right-angle triangular enclosure filled with a porous medium: effects of various thermal boundary conditions, J. Porous Media 11 (2008) 159-78. |
| [18] | Y. Varol, H.F.Oztop, T. Yilmaz, Two dimensional natural convection in a porous triangular enclosure with a square body, Int. Commun.Heat Mass Transfer 34 (2007) 238-247. |
| [19] | A. Amine, J.K. Platten, M. Hasnaoui, Thermal convection around obstacles: the case of Sierpinski carpets, Exp. Fluids 36 (2004) 717-727. |
| [20] | M.Y. Ha, I.K. Kim, H.S. Yoon, K.S. Yoon, J.R. Lee, S. Balachandar, H.H. Chun, Two-dimensional and unsteady natural convection in a horizontal enclosure with a square body, Numer. Heat Transf., A Appl. 41 (2002) 183-210. |
| [21] | H.F. Oztop, I. Dagtekin, M. Duranay, Analysis of natural convection problem in a cavity with partially heated and block inserted, Proceedings of 13rd Heat Science and Technology Congress, Turkey, 2001, pp. 217-222, (In Turkish). |
| [22] | Suvash C. Saha, Y. T. Gu, Free convection flow in a triangular enclosure with fluid-saturated porous medium enclosed with heat generation, J. ANZIAM 53 (2012) C127-C141. |
APA Style
Raju Chowdhury, Md. Abdul Hakim Khan, Md. Noor-A-Alam Siddiki. (2015). Natural Convection in Porous Triangular Enclosure with a Circular Obstacle in Presence of Heat Generation. American Journal of Applied Mathematics, 3(2), 51-58. https://doi.org/10.11648/j.ajam.20150302.14
ACS Style
Raju Chowdhury; Md. Abdul Hakim Khan; Md. Noor-A-Alam Siddiki. Natural Convection in Porous Triangular Enclosure with a Circular Obstacle in Presence of Heat Generation. Am. J. Appl. Math. 2015, 3(2), 51-58. doi: 10.11648/j.ajam.20150302.14
AMA Style
Raju Chowdhury, Md. Abdul Hakim Khan, Md. Noor-A-Alam Siddiki. Natural Convection in Porous Triangular Enclosure with a Circular Obstacle in Presence of Heat Generation. Am J Appl Math. 2015;3(2):51-58. doi: 10.11648/j.ajam.20150302.14
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Download@article{10.11648/j.ajam.20150302.14,
author = {Raju Chowdhury and Md. Abdul Hakim Khan and Md. Noor-A-Alam Siddiki},
title = {Natural Convection in Porous Triangular Enclosure with a Circular Obstacle in Presence of Heat Generation},
journal = {American Journal of Applied Mathematics},
volume = {3},
number = {2},
pages = {51-58},
doi = {10.11648/j.ajam.20150302.14},
url = {https://doi.org/10.11648/j.ajam.20150302.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150302.14},
abstract = {The flow and heat transfer due to natural convection in a triangular enclosure filled with a fluid saturated porous medium with a circular body in presence of heat generation has been numerically analyzed. The bottom wall of the enclosure is heated at a constant temperature while the left and right inclined wall of the cavity is maintained at cold temperature. The cavity contains a circular body which is insulated. The governing equations are solved numerically subject to suitable boundary conditions by Galerkin’s weighted residuals scheme of finite element method. Results are presented by streamlines, isotherms, mean Nusselt numbers for the variant parameters such as heat generation (λ) and radius of the circular body (R). Prandtl number (Pr) and Rayleigh number (Ra) are considered unchanged. It is found that these parameters have significant effect on the flow and temperature fields inside the cavity.},
year = {2015}
}
TY - JOUR T1 - Natural Convection in Porous Triangular Enclosure with a Circular Obstacle in Presence of Heat Generation AU - Raju Chowdhury AU - Md. Abdul Hakim Khan AU - Md. Noor-A-Alam Siddiki Y1 - 2015/03/21 PY - 2015 N1 - https://doi.org/10.11648/j.ajam.20150302.14 DO - 10.11648/j.ajam.20150302.14 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 51 EP - 58 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20150302.14 AB - The flow and heat transfer due to natural convection in a triangular enclosure filled with a fluid saturated porous medium with a circular body in presence of heat generation has been numerically analyzed. The bottom wall of the enclosure is heated at a constant temperature while the left and right inclined wall of the cavity is maintained at cold temperature. The cavity contains a circular body which is insulated. The governing equations are solved numerically subject to suitable boundary conditions by Galerkin’s weighted residuals scheme of finite element method. Results are presented by streamlines, isotherms, mean Nusselt numbers for the variant parameters such as heat generation (λ) and radius of the circular body (R). Prandtl number (Pr) and Rayleigh number (Ra) are considered unchanged. It is found that these parameters have significant effect on the flow and temperature fields inside the cavity. VL - 3 IS - 2 ER -
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