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Mixed Convection in Viscoelastic Boundary Layer Flow and Heat Transfer Over a Stretching Sheet

Published online by Cambridge University Press:  03 June 2015

Antonio Mastroberardino
Antonio Mastroberardino*
Affiliation:
School of Science, Penn State Erie, The Behrend College, Erie, Pennsylvania 16563, USA
*
*Corresponding author. Email: axm62@psu.edu
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Abstract

An investigation is carried out on mixed convection boundary layer flow of an incompressible and electrically conducting viscoelastic fluid over a linearly stretching surface in which the heat transfer includes the effects of viscous dissipation, elastic deformation, thermal radiation, and non-uniform heat source/sink for two general types of non-isothermal boundary conditions. The governing partial differential equations for the fluid flow and temperature are reduced to a nonlinear system of ordinary differential equations which are solved analytically using the homotopy analysis method (HAM). Graphical and numerical demonstrations of the convergence of the HAM solutions are provided, and the effects of various parameters on the skin friction coefficient and wall heat transfer are tabulated. In addition it is demonstrated that previously reported solutions of the thermal energy equation given in [1] do not converge at the boundary, and therefore, the boundary derivatives reported are not correct.

Keywords

76D1076W05Viscoelastic fluidnon-uniform heat source/sinkviscous dissipationthermal radiationhomotopy analysis method
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 3 , June 2014 , pp. 359 - 375
Copyright
Copyright © Global-Science Press 2014

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References

[1]Nandeppanavar, M. M., Abel, M. S. and Tawade, J., Heat transfer in Walter’s liquid B fluid over an impermeable stretching sheet with non-uniform heat source/sink and elastic deformation, Commun. Nonlinear Sci. Numer. Simul., 15 (2010), pp. 1791–1802.Google Scholar
[2]Blasius, H., Grenzschichten in Flussigkeiten mit kleiner Reibung, Z. Math. Phys., 56 (1908), 137.Google Scholar
[3]Liao, S. J., Proposed Homotopy Analysis Techniques for the Solution of Nonlinear Problems, Ph.D. dissertation, Shanghai Jiaotong University, Shanghai, 1992.Google Scholar
[4]Liao, S. J., A kind of approximate solution technique which does not depend upon small parameters II: an application in fluid mechanics, Int. J. Nonlinear Mech., 32 (1997), pp. 815–822.Google Scholar
[5]Liao, S. J., Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman & Hall-CRC Press, Boca Raton, FL, 2003.CrossRefGoogle Scholar
[6]Liao, S. J., Notes on the homotopy analysis method: some definitions and theorems, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), pp. 983–997.Google Scholar
[7]Liao, S. J., An optimal homotopy-analysis approach for strongly nonlinear differential equations, Commun. Nonlinear Sci. Numer. Simul., 15 (2010), pp. 2003–2016.Google Scholar
[8]Liao, S. J., Homotopy Analysis Method in Nonlinear Differential Equations, Springer & Higher Education Press, Heidelberg, 2012.Google Scholar
[9]Mastroberardino, A., Homotopy analysis method applied to electrohydrodynamic flow, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), pp. 2730–2736.Google Scholar
[10]Mastroberardino, A., Series solutions for annular axisymmetric stagnation flow on a moving cylinder, Appl. Math. Mech., 34 (2013), pp. 1043–1054.Google Scholar
[11]Sakiadis, B. C., Boundary layer behavior on continuous solid surface: II-boundary layer on a continuous flat surface, AIChE J, 7 (1961), pp. 221–225.CrossRefGoogle Scholar
[12]Crane, L. J., Flow past a stretching plate, Z. Angew. Math. Phys., 21 (1970), pp. 645–647.Google Scholar
[13]Vajravelu, K. and Rollins, D., Heat transfer in a viscoelastic fluid over a stretching sheet, J. Math. Anal. Appl., 158 (1991), pp. 241–255.Google Scholar
[14]Sarma, M.S. and Rao, B. N., Heat transfer in a viscoelastic fluid over a stretching sheet, J. Math. Anal. Appl., 222 (1998), pp. 268–275.Google Scholar
[15]Pillai, K. M. C., Sai, K. S., Swamy, N. S., Nataraja, H. R., Tiwari, S. B. and Rao, B. N., Heat transfer in a viscoelastic boundary layer flow through a porous medium, Comput. Mech., 34 (2004), pp. 27–37.Google Scholar
[16]Abel, M. S., Siddheshwar, P. G. and Nandeppanavar, M. M., Heat transfer in a viscoelastic fluid flow over a stretching sheet with viscous dissipation and non-uniform heat source, Int. J. Heat Mass Trans., 50 (2007), pp. 960–966.Google Scholar
[17]Arnold, J. C., Asir, A. A., Somasundaram, S. and Christopher, T., Heat transfer in a viscoelastic boundary layer flow over a stretching sheet, Int. J. Heat Mass Trans., 53 (2010), pp. 1112–1118.Google Scholar
[18]Pal, D. and Mondal, H., Influence of chemical reaction and thermal radiation on mixed convection heat and mass transfer over a stretching sheet in Darcian porous medium with Soret and Dufour effects, Energy Convers Manage, 62 (2012), pp. 102–108.Google Scholar
[19]Raptis, A. and Perdikis, C., Viscoelastic flow by the presence of radiation, Z. Angew Math. Mech., 78 (1998), pp. 277–279.Google Scholar
[20]Chen, C. H., On the analytic solution ofMHDflow and heat transfer for two types of viscoelastic fluid over a stretching sheet with energy dissipation, internal heat source and thermal radiation, Int. J. Heat Mass Trans., 53 (2010), pp. 4264–4273.Google Scholar
[21]Nandeppanavar, M. M., Abel, M. S. and Tawade, J., Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with thermal radiation and non-uniform heat source/sink, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), pp. 3578–3590.Google Scholar
[22]Abel, M. S., Prasad, K. V. and Mahaboob, A., Buoyancy force and thermal radiation effects in MHD boundary layer visco-elastic fluid flow over a continuously moving stretching surface, Int. J. Therm. Sci., 44 (2005), pp. 465–476.CrossRefGoogle Scholar
[23]Mastroberardino, A. and Mahabaleswar, U. S., Mixed convection in viscoelastic flow due to a stretching surface in a porous medium, J. Porous Media, 16 (2013), pp. 483–500.CrossRefGoogle Scholar
[24]Hayat, T., Abbas, Z. and Pop, I., Mixed convection in the stagnation point flow adjacent to a vertical surface in a viscoelastic fluid, Int. J. Heat Mass Trans., 51 (2008), pp. 3200–3206.Google Scholar
[25]Hayat, T., Mustafa, M. and Mesloub, S., Mixed convection boundary layer flow over a stretching surface filled with a Maxwell fluid in presence of Soret and Dufour effects, Z. Naturforsch, 65a (2010), pp. 401–410.Google Scholar
[26]Abbas, Z., Wang, Y., Hayat, T. and Oberlack, M., Mixed convection in the stagnation point flow of a Maxwell fluid towards a vertical stretching surface, Nonlinear Anal. Real World Appl., 11 (2010), pp. 3218–3228.CrossRefGoogle Scholar
[27]Van Gorder, R. A. and Vajravelu, K., Convective heat transfer in a conducting fluid over a permeable stretching surface with suction and internal heat generation/absorption, Appl. Math. Comput., 217 (2011), pp. 5810–5821.Google Scholar
[28]Hayat, T., Hussain, M., Nadeem, S. and Mesloub, S., Falkner-Skan wedge flow of a power law fluid with mixed convection and porous medium, Comput. Fluids, 49 (2011), pp. 22–28.Google Scholar
[29]Hayat, T., Shehzad, S. A. and Qasim, M., Mixed convection flow of a micropolar fluid with radiation and chemical reaction, Int. J. Numer. Meth. Fluids, 67 (2011), pp. 1418–1436.Google Scholar
[30]Beard, D. W. and Walters, K., Elastico-viscous boundary-layer flows I: two-dimensional flow heat stagnation point, Proc. Cambridge Philos. Soc., 60 (1964), pp. 667–674.Google Scholar
[31]Andersson, H. I., MHD flow of a visco-elastic fluid past a stretching surface, Acta Mech., 95 (1992), pp. 227–230.Google Scholar
[32]Brewster, M. Q., Thermal Radiative Transfer and Properties, John Wiley & Sons, Canada, 1992.Google Scholar