Abstract
The objective of the present study is to consider a dissipative and radiative visco-elastic flow over a stretching porous sheet. The applicability of the present study is numerous in the polymer industry in stretching of sheets with dissipative environment. In view of its scope, the present study brings the work of Khan (Int J Heat Mass Transf 49, 1534–1542, 2005) and Singh (Int Comm Heat Mass Transf 35, 637–642, 2008) as particular cases. The solution of the momentum equation has been taken care of by similarity transformation and applying a particular solution satisfying boundary conditions. Further, the heat and mass transfer equations are solved by applying the confluent hypergeometric function (Kummer’s function). It is interesting to note that the presence of elastic element in the fluid, external magnetic field and suction at the plate reduce the skin friction favoring the stretching of sheets whereas heat loss has been minimized due to permeability of the medium, presence of heat source in case of low diffusive fluid.
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Carragher, P.; Crane, I.J.:Heat transfer on a continuous stretching sheet. ZAMM. 62, 564–565 (1982)
Naseem, A.; Khan, N.:Boundary layer flow past a stretching sheet in porous media and heat transfer with internal heat source, Int. J. Eng. Mater. Sci. 7, 51–53 (2000)
Parida, S.K.; Acharya, M.; Dash, G.C.; Panda S.: MHD heat and mass transfer in a rotating system with periodic suction. AJSE. 36(6), 1139–1151 (2011)
Anjali Devi, S.P.; Ganga, B.: Viscous dissipation effects on nonlinear MHD flow in a porous medium over a stretching porous surface. Ind. J. Appl. Math. 5(7), 45–49 (2009)
Abdhulla, I.A.: Analytic solution of heat and mass transfer over a permeable stretching plate affected by chemical reaction, internal heating, dufour-soret and Hall effect. Therm. Sci. 13, 183–197 (2009).
Khan, S.K.; Abel, M.S.;Sonth, R.M.: Visco-elastic MHD flow, heat and mass transfer over a porous stretching sheet with dissipation of energy and stress work. Heat Mass Transf. 44, 233–244 (1996)
Singh, A.K.: Heat source and radiation effect on magnetoconvection flow a viscoelastic fluid past a stretching sheet: analysis with Kummer’s function, Int. Comm. Heat Mass Transf. 35, 637–642 (2008)
Sidheswar, P.G.; Mahabaleswar, U.S.: Effect of radiation and heat source on MHD flow of a visco-elastic liquid and heat transfer over a stretching sheet. Int. J. Non-Linear Mech. 49, 807–820 (2005)
Datti, P.S.; Prasad, K.V.;Abel, M.S.; Joshi, A.: MHD visco-elastic fluid flow over a non-isothermal stretching sheet. Int. J. Eng. Sci. 42, 935–946 (2004)
Abel, S.; Prasadab, K.V.;Mahaboob, A.: Buoyancy force and thermal radiation effects in MHD boundary layer visco-elastic fluid flow over continuously moving stretching surface. Int. J. Therm. Sci. 44, 465–476 (2005)
Cortell, R.: Similarity solutions for flow and heat transfer of a viscoelastic fluid over a stretching sheet. Int. J. Non-linear Mech. 29(2), 155–161 (1994)
Seddeek, M.A.: Heat and mass transfer on a stretching sheet with a magnetic field in a visco-elastic fluid flow through a porous medium with heat source or sink. Comput. Mater. Sci. 38, 781–787 (2007)
Vajravelu, K.; Soewono, E.: Fourth order nonlinear systems arising in combined free and forced convection flow of a second order fluid. Int. J. Non-linear Mech. 29(6), 861–869 (1994)
Abel, M.S.; Nandeppanavar, M.M.: Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with non-uniform heat source/sink. Commun. Nonlinear Sci. Numer. Simulat. 14, 2120–2131 (2009)
Khan, S.K.: Heat transfer in a viscoelastic fluid over a stretching surface with heat source/sink, suction/blowing and radiation, Int. J. Heat Mass Transf. 49, 1534–1542 (2005)
Sahoo, S.N.; Dash, G.C.: Heat and mass transfer of MHD convective boundary layer flow past a stretching porous wall embedded in a porous medium. J. Eng. Thermophys. 21(3), 181–192 (2012)
Rajgopal, K.R.; Na, T.Y.; Gupta, A.S.: Flow of viscoelastic fluid over a stretching sheet. Rheol. Acta. 23, 213–215 (1984)
Mcleod, J.B.; Rajagopal, K.R.: On the uniqueness of flow of Navier Stokes fluid due to stretching boundary. Arch. Ration. Mech. Annal. 98, 385–395 (1987)
Troy, W.C.; Overman, E.A.; Ermentrout, H.G.B.; Keener, J.P.: Uniqueness of flow of a second order fluid past a stretching sheet. Quart. Appl. Math. 44, 753–755 (1987)
Chang, W.D.: The non-uniqueness of the flow of a visco-elastic fluid over a stretching sheet. Quart. Appl. Math. 47(20), 365–366 (1989)
Rao, B.N.: Technical note: flow of a fluid of second grade over a stretching sheet. Int. J. Non-linear Mech. 31(4), 547–550 (1996)
Lawrence, P.S.; Rao, B.N.: The non-uniqueness of the MHD flow of a viscoelastic fluid past a stretching sheet. Acta Mech. 112, 223–228 (1995)
Brewstar, M.Q.: Thermal Radiative Transfer Properties. Wiley, New York (1972)
Nield, D.A.; Bejan, A.: Convection in Porous Media. vol. 107, Springer, New York (1992)
Abramowitz, M.; Stegum, L.A.: Handbook of Mathematical Functions, vol. 55. National Bureau of Standards/American Mathematical Society, Providence (1972)
Acharya, M.; Dash, G.C.; Singh, L.P.: Magnetic field effect on free convection and mass transfer flow through porous medium with constant suction and constant heat flux. Indian J. Pure Appl. Math. 31(1), 1–16 (2000)
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Kar, M., Sahoo, S.N., Rath, P.K. et al. Heat and Mass Transfer Effects on a Dissipative and Radiative Visco-Elastic MHD Flow over a Stretching Porous Sheet. Arab J Sci Eng 39, 3393–3401 (2014). https://doi.org/10.1007/s13369-014-0991-0
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DOI: https://doi.org/10.1007/s13369-014-0991-0