SIMILARITY SOLUTION OF NATURAL CONVECTIVE BOUNDARY LAYER FLOW AROUND A VERTICAL SLENDER BODY WITH SUCTION AND BLOWING

admin June 27, 2017

Authors:

Md. Hasanuzzaman,Akio Miyara ,

DOI NO:

https://doi.org/10.26782/jmcms.2017.01.00002

Keywords:

Similarity solution,natural convective,vertical slender body,suction or blowing,

Abstract

In this paper, the similarity solution of natural convective laminar boundary layer flow around a vertical slender body with suction and 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 a ordinary differential equations. The transformed complete similarity equations are solved numerically by using Fourth order Runge-Kutta method as well as MATLAB. 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. The effects of dimensionless 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. 

Refference:

1)   Clarke, J. F. Riley, N. : Natural convection induced in a gas by the presence of a hot porous horizontal surface, Q. J. Mech. Appl. Math., 28, 373–396, 1975.

2)   Schneider, W. : A similarity solution for combined forced and free convection flow over a horizontal plate, Int. J. Heat Mass Transfer, 22, 1401–1406, 1979.

3)   Merkin, J. H. Ingham, D. B.: Mixed convection similarity solutions on a horizontal surface, ZAMP, 38, 102–116, 1987.

4)   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.

5)   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,  27(2), 188–198, 2009.

6)   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.  Appl. Math.  Mech., 6(4), 1–16, 2010.

7)   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.

8)   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, 56,134–140, 2013.

9)   Van Dyke, M. : Free convection from a vertical needle, Problems of Hydrodynamics and Continuum Mechanics (SIAM Publication, Philadelphia, Penn.), 1969.

10) Kuiken, H. K. : The thick free-convective boundary layer along a semi-infinite   isothermal vertical cylinder, ZAMP, 25, 497, 1974.

Author(s): Md. Hasanuzzaman, Akio Miyara View Download