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ISSN Imprimer: 1064-2285
ISSN En ligne: 2162-6561
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MHD THIN FILM OLDROYD-B FLUID WITH HEAT AND VISCOUS DISSIPATION OVER OSCILLATING VERTICAL BELTS
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RÉSUMÉ
In this paper, we investigated magnetohydrodynamic (MHD) thin film flow of an Oldroyd-B fluid in the presence of heat transfer with effect of viscous dissipation over an oscillating vertical belt. The fluid is assumed to be unsteady, and the basic governing equations are modeled in the form of nonlinear coupled partial differential equations with pertinent initial and boundary conditions. For the analytical solutions of the problem we use the optimal homotopy asymptotic method (OHAM). For comprehension, the physical presentation of such modeled parameters as the Prandtl number Pr, Brinkman number Br, time retardation parameter a, time relaxation parameter β, gravitational parameter St, and magnetic parameter M are plotted graphically and discussed. An increase in M increases the velocity and temperature distribution, the boundary-layer thickness decreases by increasing the Prandtl number, and the velocity decreases by increasing the gravitational parameter.
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Aiyesimi, Y.M., Okedyao, G.T., and Lawal, W.O., Unsteady MHD Thin Film Flow of a Third Grade Fluid with Heat Transfer and No Slip Boundary Condition Down an Inclined Plane, Int. J. Sci. Eng. Res., vol. 4, no. 6., pp. 420–432, 2013.
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Aksel, N., Fetecau, C., and Scholl, M., Starting Solution for Some Unsteady Unidirectional Flows of Oldroyd-B Fluids, Z. Angew. Math. Phys., vol. 57, pp. 825–831, 2006.
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Aman, S., Khan, I., and Hussanan, A., Effects of MoS<sub>2</sub> Nanoparticles on MHD Slip Flow of Molybdenum Disulphide Nanofl uid in a Porous Medium, J. Mol. Liq., 2017. DOI: 10.1016/j.molliq.2017.03.009
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Anjum, A., Ayub, M., and Khan, M., Starting Solutions for Oscillating Motions of an Oldroyd-B Fluid over a Plane Wall, Commun. Nonlin. Sci. Numer. Simul., vol. 17, no. 1, pp. 472–482, 2012.
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Burdujan, L., The Flow of a Particular Class of Oldroyd-B Fluids, J. Series Math. Appl., vol. 3, pp. 23–45, 2011.
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Fetecau, C., Hayat, T., and Fetecau, C., Starting Solutions for Oscillating Motions of Oldroyd-B Fluids in Cylindrical Domains, J. Non-Newtonian Fluid Mech., vol. 153, no. 3, pp. 191–201, 2008.
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Fetecau, C., Sharat, C., Prasad, S.C., and Rajagopal, K.R., A Note on the Flow Induced by a Constantly Accelerating Plate in an Oldroyd-B Fluid, Appl. Math. Model., vol. 31, pp. 647–654, 2007.
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Ghosh, A.K. and Sana, P., On Hydromagnetic Flow of an Oldroyd-B Fluid near a Pulsating Plate, Acta Astronaut., vol. 64, pp. 272–280, 2009.
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Ghosh, A.K., Datta, S.K., and Pulakesh, S., A Note on Hydro Magnetic Flow of an Oldroyd-B Fluid near an Infi nite Plate Induced by Half Rectifi ed Sine Pulses, Open. J. Fluid Dyn., vol. 4, no. 2, pp. 226–240, 2014.
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Ghosh, A.K. and Sana, P., On Hydromagnetic Channel Flow of an Oldroyd-B Fluid Induced by Rectifi ed Sine Pulses, Comput. Appl. Math., vol. 28, no. 3, pp. 365–395, 2009.
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Haita, Q. and Mingyu, X., Some Unsteady Unidirectional Flows of a Generalized Oldroyd-B Fluid with Fractional Derivative, Appl. Math. Model., vol. 33, pp. 4184–4191, 2009.
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Hayat, T., Siddiqui, A.M., and Asghar, A., Some Simple Flows of an Oldroyd-B Fluid, Int. J. Eng. Sci., vol. 39, no. 2, pp. 135–147, 2001.
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Khan, I. and Dennis, L.C.C., A Scientifi c Report on Heat Transfer Analysis in Mixed Convection Flow of Maxwell Fluid over an Oscillating Vertical Plate, Sci. Rep., 2017. DOI: 10.1038/srep40147
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Khan, I., Fakhar, K., and Anwar, M.I., Hydro-Magnetic Rotating Flows of an Oldroyd-B Fluid in a Porous Medium, Spec. Top. Rev. Porous Media, vol. 3, no. 1, pp. 89–95, 2012.
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Khan, I., Gul, I., and Sharidan, S., Shape Effects of Magnetic Field on Molybdenum Disulfi de Nanofl uids in Mixed Convection Flow inside a Channel Filled with a Saturated Porous Medium, J. Porous Media, vol. 20, no. 5, pp. 1–14, 2017.
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Khan, I., Imran, M., and Fakhar, K., New Exact Solutions for Some Unsteady Flow of an Oldroyd-B Fluid in a Porous Medium, Int. J. Math Math. Sci., 2011. DOI: 10.1155/2011/408132
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Khan, M. and Zeeshan, A., MHD Flow of an Oldroyd-B Fluid through a Porous Space Induced by Tooth Pulses, Chin. Phys. Lett., vol. 28, no. 8, pp. 470–478, 2011.
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Lie, L. and Zhang, L., Axial MHD Flow of Generalized Oldroyd-B Fluid Due to Two Oscillating Cylinders, Adv. Mat. Res., vol. 335, pp. 83–86, 2012.
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Marinca, V. and Ene, R.D., Dual Approximate Solutions of the Unsteady Viscous Flow over a Shrinking Cylinder with Optimal Homotopy Asymptotic Method, Adv. Math. Phys., vol. 2014, Article ID 417643, 11 pp., 2014.
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Marinca, V., Herisanu, N., Bota, C., and Marinca, B., An Optimal Homotopy Asymptotic Method Applied to the Steady Flow of a Fourth Grade Fluid past a Porous Plate, Appl. Math. Lett., vol. 22, pp. 245–254, 2009.
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Shahid, N., Rana, M., and Siddique, I., Exact Solution for Motion of an Oldroyd-B Fluid over an Infi nite Flat Plate that Applies an Oscillating Shear Stress to the Fluid, Boundary-Value Probl., vol. 48, pp. 1–19, 2012.
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Siddiqui, A.M., Mahmood, R., and Ghori, Q.K., Thin Film Flow of a Third Grade Fluid on a Moving Belt by He's Homotopy Perturbation Method, Int. J. Nonlin. Sci. Numer. Simul., vol. 7, no. 1, pp. 7–14, 2006.
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Siddiqui, A.M., Farooq, A.A., Haroon, T., and Rana, M.A., A Study of Thin Film Flow of an Oldroyd B-Constant Fluid on a Moving Belt Using Variational Iteration Approach, Can. J. Phys., vol. 92, no. 10, pp. 1196–1202, 2014.
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Ullah, H., Islam, S., and Idrees, M., Solution of the Boundary Layer Problems with Heat Transfer by Optimal Homotopy Asymptotic Method, Abs. Appl. Anal., vol. 2013, ID 324869, 10 pp., 2013.
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Ullah, H., Islam, S., Khan, I., and Fiza, M., Analytical Solution for Three-Dimensional Problem of Condensation Film on Inclined Rotating Disk by EOHAM, Iran. J. Sci. Tech. Mech. Eng., 2016. DOI: 10.1007/s40997-016-0030-8
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Ullah, H., Islam, S., Sharidan, S., and Fiza, M., MHD Boundary Layer Flow of an Upper Convected Maxwell Fluid by Optimal Homotopy Asymptotic Method, Sci. Iran., vol. 22, no. 6, pp. 1972–1980, 2014.