Unsteady Boundary Layer Flow and Heat Transfer Due to a Stretching Sheet by Quasilinearization Technique

Wubshet Ibrahim, Bandari Shanker

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DOI: 10.4236/wjm.2011.16036                

Abstract

In this paper, the problem of unsteady laminar boundary-layer flow and heat transfer of a viscous income-pressible fluid over stretching sheet is studied numerically. The unsteadiness in the flow and temperature is caused by the time-dependent stretching velocity and surface temperature. A similarity transformation is used to reduce the governing boundary-layer equations to couple higher order non-linear ordinary differential equations. These equations are numerically solved using quasi-linearization technique. The effect of the governing parameters unsteadiness parameter and Prandtl number on velocity and temperature profile is discussed. Besides the numerical results for the local skin friction coefficient and local Nusselt number are presented. The computed results are compared with previously reported work.

Keywords

Quasi-Linearization Technique, Stretching Sheet, Boundary-Layer, Unsteady Flow, Heat Transfer

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	L. J Crane, “Flow past a stretching plate”, Journal of Applied Mathematic and Physics (ZAMP), Vol. 21, pp. 645-647, 1970.
[2]	P. Carragher and L.J. Crane, “Heat transfer on a con- tinuous stretching sheet”, Journal of Applied Mathema- tic and Mechanics, Vol. 62, Issue 10, pp. 564-565, 1982
[3]	B.K. Dutta, P. Roy and A.S.Gupta, “Temperature field in flow over a stretching surface with uniform heat flux”, International Communication in Heat Mass Transfer, Vol. 12, pp. 89-94, 1985
[4]	L.J. Grubka and K.M. Bobba, “ Heat transfer character- istic of a continuous stretching surface with variable tem- perature”, Journal of Heat Transfer, Vol. 107, pp. 248-250, 1985
[5]	E.M.A. Elbashbeshy, “Heat transfer over a stretching surface with variable surface heat flux”, Journal of Phys- ics D: Applied Physics, Vol. 31, No. 16, pp. 1951-1954, 1998.
[6]	E.M.A. Elbashbeshy and M.A.A. Bazid, “Heat transfer over an unsteady stretching surface”, Journal of Heat and Mass Transfer, Vol. 41, pp. 1-4, 2004
[7]	S. Sharidan , T.Mahood and I. Pop, “Similarity solutions for the unsteady boundary layer flow and heat transfer due to a stretching sheet”, International Journal of Ap- plied Mechanics and Engineering, 2006, Vol. 11, No. 3, pp. 647-654
[8]	Anuar Ishak, Roslinda Nazar and Ioan Pop, “Boundary layer flow and heat transfer over unsteady stretching vertical surface” , Meccanica (2009) 44: pp. 369-375
[9]	E.M.A.Elbashbeshy and D.A.Aldawody, “Heat transfer over an unsteady stretching surface with variable heat flux in the presence of heat source or sink”, Computers and mathematics with applications 60(2010) pp. 2806-2811
[10]	R.E. Bellman ,R.E.Kalaba,” Quasilinearization and non- linear boundary value problems”, American Elsevier, Newyork, 1965
[11]	M.Massoudi and C.E.Maneschy, “Numerical solution to the flow of a second grade fluid over a stretching sheet using the method of quasilinearization”, journal of Applied mathematics and computation 149(2004), pp. 165-173
[12]	T. Hymavathi and B.shanker, “Quasilinearization ap- proach to heat transfer in MHD visco-elastic fluid flow”, journal of Applied mathematics and computation 215(2009) 2045-2054
[13]	R. Bhargava, L. Kumar and H.S. Takhar, “Numerical solution of free convection MHD micropolar fluid flow between two parallel porous vertical plates”, International Journal of Engineering Science 41 (2003) 123-136.
[14]	D. Srinivasacharya and M. Shiferaw, “Numerical solution to the MHD flow of micro polar fluid between two con- centric porous cylinders, International Journal of Applied Mathematics and Mechanics 4(2): 77-86, 2008.
[15]	C.L.Huang, “Application of quasi-linearization technique to the vertical channel flow and heat convection”, Inter- national Journal of Non-Linear mechanics Vol. 13, pp. 55-60
[16]	Chi-Lung Hunge, “Applying quasi-linearization to the problem of flow through an annulus with porous walls of different permeability”, Journal of Applied scientific re- search, Vol. 29 ,1974
[17]	M. M. Rashidi and S. A. Mohimanian Pour, “Analytic ap- proximate solutions for unsteady boundary-layer and heat transfer due to a stretching sheet by homotopy analysis method”, Non-linear Analysis: modelling and control, 2010, Vol. 15. No. 1, pp. 83-95