Abstract
In the present work, the effect of MHD flow and heat transfer within a boundary layer flow on an upper-convected Maxwell (UCM) fluid over a stretching sheet is examined. The governing boundary layer equations of motion and heat transfer are non-dimensionalized using suitable similarity variables and the resulting transformed, ordinary differential equations are then solved numerically by shooting technique with fourth order Runge–Kutta method. For a UCM fluid, a thinning of the boundary layer and a drop in wall skin friction coefficient is predicted to occur for higher the elastic number. The objective of the present work is to investigate the effect of Maxwell parameter β, magnetic parameter Mn and Prandtl number Pr on the temperature field above the sheet.
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Abbreviations
- b :
-
stretching rate [s−1]
- x :
-
horizontal coordinate [m]
- y :
-
vertical coordinate [m]
- u :
-
horizontal velocity component [m s−1]
- v :
-
vertical velocity component [m s−1]
- T :
-
temperature [K]
- t :
-
time [s]
- C p :
-
specific heat [J kg−1 K−1]
- f :
-
dimensionless stream function
- Pr :
-
Prandtl number, \(\frac{\mu C_{p}}{k}\)
- M 2 :
-
Magnetic parameter, \(\frac{\sigma B_{0}^{2}}{\rho b}\)
- q :
-
heat flux, \(- k\frac{\partial T}{\partial y}\) [J s−1 m−2]
- Nu x :
-
local Nusselt number
- β :
-
Maxwell parameter
- η :
-
similarity variable, (4)
- θ :
-
dimensionless temperature
- k :
-
thermal diffusivity [m2 s−1]
- μ :
-
dynamic viscosity [kg m−1 s−1]
- υ :
-
kinematic viscosity [m2 s−1]
- ρ :
-
density [kg m−3]
- τ :
-
shear stress, μ∂u/∂y [kg m−1 s−2]
- ψ :
-
stream function [m2 s−1]
- x :
-
local value
- ′:
-
first derivative
- ″:
-
second derivative
- ‴:
-
third derivative
References
Sarpakaya T (1961) Flow of non-Newtonian fluids in a magnetic field. AIChE J 7:324–328
Crane LJ (1970) Flow past a stretching plate. Z Angew Math Phys 21:645–647
Grubka LG, Bobba KM (1985) Heat transfer characteristics of a continuous stretching surface with variable temperature. J Heat Transf 107:248–250
Dutta BK, Gupta AS (1987) Cooling of a stretching sheet in a various flow. Ind Eng Chem Res 26:333–336
Jeng DR, Chang TCA, Dewitt KJ (1986) Momentum and heat transfer on a continuous surface. J Heat Transf 108:532–539
Chakrabarti A, Gupta AS (1979) Hydromagnetic flow and heat transfer over a stretching sheet. Q Appl Math 37:73–78
Andersson HI, Bech KH, Dandapat BS (1992) Magnetohydrodynamic flow of a power-law fluid over a stretching sheet. Int J Non-Linear Mech 27:929–936
Afzal N (1993) Heat transfer from a stretching surface. Int J Heat Mass Transf 36:1128–1131
Prasad KV, Abel S, Datti PS (2003) Diffusion of chemically reactive species of a non-Newtonian fluid immersed in a porous medium over a stretching sheet. Int J Non-Linear Mech 38:651–657
Agassant JF, Avens P, Sergent J, Carreau PJ (1991) Polymer processing: principles and modelling. Hanser Publishers, Munich
Schulz DN, Glass JE (1991) Polymers as rheology modifiers. ACS symposium series, vol 462. American Chemical Society, Washington
Bird RB, Armstrong RC, Hassager O (1987) Dynamics of polymeric liquids, vol 1. Wiley, New York
Fosdick RL, Rajgopal KR (1979) Anamolous features in the model of second-order fluids. Arch Ration Mech Anal 70:145
Hayat T, Abbas Z, Sajid M (2006) Series solution for the upper-convected Maxwell fluid over a porous stretching plate. Phys Lett A 358:396–403
Sadeghy K, Najafi AH, Saffaripour M (2005) Sakiadis flow of an upper convected Maxwell fluid. Int J Non-Linear Mech 40:1220–1228
Alizadeh-Pahlavan A, Aliakbar V, Vakili-Farahani F, Sadeghy K (2009) MHD flows of UCM fluids above porous stretching sheets using two-axillary-parameter homotopy analysis method. Commun Nonlinear Sci Numer Simul 14:473–488
Renardy M (1997) High Weissenberg number boundary layers for the upper convected Maxwell fluid. J Non-Newton Fluid Mech 68:125
Rao IJ, Rajgopal KR (2007) On a new interpretation of the classical Maxwell model. Mech Res Commun 34:509–514
Sadeghy K, Hajibeygi H, Taghavi S-M (2006) Stagnation point flow of upper-convected Maxwell fluids. Int J Non-Linear Mech 41:1242–1247
Aliakbar V, Alizadeh-Pahlavan A, Sadeghy K (2009) The influence of thermal radiation on MHD flow of Maxwellian fluids above stretching sheets. Commun Nonlinear Sci Numer Simul 14(3):779–794
Alizadeh-Pahlavan A, Sadeghy K (2009) On the use of homotopy analysis method for solving unsteady MHD flow of Maxwellian fluids above impulsively stretching sheets. Commun Nonlinear Sci Numer Simul 14(4):1355–1365
Conte SD, de Boor C (1972) Elementary numerical analysis. McGraw-Hill, New York
Cebeci T, Bradshaw P (1984) Physical and computational aspects of convective heat transfer. Springer, New York
Rajagopal KR In: Montieivo Marques MDP, Rodrigues JF (eds) Boundary layers in non-Newtonian fluids
Hsiao K-L (2011) MHD mixed convection for viscoelastic fluid past a porous wedge. Int J Non-Linear Mech 46:1–8
Hsiao K-L (2010) Viscoelastic fluid over a stretching sheet with electromagnetic effects and non-uniform heat source/sink. Math Probl Eng 2010:740943, 14 pages
Ishak A, Nazar R, Pop I (2009) Boundary layer flow and heat transfer over an unsteady stretching vertical surface. Meccanica 44:369–375
Babaelahi M, Domairry G, Joneidi AA (2010) Viscoelastic MHD flow boundary layer over a stretching surface with viscous and ohmic dissipations. Meccanica 45:817–827
Hayat T, Abbas Z, Sajjid M (2009) MHD stagnation point flow of an upper convected Maxwell fluid over a stretching sheet. Chaos Solitons Fractals 39:840–848
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Subhas Abel, M., Tawade, J.V. & Nandeppanavar, M.M. MHD flow and heat transfer for the upper-convected Maxwell fluid over a stretching sheet. Meccanica 47, 385–393 (2012). https://doi.org/10.1007/s11012-011-9448-7
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DOI: https://doi.org/10.1007/s11012-011-9448-7