Three-dimensional MHD boundary layer flow due to an axisymmetric shrinking sheet with radiation, viscous dissipation and heat source/sink
More details
Hide details
Department of Mathematics, Osmania University, Hyderabad, Telangana, INDIA
Online publication date: 2016-05-28
Publication date: 2016-05-01
International Journal of Applied Mechanics and Engineering 2016;21(2):393-406
An analysis is made to study a three dimensional MHD boundary layer flow and heat transfer due to a porous axisymmetric shrinking sheet. The governing partial differential equations of momentum and energy are transformed into self similar non-linear ordinary differential equations by using the suitable similarity transformations. These equations are, then solved by using the variational finite element method. The flow phenomena is characterised by the magnetic parameter M, suction parameter S, porosity parameter Kp, heat source/sink parameter Q, Prandtl number Pr, Eckert number Ec and radiation parameter Rd. The numerical results of the velocity and temperature profiles are obtained and displayed graphically.
Sakidis B.C. (1961): Boundary-layer behavior on a continuous solid surface: II- The boundary layer on a continuous flat surface. – AIChE Journal, vol.7, pp.221-225.
Crane L.J. (1970): Flow past a stretching plate. – Journal of Applied Mathematics and Physics (ZAMP), vol.21, pp.590-595.
Grubka L.J. and Bobba K.M. (1985): Heat transfer characteristics of a continuous stretching surface with variable temperature. – ASME Trans, vol.107, pp.248-256.
Gupta P.S. and Gupta A.S. (1979): Heat and mass transfer on a strtching surface with suction or blowing. – Cand. J. Chem. Eng, vol.55, pp.744-746.
Wang C.Y. (1990): Liquid film on an unsteady stretching sheet. – Quart. Appl. Math., vol.48, pp.601-610.
Miklavcic M. and Wang C.Y. (2006): Viscous flow due to a shrinking sheet. – Quart. of Appl. Math., vol.64, No.2, pp.283-290.
Fang T. and Zhang J. (2010): Thermal boundary layer over a shrinking sheet: an analytical solution. – Acta Mech., vol.209, pp.325-343.
Noor N.F.M. and Kechilb S.A. (2010): Hashimc I, Simple non-perturbative solution for MHD viscous flow due to a shrinking sheet. – Commun. in Nonlinear Sc. and Numer. Simul., vol.15, No.2, pp.144-148.
Sajid M. and Hayat T. (2009): The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet. – Chaos, Solitons and Fractals, vol.39, No.3, pp.1317-1323.
Midya C. (2012a): Hydromagnetic boundary layer flow and heat transfer over a linearly shrinking permeable surface. – Int. J. of Appl. Math. and Mech., vol.8, No.3, pp.57-68.
Muhaimin, Ramasamy Kandasamy I., Hashim and Azme B. Khamis (2009): On the effect of chemical reaction, heat and mass transfer on nonlinear MHD boundary layer past a porous shrinking sheetwith suction. – Theoret. Appl. Mech., vol.36, No.2, pp.101-117.
Bhattacharyya K. (2011): Dual solutions in boundary layer stagnation point flow and mass transfer with chemical reaction past a stretching/shrinking sheet. – Int. Commun. Heat Mass Transfer, vol.38, pp.917-922.
Van Gorder R.A., Vajravelu K. and Pop I. (2012): Hydromagnetic stagnation-point flow of a viscous fluid over a stretching/shrinking sheet. – Meccanica, vol.47, pp.31-50.
Hunegnaw Dessie and Kishan N. (2014): MHD effects on heat transfer over stretching sheet embedded in porous medium with variable viscosity, viscous dissipation and heat source/sink. – Ain Shams Eng. J., vol.5, pp.967-977.
Lok Y.Y., Ishak A. and Pop I. (2011): MHD stagnation-point flow towards a shrinking sheet. – Int. J. Numer. Methods Heat Fluid Flow, vol.21, pp.61-72.
Van Rij J., Ameel T. and Harman T. (2009): The effect of viscous dissipation and rarefaction on rectangular microchannel convective heat transfer. – Int. J. Therm. Sci., vol.48, pp.271-281.
Gebhart B. and Mollendrof J. (): Viscous dissipation in external natural convection flows. – Journal of Fluids, vol.38, 969, pp.97-107.
Koo J. and Kleinstreuer C. (2004): Viscous dissipation effects in microtubes and microchannels. – Int. J. Heat Mass Transf., vol.47, pp.3159-3169.
Sparrow E.M. and Cess R.D. (1961): Temperature-dependent heat sources or sinks in a stagnation point flow. – Applied Scientific Research, vol.10, No.1, pp.185-197.
Azim M.A., Mamun A.A. and Rahman M.M. (2010): Viscous Joule heating MHD-conjugate heat transfer for a vertical flat plate in the presence of heat generation. – International Communications in Heat and Mass Transfer, vol.37, No.6, pp.666-674.
Tania S. Khaleque and Samad M.A. (2010): Effects of radiation, heat generation and viscous dissipation on MHD free convection flow along a stretching sheet. – Research J. of Appl. Sci., Eng. and Tech., vol.2, No.4, pp.368-377.
Chamkha A.J. (1999): Hydro magnetic three-dimensional free convection on a vertical stretching surface with heat generation or absorption. – Int. J. Heat and Fluid Flow, vol.20, pp.84-92.
Raptis A. (1998): Flow of a micropolar fluid past a continuously moving plate by the presence of radiation. – Int. J. Heat Mass Transfer, vol.41, pp.2865-2866.
Cortell R. (2008): Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet. – Vol.372, No.5, pp.631-636.
Hossain M.A. and Takhar H.S. (1996): Radiation effect on mixed convection along a vertical plate with uniform surface temperature. – Int. J. Heat Mass Transfer, vol.31, pp.243-248.
Takhar H.S., Gorla R.S.R. and Soundalgekar V.M. (1996): Radiation effects on MHD free convection flow of a gas past a semi-infinite vertical plate. – Int. J. N. Meth Heat Fluid Flow, vol.6, pp.77-83.
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, vol.45, pp.931-935.
Hunegnaw Dessie and Kishan N. (2014): MHD booundary layer flow and heat transfer over a non-linearly permeable stretching/shrinking sheet in a nanofluid with suction effect, thermal radiation and chemical reaction. – Journal of Nanofluids, vol.3, pp.1-9.
Rajesh V. (2011): Chemical reaction and radiation effects on the transient MHD free convection flow of dissipative fluid past an infinite vertical porous plate with ramped wall temperature. – Chemical Industry and Chemical Engineering Quarterly, vol.17, No.2, pp.189-198.
Journals System - logo
Scroll to top