Development of Boundary Layer of Highly Elastic Flow of the Upper Convected Maxwell Fluid over a Stretching Sheet

Subject Areas : Mechanical Engineering

Meysam Mohamadali ¹ , Nariman Ashrafi ²

1 - Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Department of Mechanical and Aerospace Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

Received: 2015-11-12 Accepted : 2017-10-31 Published : 2016-06-01

Keywords:

References:

[1]     Crane, L. J., “Flow past a stretching sheet”, ZAMP, Vol. 21, 1970, pp. 645–647.

[2]     Prasad, K. V., Santhi, S. R., and Datti, P. S:, “Non-Newtonian power-law fluid flow and heat transfer over a non-linearly stretching surface”, Appl. Math., Vol. 3, No. 5, 2012, pp. 425-435.

[3]     Xu, H., and Liao, S. J:, “Laminar flow and heat transfer in the boundary-layer of non-Newtonian fluids over a stretching flat sheet”, Comput. Math. Appl., Vol. 57, 2009, pp. 1425-1431.

[4]     Abel, M. S., Datti, P. S., and Mahesha, N., “Flow and heat transfer in a power-law fluid over a stretching sheet with variable thermal conductivity and nonuniform heat source”, Int. J. Heat Mass Transfer, Vol. 52, 2009, pp. 2902–2913.

[5]     Wang, C., “Analytic solutions for a liquid film on an unsteady stretching surface”, Heat Mass Transfer, Vol. 42, 2006, pp.759–766.

[6]     Ashrafi, N., Mohamadali, M., “High Weissenberg Number Stress Boundary Layer for the Upper Convected Maxwell Fluid”, Proceedings of the ASME International Mechanical Engineering Congress & Exposition, Vol. 8B, Heat Transfer and Thermal Engineering, Montreal , 2014, pp. 201-207.

[7]     Hassanien, I. A., “Flow and heat transfer on a continuous flat surface in a parallel free stream of viscoelastic second-order fluid”, Appl. Sci. Res., Vol. 49, 1992, pp. 335-344.

[8]     Schichting., H., “Boundary Layer Theory”, sixth ed., McGraw Hill, New York, 1964, Chap 7.

[9]     Hayat, T., Fetecau, C., Abbas, Z., and Ali, N., “Flow of a viscoelastic fluid with fractional Maxwell model between two side walls due to suddenly moved plate”, Nonlinear Anal. Real World Appl., Vol. 9, 2008, pp. 2288-2295.

[10]  Shateyi, S., “A new numerical approach to MHD flow of a Maxwell fluid past a vertical stretching sheet in the presence of thermophoresis and chemical reaction”, Bound. Val. Prob., Vol. 196, 2013.

[11]  Fetecau, C., Jamil, M., Fetecau, C., and Siddique, I., “A note on the second problem of Stokes for Maxwell fluids”, Int. J. Non-Linear Mech., Vol. 44, 2009, pp. 1085-1090.

[12]  Hayat, T., Shehzad, S. A., and Alsaedi, A., “Study on three-dimensional flow of Maxwell fluid over a stretching surface with convective boundary conditions”, Int. J. Phys. Sci., Vol. 7, No. 5, 2012, pp.761-768.

[13]  Awais, M., Hayat, T., Alsaedi, A., and Asghar, S., “Time-dependent three-dimensional boundary layer flow of a Maxwell fluid”, Computers & Fluids, Vol. 91, 2014, pp. 21–27.

[14]  Rajagopal, K. R., Boundary layers in non-linear fluids, in: M.D.P. Monteivo Marques, Trends in Applications of Mathematics to Mechanics, in: Pittman Monographs and Surveys in Pure and Applied Mathematics, Vol. 77, Longman, New York, 1995.

[15]  Renardy, M., and Wang, X., “Boundary layers for the upper convected Maxwell fluid”, J. Non-Newtonian Fluid Mech., Vol. 189, 2013, pp. 14–18.

[16]  Renardy, M., “High Weissenberg number boundary layers for the upper convected Maxwell fluid”, J. Non-Newtonian Fluid Mech., Vol. 68, 1997, pp. 125-132.

[17]  Hagen, T., and Renardy, M., “Boundary layer analysis of the Phan–Tien–Tanner and Giesekus model in high Weissenberg number flow”, J. Non-Newtonian Fluid Mech., Vol. 73, 1997, pp. 181–189.

[18]  Renardy, M., “Prandtl boundary layers for the Phan-Thien Tanner and Giesekus fluid”, Z. Angew. Math. Phys., Vol. 66, 2014, pp. 1061- 1070.

[19]  Renardy, M., “Wall Boundary Layers for Maxwell Liquids”, Arch. Rational Mech. Anal., Vol. 152, 2000, pp. 93–102.

[20]  Renardy, M. and Wang, X., “Well-posedness of boundary layer equations for time-Dependent flow of Non-Newtonian fluids”, J. Math. Fluid Mech., Vol. 16, 2014, pp. 179–191

[21]  Renardy, M., “The initial value problem for creeping flow of the upper convected Maxwell fluid at high Weissenberg number”, Math. Meth. Appl. Sci., Vol. 38, 2014, pp. 959–965.

[22]  Ogilvie, G. I., Proctor, M. R. E., “On the relation between viscoelastic and magneto-hydrodynamic flows and their instabilities”, J. Fluid Mech., Vol. 476, 2003, pp. 389-409.

[23]  Bird, R. B., Armstrong, R. C., “Dynamics of polymeric Liquids”, second ed., John Wiley & Sons, New York, 1987, Chap 5.

[24]  [24] Evans, J. D., “Re-entrant corner flows of the Upper Convected Maxwell fluid,” Proc. Roy. Soc. A, Vol.461, 2005, pp.117–142.

[25]  Renardy, M.,“A matched solution for corner flow of the upper convected Maxwell fluid”, J. Non-Newtonian Fluid Mech.,Vol. 58, 1995, pp. 83-89.

[26]  Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., Numerical Recipes )in Fortran 77(, 2nd ed., Cambridge University Press, New York, 2007.Chap12.