Abstract
The effect of radiation on the flow near the two-dimensional stagnation point of an incompressible, viscous, electrically conducting dusty fluid towards stretching sheet is analyzed. Rosseland approximation is used to model the radiative heat transfer. Highly non-linear momentum boundary layer equations and thermal boundary layer equations are converted into similarity equations and then solved numerically using Runge Kutta Fehlberg fourth–fifth order method. The thermal results are analyzed for the situation when stretching boundary is prescribed with surface temperature and prescribed with heat flux. Comparison with previously published work is performed and full agreement is obtained. Variation of physical parameters with the ratio of free stream velocity parameter to stretching sheet parameter have been illustrated graphically and in tabular form to depict special features of the solutions.
Similar content being viewed by others
References
Crane, L.J.: Flow past a stretching sheet. Z. Angew. Math. Phys (ZAMP)21, 645–647 (1970)
Grubka, L.J., Bobba, K.M.: Heat transfer characteristics of a continuous stretching surface with variable temperature. J. Heat Transf. 107, 248–250 (1985)
Chen, C.H.: Laminar mixed convection adjacent to vertical, continuously stretching sheets. Heat Mass Transf. 33, 471–476 (1998)
Cortell, R.: A note on magnetohydrodynamic flow of a power-law fluid over a stretching sheet. Appl. Math. Comput. 168, 557–566 (2005)
Hiemenz, K.: Die grenzschicht an einem in dengleich formigen flussigkeitsstrom eingetauchten geraden kreiszlinder. Dingl. Polytec. J. 326, 321–328 (1911)
Chiam, T.C.: Stagnation-point flow towards a stretching plate. J. Phys. Soc. Jpn 63, 2443–2444 (1994)
Roy Mahapatra, T., Gupta, A.S.: Magnetohydrodynamics stagnation point flow towards a stretching sheet. Acta Mechnica 152, 191–196 (2001)
Roy Mahapatra, T., Gupta, A.S.: Heat transfer in stagnation pint flow todards a stretching sheet. Heat Mass Transf. 38, 517–521 (2002)
Ishak, A., Jafar, K., Nazar, R., Pop, I.: MHD stagnation point flow towards a stretching sheet. Physica A 388, 3377–3383 (2009)
Pop, S.R., Grosan, T., Pop, I.: Radiation effects on the flow near the stagnation point of a stretching sheet. Technische Mechanik 29, 100–106 (2004)
Pal, D.: Heat and mass transfer in stagnation-point flow towards a stretching surface in the presence of buoyancy force and thermal radiation. Meccanica 44, 145–158 (2009)
Singh, P., Jangid, A., Tomer, N.S., Sinha, D.: Effects of thermal radiation and magnetic field on unsteady stretching permeable sheet in presence of free stream velocity. Int. J. Inforn. Mathe. Sci 03, 160–166 (2010)
Pop, I., Ishak, A., Aman, F.: Radiation effects on the MHD flow near the stagnation point of a stretching sheet: revisited. Z. Angew. Math. Phys. (2011). doi:10.1007/s00033-011-0131-6
Abel, M.S., Mahesha, N.: Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity, non-uniform heat source and radiation. App. Math. Model 32, 1965–1983 (2008)
Chen, C.H.: Magneto-hydrodynamic mixed convection of a power-law fluid past a stretching surface in the presence of thermal radiation and internal heat generation/absorption. Int. J. Non-Linear Mechs. 44, 596–603 (2009)
Makinde, O.D.: On MHD boundary-layer flow and mass transfer past a vertical plate in a porous medium with constant heat flux. Int. J. Num. Methods Heat Fluid Flow. 19(3/4), 546–554 (2009)
Saffman, P.G.: On the stability of laminar flow of a dusty gas. J. Fluid Mechs 13, 120–128 (1962)
Chakrabarti, K.M.: Note on Boundary layer in a dusty gas. AIAA J. 12(8), 1136–1137 (1974)
Agranat, V.M.: Effect of pressure gradient on friction and heat transfer in a dusty boundary layer. Fluid Dyn. 23(5), 729–732 (1988)
Vajravelu, K., Nayfeh, J.: Hydromagnetic flow of a dusty fluid over a stretching sheet. Int. J. Non-linear Mech. 27, 937–945 (1992)
Datta, N., Mishra, S.K.: Two-dimensional stagnation point flow of a dusty fluid near an oscillating plate. Acta Mechanica 36(1–2), 71–78 (1980)
Gireesha, B.J., Ramesh, G.K., Subhas Abel, M., Bagewadi, C.S.: Boundary layer flow and heat transfer of a dusty fluid flow over a stretching sheet with non-uniform heat source/sink. Int. J. Multiph. Flow 37(8), 977–982 (2011)
Gireesha, B.J., Manjunatha, S., Bagewadi, C.S.: Unsteady hydromagnetic boundary layer flow and heat transfer of dusty fluid over a stretching sheet. Afr. Mat 22 (2011). doi:10.1007/s13370-011-0031-0
Ishak, A., Nazar, R., Pop, I.: Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet. Heat Mass Transf. 44, 921–927 (2008)
Pal, D., Mondal, H.: MHD non-Darcy mixed convective diffusion of species over a stretching sheet embedded in a porous medium with non-uniform heat source/sink, variable viscosity and Soret effect. Commun. Nonlinear. Sci. Numer. Simulat (2011). doi:10.1016/j.cnsns.2011.05.035
Aziz, A.: A similarity solution for laminar thermal boundary layer over aflat plate with a convective surface boundary condition. Com. Non. Sci Numer Simulat 14, 1064–1068 (2009)
Schlichting, H.: Boundary layer theory, McGraw-Hill, New York (1968)
Acknowledgments
The authors are very much thankful to the editor and referee for their encouraging comments and constructive suggestions to improve the presentation of this manuscript.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ramesh, G.K., Gireesha, B.J. & Bagewadi, C.S. Stagnation point flow of a MHD dusty fluid towards a stretching sheet with radiation. Afr. Mat. 25, 237–249 (2014). https://doi.org/10.1007/s13370-012-0114-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13370-012-0114-6
Keywords
- Boundary layer flow
- Dusty fluid
- Fluid-particle interaction parameter
- Radiation
- Stagnation point flow
- Numerical solution