In this paper, the numerical solution of mixed convective laminar boundary layer flow around a vertical slender body with suction or blowing has been investigated. Firstly, the governing boundary layer partial differential equations have been made dimensionless and then simplified by using Boussinesq approximation. Secondly, similarity transformations are introduced on the basis of detailed analysis in order to transform the simplified coupled partial differential equations into a set of ordinary differential equations. The transformed complete similarity equations are solved numerically by using computer software. Finally, the flow phenomenon has been characterized with the help of obtained flow controlling parameters such as suction parameter, buoyancy parameter, Prandtl number, body-radius parameter and other driving parameters. Finally the effects of involved parameters on the velocity and temperature distributions are presented graphically. It is found that a small suction or blowing can play a significant role on the patterns of flow and temperature fields.
| Published in | American Journal of Applied Mathematics (Volume 3, Issue 1) |
| DOI | 10.11648/j.ajam.20150301.14 |
| Page(s) | 14-20 |
| 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 |
Similarity Solution, Mixed Convection, Vertical Slender Body, Suction or Blowing
| [1] | Ramanaiah, G. Malarvizhi, G. and Merkin, J. H.: A unified treatment of mixed convection on a permeable horizontal plate, Wäfirme-und Stoffübertragung, 26, 187–192, 1991. |
| [2] | Sparrow, E. M., Eichorn, E. and Gregg, J. L.: Combined forced and free convection in boundary layer flow, Phys. Fluids, 2, 319–328, 1959. |
| [3] | Afzal, N. and Banthiya, N. K.: Mixed convection over a semi-infinite vertical flat plate, J. Appl. Math. Phys., 28, 993–1004, 1977. |
| [4] | Hussain, T. and Afzal, N.: Computer extension of perturbation series for mixed convection on a vertical plate: favourable and adverse flows, Fluid Dyn. Res., 4, 107–121, 1988. |
| [5] | Merkin, J. H., Pop, I. and Mahmood, T: Mixed convection on a vertical surface with a prescribed heat flux: the solution for small and large Prandtl numbers, J. Eng. Math., 25, 165–190, 1991. |
| [6] | Watanabe, T.: Forced and free mixed convection boundary layer flow with uniform suction or injection on a vertical flat plate, Acta Mech., 89, 123–132, 1991. |
| [7] | Sattar M.A.: Free and forced convection boundary layer flow through a porous medium with large suction, International Journal of Energy Research, 17, 1–7, 1993. |
| [8] | Deswita, L. Nazar, R., Ahmad R., Ishak, A and Pop, I.: Similarity Solutions of Free Convection Boundary Layer Flow on a Horizontal Plate with Variable Wall Temperature, European Journal of Scientific Research, Vol. 27(2), 188–198, 2009. |
| [9] | Hossain, M. M. T. and Mojumder, R.: Similarity solution for the steady natural convection boundary layer flow and heat transfer above a heated horizontal surface with transpiration, Int. J. of Appl. Math. and Mech., 6(4), 1–16, 2010. |
| [10] | Hossain, M. M. T., Mojumder, R. and Hossain, M. A.: Solution of natural convection boundary layer flow above a semi-infinite porous horizontal plate under similarity transformations with suction and blowing, Daffodil International University Journal of Science and Technology, 6(1), 43–51, 2011. |
| [11] | Hossain, M. A., Hossain, M. M. T. and Mojumder, R.: Further study of similarity solutions of unsteady natural convection flow above a heated horizontal semi-infinite porous plate with suction and blowing, Proceeding of the International Conference on Mechanical, Industrial and Energy Engineering 2010, 23-24 December, MIE10-095-1–6, 2010. |
| [12] | Ishak, A. Nazar, R. and Pop, I.: Dual solutions in mixed convection boundary-layer flow with suction or injection, IMA Journal of Applied Mathematics, 1−13, 2007. |
| [13] | Ramanaiah, G. and Malarvizhi, G.: Unified treatment of similarity solutions of free, mixed and forced convection problems in saturated porous media, Proceedings of Sixth Int. Conf. on Numerical Methods in Thermal Problems, Swansea, U.K. 431−439, 1989. |
| [14] | Hossain, M. M. T., Mandal B. and Hoossain M. A.: Similarity Solution of Unsteady Combined Free and Force Convective Laminar Boundary Layer Flow about a Vertical Porous Surface with Suction and Blowing, Procedia Engineering, 56 (2013), 134–140. |
| [15] | Van Dyke, M.: Free convection from a vertical needle, Problems of Hydrodynamics and Continuum Mechanics (SIAM Publication, Philadelphia, Penn.), 1969. |
| [16] | Kuiken, H. K.: The thick free-convective boundary layer along a semi-infinite isothermal vertical cylinder, ZAMP, 25, 497, 1974. |
| [17] | Md. Hasanuzzaman, B. Mandal and M.M.T. Hossain: A Study of Similarity Solution of Unsteady Combined Free and Force Convective Laminar Boundary Layer Flow About a Vertical Porous Surface with Suction and Blowing, Annals of Pure and Applied Mathematics, Vol.6, No.1( 2014), 85-97. |
APA Style
Md. Hasanuzzaman, Masud Rabbani, M. M. Touhid Hossain, M. Arif Hossain, R. Nandi. (2015). Numerical Solution of Mixed Convective Laminar Boundary Layer Flow around a Vertical Slender Body with Suction or Blowing. American Journal of Applied Mathematics, 3(1), 14-20. https://doi.org/10.11648/j.ajam.20150301.14
ACS Style
Md. Hasanuzzaman; Masud Rabbani; M. M. Touhid Hossain; M. Arif Hossain; R. Nandi. Numerical Solution of Mixed Convective Laminar Boundary Layer Flow around a Vertical Slender Body with Suction or Blowing. Am. J. Appl. Math. 2015, 3(1), 14-20. doi: 10.11648/j.ajam.20150301.14
AMA Style
Md. Hasanuzzaman, Masud Rabbani, M. M. Touhid Hossain, M. Arif Hossain, R. Nandi. Numerical Solution of Mixed Convective Laminar Boundary Layer Flow around a Vertical Slender Body with Suction or Blowing. Am J Appl Math. 2015;3(1):14-20. doi: 10.11648/j.ajam.20150301.14
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.ajam.20150301.14,
author = {Md. Hasanuzzaman and Masud Rabbani and M. M. Touhid Hossain and M. Arif Hossain and R. Nandi},
title = {Numerical Solution of Mixed Convective Laminar Boundary Layer Flow around a Vertical Slender Body with Suction or Blowing},
journal = {American Journal of Applied Mathematics},
volume = {3},
number = {1},
pages = {14-20},
doi = {10.11648/j.ajam.20150301.14},
url = {https://doi.org/10.11648/j.ajam.20150301.14},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150301.14},
abstract = {In this paper, the numerical solution of mixed convective laminar boundary layer flow around a vertical slender body with suction or blowing has been investigated. Firstly, the governing boundary layer partial differential equations have been made dimensionless and then simplified by using Boussinesq approximation. Secondly, similarity transformations are introduced on the basis of detailed analysis in order to transform the simplified coupled partial differential equations into a set of ordinary differential equations. The transformed complete similarity equations are solved numerically by using computer software. Finally, the flow phenomenon has been characterized with the help of obtained flow controlling parameters such as suction parameter, buoyancy parameter, Prandtl number, body-radius parameter and other driving parameters. Finally the effects of involved parameters on the velocity and temperature distributions are presented graphically. It is found that a small suction or blowing can play a significant role on the patterns of flow and temperature fields.},
year = {2015}
}
TY - JOUR T1 - Numerical Solution of Mixed Convective Laminar Boundary Layer Flow around a Vertical Slender Body with Suction or Blowing AU - Md. Hasanuzzaman AU - Masud Rabbani AU - M. M. Touhid Hossain AU - M. Arif Hossain AU - R. Nandi Y1 - 2015/01/27 PY - 2015 N1 - https://doi.org/10.11648/j.ajam.20150301.14 DO - 10.11648/j.ajam.20150301.14 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 14 EP - 20 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20150301.14 AB - In this paper, the numerical solution of mixed convective laminar boundary layer flow around a vertical slender body with suction or blowing has been investigated. Firstly, the governing boundary layer partial differential equations have been made dimensionless and then simplified by using Boussinesq approximation. Secondly, similarity transformations are introduced on the basis of detailed analysis in order to transform the simplified coupled partial differential equations into a set of ordinary differential equations. The transformed complete similarity equations are solved numerically by using computer software. Finally, the flow phenomenon has been characterized with the help of obtained flow controlling parameters such as suction parameter, buoyancy parameter, Prandtl number, body-radius parameter and other driving parameters. Finally the effects of involved parameters on the velocity and temperature distributions are presented graphically. It is found that a small suction or blowing can play a significant role on the patterns of flow and temperature fields. VL - 3 IS - 1 ER -
Information
Email: