Abstract
Numerical investigation is carried out for steady two dimensional boundary layer flow of a viscous, incompressible and electrically conducting fluid over a nonlinearly stretching non-isothermal sheet in the presence of variable transverse magnetic field, thermal radiation, viscous dissipation and nonlinearly moving free stream. Similar solution of the fluid flow problem is obtained using forth-order Runge-Kutta method along with shooting technique. Influence of various pertinent parameters such as stretching parameter, stretching index, Hartmann number, Prandtl number, Eckert number and radiation parameter are displayed through graphs and tables.
Similar content being viewed by others
References
Sakiadis BC (1961) Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two dimensional and axisymmetric flow. AIChE J 7:26–28
Crane LJ (1970) Flow past a stretching sheet. Z Angew Math Phys 21:645–647
Gupta PS, Gupta AS (1977) Heat and mass transfer on a stretching sheet with suction or blowing. Can J Chem Eng 55:744–746
Sajid M, Hayat T (2008) Influence of thermal radiation on the boundary layer flow due to an exponentially stretching sheet. Int Commun Heat Mass Transf 35:347–356
Pavlov KB (1974) Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a plane surface. Magnitnaya Gidrodinamika 10(4):146–148
Vajravelu K (2001) Viscous flow over a nonlinearly stretching sheet. Appl Math Comput 124:281–288
Cortell R (2007) Viscous flow and heat transfer over a nonlinearly stretching sheet. Appl Math Comput 184(2):864–873
Hayat T, Abbas Z, Sajid M, Asghar S (2007) The influence of thermal radiation on MHD flow of a second grade fluid. Int J Heat Mass Transf 50:931–941
Cortell R (2008) Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet. Phys Lett A 372:631–636
Raptis A, Perdikis C (2006) Viscous flow over a non-linearly stretching sheet in the presence of a chemical reaction and magnetic field. Int J Non-Linear Mech 41:527–529
Prasad KV, Vajravelu K (2009) Heat transfer in the MHD flow of a power law fluid over a non-isothermal stretching sheet. Int J Heat Mass Transf 52:4956–4965
Afzal N (2010) Momentum and thermal boundary layers over a two-dimensional or axisymmetric non-linear stretching surface in a stationary fluid. Int J Heat Mass Transf 53:540–547
Nandeppanavar MM, Vajravelu K, Abel MS, Ng C (2011) Heat transfer over a nonlinearly stretching sheet with non-uniform heat source and variable wall temperature. Int J Heat Mass Transf 54:4960–4965
Nadeem S, Hussain A (2009) MHD flow of a viscous fluid on a nonlinear porous shrinking sheet with homotopy analysis method. Appl Math Mech -Engl Ed 30(12):1569–1578
Alinejad J, Samarbakhsh S (2012) Viscous flow over nonlinearly stretching sheet with effects of viscous dissipation. J Appl Math 2012, Article ID 587834, doi:10.1155/2012/587834
Grubka LJ, Bobba KM (1985) Heat transfer characteristics of a continuous, stretching surface with variable temperature. J Heat Transf 107(1):248–250
Anjali Devi SP, Gururaj ADM (2012) Effects of variable viscosity and nonlinear radiation on MHD flow with heat transfer over a surface stretching with a power-law velocity. Adv Appl Sci Res 3(1):319–334
Bachok N, Ishak A (2011) Similarity solutions for the stagnation-point flow and heat transfer over a nonlinearly stretching/shrinking Sheet. Sains Malaysiana 40(11):1297–1300
Vyas P, Ranjan A (2010) Dissipative MHD boundary-layer flow in a porous medium over a sheet stretching nonlinearly in the presence of radiation. Appl Math Sci 4(63):3133–3142
Singh PK, Singh J (2012) MHD flow with viscous dissipation and chemical reaction over a stretching porous plate in porous medium. Int J Eng Res App 2(2):1556–1564
Jain MK, Jain RK, Iyengar SRK (2012) Numerical methods for scientific and engineering computation. New Age International, New Delhi
Mahapatra TR, Gupta AS (2002) Heat transfer in stagnation-point flow towards a stretching sheet. Heat Mass Transf 38:517–521
Layek GC, Mukhopadhyay S, Ahmad SA (2007) Heat and mass transfer analysis for boundary layer stagnation-point flow towards a heated porous stretching sheet with heat absorption/generation and suction/blowing. Int Commun Heat Mass Transf 34:347–356
Chakraborty A, Gupta AS, Das BK, Jana RN (2005) Hydromagnetic flow past a rotating porous plate in a conducting fluid rotating about a noncoincident parallel axis. Acta Mech 176:107–119
Mukhopadhyay S, Layek GC, Ahmad SA (2005) Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity. Int J Heat Mass Transf 48:4460–4466
Kandasamy R, Periasamy K, Sivagnana Prabhu KK (2005) Chemical reaction, heat and mass transfer on MHD flow over a vertical stretching surface with heat source and thermal stratification effects. Int J Heat Mass Transf 48:4557–4561
Makinde OD (2012) Computational modelling of MHD unsteady flow and heat transfer toward a flat plate with Navier slip and Newtonian heating. Braz J Chem Eng 29(1):159–166
Seth GS, Jana RN, Maiti MK (1981) Unsteady hydromagnetic flow past a porous plate in a rotating medium with time dependent free stream. Rev Roumaine Sci Techn Serie Mec Appl 26(3):383–400
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kumbhakar, B., Sriniivasa Rao, P. Dissipative Boundary Layer Flow over a Nonlinearly Stretching Sheet in the Presence of Magnetic Field and Thermal Radiation. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 85, 117–125 (2015). https://doi.org/10.1007/s40010-014-0187-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40010-014-0187-8