Radiation Effect on Unsteady MHD Flow over a Stretching Surface
Unsteady magnetohydrodynamics (MHD) boundary
layer flow and heat transfer over a continuously stretching surface in
the presence of radiation is examined. By similarity transformation,
the governing partial differential equations are transformed to a set of
ordinary differential equations. Numerical solutions are obtained by
employing the Runge-Kutta-Fehlberg method scheme with shooting
technique in Maple software environment. The effects of
unsteadiness parameter, radiation parameter, magnetic parameter and
Prandtl number on the heat transfer characteristics are obtained and
discussed. It is found that the heat transfer rate at the surface
increases as the Prandtl number and unsteadiness parameter increase
but decreases with magnetic and radiation parameter.
[1] Salleh, M.Z., Nazar, R. & Pop, I. (2010). Boundary layer flow and heat
transfer over a stretching sheet with Newtonian heating. Journal of the
Taiwan Institute of Chemical Engineers, 41, pp. 651-655.
[2] Abbas, Z., & Hayat, T. (2008). Radiation effects on MHD flow in a
porous space. International Journal of Heat and Mass Transfer, 51, pp.
1024-1033.
[3] Ghaly, A.Y. (2002). Radiation effects on a certain MHD free convection
flow. Chaos, Solitons and Fractals, 13, pp. 1843-1850.
[4] Subhashini, S.V., Samuel, N., & Pop, I. (2011). Effects of buoyancy
assisting and opposing flows on mixed convection boundary layer flow
over a permeable vertical surface. Internationl Communications in Heat
and Mass Transfer, 38, pp. 499-503.
[5] Raptis, A. (2004). Effect of thermal radiation on MHD flow. Applied
Mathematics and Computation, 153, pp. 645-649.
[6] Chiam, T.C. (1995). Hydromagnetic flow over a surface stretching with
a power-law velocity. International Journal Engineering Sciences,
33(3), pp. 429-435.
[7] Chen, C.H. (2010). On the analytic solution of MHD flow and heat
transfer for two types of viscoelastic fluid over a stretching sheet with
energy dissipation, internal heat source and thermal radiation.
International Journal of Heat and Mass Transfer,5 3, pp. 4264-4273.
[8] Magyari, E., & Keller, B. (2000). Exact solutions for self-similar
boundary-layer flows induced by permeable stretching walls. Eur. J.
Mech. B-Fluids, 19, pp. 109-122.
[9] Fang, T., Zhang, J., & Zhong, Y. (2012). Boundary layer flow over a
stretching sheet with variables thickness. Applied Mathematics and
Computation, 218, pp. 7241-7252.
[10] Liao, S. (2010). A new branch of solutions of boundary-layer flows over
an impermeable stretched plate. International Journal of Heat and Mass
Transfer, 48, pp. 2529-2539.
[11] Sakiadis, B.C. (1961). Boundary-layer behavior on continuous solid
surfaces: I. boundary layer equations for two dimensional and
assymmetric flow. AICHE J, 7, pp. 26-28.
[12] El-Aziz, M.A. (2009). Radiation effect on the flow and heat transfer
over an unsteady stretching sheet. International Communications in Heat
and Mass Transfer, 36, pp. 521-524.
[13] Elbashbeshy, E.M.A., & Bazid, M.A.A. (2004). Heat transfer over an
unsteady stretching surface. Heat Mass Transfer, 41, pp. 1-4.
[14] El-Aziz, M.A. (2010). Unsteady fluid and heat flow induced by a
stretching sheet with mass transfer and chemical reaction. Chemical
Engineering Communications, 197, pp. 1261-1272.
[15] Ishak, A., Nazar, R., & Pop, I. (2009). Boundary layer flow and heat
transfer over an unsteady stretching vertical surface. Meccanica , 44, pp.
369-375.
[16] Bachok, N., Ishak, A., & Nazar, R. (2011). Flow and heat transfer over
an unsteady stretching sheet in a micropolar fluid. Meccanica, 46, pp.
935-942.
[17] Liu, I.C., & Andersson, H.I. (2008). Heat transfer in a liquid film on an
unsteady stretching sheet. International Journal of Thermal Sciences, 47,
pp. 766-772.
[18] Ishak, A. (2010). Unsteady MHD flow and heat transfer over a
stretching plate. Journal of Applied Sciences, 10, pp. 2127-2131.
[19] Andersson, H.I., Aarseth, J.B., & Dandapat, B.S. (2000). Heat transfer
in a liquid film on an unsteady stretching surface. International Journal
of Heat and Mass Transfer, 43, pp. 69-74
[20] Liu, I.C. (2005). A note on heat and mass transfer for a hydromagnetic
flow over a stretching sheet. International Communications in Heat and
Mass Transfer, 32, pp. 1075-1084.
[1] Salleh, M.Z., Nazar, R. & Pop, I. (2010). Boundary layer flow and heat
transfer over a stretching sheet with Newtonian heating. Journal of the
Taiwan Institute of Chemical Engineers, 41, pp. 651-655.
[2] Abbas, Z., & Hayat, T. (2008). Radiation effects on MHD flow in a
porous space. International Journal of Heat and Mass Transfer, 51, pp.
1024-1033.
[3] Ghaly, A.Y. (2002). Radiation effects on a certain MHD free convection
flow. Chaos, Solitons and Fractals, 13, pp. 1843-1850.
[4] Subhashini, S.V., Samuel, N., & Pop, I. (2011). Effects of buoyancy
assisting and opposing flows on mixed convection boundary layer flow
over a permeable vertical surface. Internationl Communications in Heat
and Mass Transfer, 38, pp. 499-503.
[5] Raptis, A. (2004). Effect of thermal radiation on MHD flow. Applied
Mathematics and Computation, 153, pp. 645-649.
[6] Chiam, T.C. (1995). Hydromagnetic flow over a surface stretching with
a power-law velocity. International Journal Engineering Sciences,
33(3), pp. 429-435.
[7] Chen, C.H. (2010). On the analytic solution of MHD flow and heat
transfer for two types of viscoelastic fluid over a stretching sheet with
energy dissipation, internal heat source and thermal radiation.
International Journal of Heat and Mass Transfer,5 3, pp. 4264-4273.
[8] Magyari, E., & Keller, B. (2000). Exact solutions for self-similar
boundary-layer flows induced by permeable stretching walls. Eur. J.
Mech. B-Fluids, 19, pp. 109-122.
[9] Fang, T., Zhang, J., & Zhong, Y. (2012). Boundary layer flow over a
stretching sheet with variables thickness. Applied Mathematics and
Computation, 218, pp. 7241-7252.
[10] Liao, S. (2010). A new branch of solutions of boundary-layer flows over
an impermeable stretched plate. International Journal of Heat and Mass
Transfer, 48, pp. 2529-2539.
[11] Sakiadis, B.C. (1961). Boundary-layer behavior on continuous solid
surfaces: I. boundary layer equations for two dimensional and
assymmetric flow. AICHE J, 7, pp. 26-28.
[12] El-Aziz, M.A. (2009). Radiation effect on the flow and heat transfer
over an unsteady stretching sheet. International Communications in Heat
and Mass Transfer, 36, pp. 521-524.
[13] Elbashbeshy, E.M.A., & Bazid, M.A.A. (2004). Heat transfer over an
unsteady stretching surface. Heat Mass Transfer, 41, pp. 1-4.
[14] El-Aziz, M.A. (2010). Unsteady fluid and heat flow induced by a
stretching sheet with mass transfer and chemical reaction. Chemical
Engineering Communications, 197, pp. 1261-1272.
[15] Ishak, A., Nazar, R., & Pop, I. (2009). Boundary layer flow and heat
transfer over an unsteady stretching vertical surface. Meccanica , 44, pp.
369-375.
[16] Bachok, N., Ishak, A., & Nazar, R. (2011). Flow and heat transfer over
an unsteady stretching sheet in a micropolar fluid. Meccanica, 46, pp.
935-942.
[17] Liu, I.C., & Andersson, H.I. (2008). Heat transfer in a liquid film on an
unsteady stretching sheet. International Journal of Thermal Sciences, 47,
pp. 766-772.
[18] Ishak, A. (2010). Unsteady MHD flow and heat transfer over a
stretching plate. Journal of Applied Sciences, 10, pp. 2127-2131.
[19] Andersson, H.I., Aarseth, J.B., & Dandapat, B.S. (2000). Heat transfer
in a liquid film on an unsteady stretching surface. International Journal
of Heat and Mass Transfer, 43, pp. 69-74
[20] Liu, I.C. (2005). A note on heat and mass transfer for a hydromagnetic
flow over a stretching sheet. International Communications in Heat and
Mass Transfer, 32, pp. 1075-1084.
@article{"International Journal of Information, Control and Computer Sciences:55227", author = "Zanariah Mohd Yusof and Siti Khuzaimah Soid and Ahmad Sukri Abd Aziz and Seripah Awang Kechil", title = "Radiation Effect on Unsteady MHD Flow over a Stretching Surface", abstract = "Unsteady magnetohydrodynamics (MHD) boundary
layer flow and heat transfer over a continuously stretching surface in
the presence of radiation is examined. By similarity transformation,
the governing partial differential equations are transformed to a set of
ordinary differential equations. Numerical solutions are obtained by
employing the Runge-Kutta-Fehlberg method scheme with shooting
technique in Maple software environment. The effects of
unsteadiness parameter, radiation parameter, magnetic parameter and
Prandtl number on the heat transfer characteristics are obtained and
discussed. It is found that the heat transfer rate at the surface
increases as the Prandtl number and unsteadiness parameter increase
but decreases with magnetic and radiation parameter.", keywords = "Heat transfer, magnetohydrodynamics, radiation, unsteadiness.", volume = "6", number = "12", pages = "1655-4", }
