Effects of Thermal Radiation on the Stagnation-Point Flow of Upper-Convected Maxwell Fluid over a Stretching Sheet
Publication: Journal of Aerospace Engineering
Volume 27, Issue 4
Abstract
Influence of thermal radiation on the laminar two-dimensional incompressible flow of upper-convected Maxwell (UCM) fluid is investigated. An entirely different aspect of Rosseland approximation for thermal radiation is captured. The relevant equations are first modeled and then solved numerically by the shooting method using a fourth-order Runge-Kutta integration technique. The solutions are validated with the built-in solver bvp4c of the software MATLAB. Graphs are sketched to examine the behaviors of interesting parameters entering into the problem.
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Acknowledgments
The authors are thankful to the reviewers for their constructive and valuable suggestions. The research of Dr. Alsaedi was partially supported by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, Saudi Arabia.
References
Abbas, Z., Wang, Y., Hayat, T., and Oberlack, M. (2010). “Mixed convection in the stagnation-point flow of a Maxwell fluid towards a vertical stretching surface.” Nonlinear Anal. Real World Appl., 11(4), 3218–3228.
Ahmed, A., and Asghar, S. (2012). “Flow and heat transfer over hyperbolic stretching sheets.” Appl. Math. Mech., 33(4), 445–454.
Aliakbar, V., Alizadeh-Pahlavan, A., and Sadeghy, K. (2009). “The influence of thermal radiation on MHD flow of Maxwellian fluids above stretching sheets.” Commun. Nonlinear Sci. Num. Simul., 14(3), 779–794.
Alizadeh-Pahlavan, A., Aliakbar, V., Vakili-Farahania, F., and Sadeghy, K. (2009). “MHD flows of UCM fluids above porous stretching sheets using two-auxiliary-parameter homotopy analysis method.” Commun. Nonlinear Sci. Num. Simul., 14(2), 473–488.
Bachok, N., Ishak, A., and Pop, I. (2010). “Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet.” Phys. Lett. A, 374(40), 4075–4079.
Bataller, R. C. (2008). “Radiation effects in the Blasius flow.” Appl. Math. Comput., 198(1), 333–338.
Blasius, H. (1908). “Grenzschichten in FlussigkeitenmitKleinerReibung.” Z. Angew. Math. Phys., 56(1), 1–37 (in German).
Cortell, R. (2007). “MHD flow and mass transfer of an electrically conducting fluid of second grade in a porous medium over a stretching sheet with chemically reactive species.” Chem. Eng. Process, 46(8), 721–728.
Crane, L. J. (1970). “Flow past a stretching plate.” Zeitschrift Fur AngewandteMathematik Und Physik, 21(4), 645–647.
Dutta, B. K. (1989). “Heat transfer from a stretching sheet with uniform suction and blowing.” Acta Mechanica, 78(3–4), 255–262.
Gupta, P. S., and Gupta, A. S. (1977). “Heat and mass transfer on a stretching sheet with suction or blowing.” Can. J. Chem. Eng., 55(6), 744–746.
Hayat, T., Abbas, Z., and Sajid, M. (2006). “Series solution for the upper-convected Maxwell fluid over a porous stretching plate.” Phys. Lett. A, 358(5–6), 396–403.
Hayat, T., Abbas, Z., and Sajid, M. (2009a). “MHD stagnation-point flow of an upper-convected Maxwell fluid over a stretching surface.” Chaos Solitons Fractals, 39(2), 840–848.
Hayat, T., and Awais, M. (2011). “Three-dimensional flow of upper-convected Maxwell (UCM) fluid.” Int. J. Num. Meth. Fluids, 66(7), 875–884.
Hayat, T., Iqbal, Z., Mustafa, M., and Alsaedi, A. (2012). “Momentum and heat transfer of an upper-convected Maxwell fluid over a moving surface with convective boundary conditions.” Nucl. Eng. Des., 252, 242–247.
Hayat, T., Mustafa, M., and Mesloub, S. (2010). “Mixed convection boundary layer flow over a stretching surface filled with a Maxwell fluid in presence of Soret and Dufour effects.” Z. Naturforsch., 65, 401–410.
Hayat, T., Mustafa, M., and Sajid, M. (2009b). “Influence of thermal radiation on Blasius flow of a second grade fluid.” Z. Naturforsch., 64, 827–833.
Hayat, T., and Sajid, M. (2007). “Homotopy analysis of MHD boundary layer flow of an upper-convected Maxwell fluid.” Int. J. Eng. Sci., 45(2–8), 393–401.
Kumari, M., and Nath, G. (2009). “Steady mixed convection stagnation-point flow of upper convected Maxwell fluids with magnetic field.” Int. J. Nonlinear Mech., 44(10), 1048–1055.
Kuznetsov, G. V., and Sheremet, M. A. (2009). “Conjugate natural convection with radiation in an enclosure.” Int. J. Heat Mass Transfer, 52(9–10), 2215–2223.
Liu, I. C., Wang, H. H., and Peng, Y. F. (2013). “Flow and heat transfer for three-dimensional flow over an exponentially stretching surface.” Chem. Eng. Commun., 200(2), 253–268.
Magyari, E. (2010). “Comment on ‘Mixed convection boundary layer flow over a horizontal plate with thermal radiation’ by A. Ishak.” Heat Mass Transfer, 46(8–9), 809–810.
Magyari, E., and Pantokratoras, A. (2011). “Note on the effect of thermal radiation in the linearized Rosseland approximation on the heat transfer characteristics of various boundary layer flow.” Int. Commun. Heat Mass Transfer, 38(5), 554–556.
Mahapatra, T. R., and Gupta, A. S. (2002). “Heat transfer in stagnation-point flow towards a stretching surface.” Heat Mass Transfer, 38(6), 517–521.
Mustafa, M., Hayat, T., and Obaidat, S. (2012). “Stagnation-point flow and heat transfer of a Casson fluid towards a stretching sheet.” Z. Naturforsch., 67, 70–76.
Raftari, B., and Yildirim, A. (2010). “The application of homotopy perturbation method for MHD flows of UCM fluids above porous stretching sheets.” Comp. Math. Appl., 59(10), 3328–3337.
Raptis, A., and Perdikis, C. (1998). “Viscoelastic flow by the presence of radiation.” J. Appl. Math. Mech., 78(4), 277–279.
Raptis, A., Perdikis, C., and Takhar, H. S. (2004). “Effect of thermal radiation on MHD flow.” Appl. Math. Comput., 153(3), 645–649.
Sadeghy, K., Najafi, A. H., and Saffaripour, M. (2005). “Sakiadis flow of an upper-convected Maxwell fluid.” Int. J. Nonlinear Mech., 40(9), 1220–1228.
Sakiadis, B. C. (1961). “Boundary-layer behavior on continuous solid surfaces. I. Boundary-layer equations for two-dimensional and axisymmetric flow.” AIChE J., 7(1), 26–28.
Seddeek, M. A. (2002). “Effects of radiation and variable viscosity on a MHD free convection flow past a semi infinite flat plate with an aligned magnetic field in the case of unsteady flow.” Int. J. Heat Mass Transfer, 45(4), 931–935.
Vleggar, J. (1977). “Laminar boundary layer behavior on continuous accelerating surfaces.” Chem. Eng. Sci., 32(12), 1517–1525.
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© 2014 American Society of Civil Engineers.
History
Received: Jan 11, 2013
Accepted: Jun 6, 2013
Published online: Jun 8, 2013
Published in print: Jul 1, 2014
Discussion open until: Sep 30, 2014
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