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Abstrakty
The flow of a second grade fluid past a porous plate has been studied using a modified model of second grade fluid that has shear dependent viscosity and can predict the normal stress difference. The boundary value problem subject to two different sets of boundary conditions is investigated. In the first instance, we consider that the plate is at temperature higher than the fluid. The second case deals with the analysis of an insulated plate. The differential equations governing the flow are solved using the homotopy analysis method (HAM). Expressions for velocity and temperature profiles are plotted and discussed.
Rocznik
Tom
Strony
101--121
Opis fizyczny
Bibliogr. 30 poz., wykr.
Twórcy
autor
autor
autor
- Department of Mathematics Quaid-i-Azam University 45320, Islamabad, PAKISTAN, tjJensy@hotmail.com
Bibliografia
- Ayub M., Rasheed A. and Hayat T. (2003): Exact flow of a third grade fluid past a porous plate using homotopy analysis method. - Int. J. Eng. Sci., vol.41, pp.2091-2103.
- Bandelli R. (1995): Unsteady unidirectional flows of second grade fluids in domains with heated boundaries. - Int. J. Non-Linear Mech., vol.30, pp.263-269.
- Bandelli R. and Rajagopal K.R. (1996): On the falling of objects in non-Newtonian fluids. - Ann. Ferrara, vol.39, pp.1-18.
- Benharbit A.M. and Siddiqui A.M. (1992): Certain solutions of the equations of the planar motion of a second grade fluid for steady and unsteady cases. - Acta Mech., vol.94, pp.85-96.
- Bird R.B., Armstrong R.C. and Hassager J. (1977): Dynamics of polymeric liquids. - Vol.1. New York: Wiley.
- Dunn J.E. and Fosdick R.L. (1974): Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade. - Arch. Rat. Mech. Anal., vol.56, pp.191-252.
- Dunn J.E. and Rajagopal K.R. (1995): Fluids of differential type: critical review and thermodynamic analysis. - Int. J. Eng. Sci., vol.33, pp.689-729.
- Fosdick R.L. and Rajagopal K.R. (1979): Anomalous features in the model of second order fluids. - Arch. Rat. Mech. Anal., vol.70, pp.145-152.
- Franchi H. and Straughan B. (1993): Stability and nonexistence results in the generalized theory of a fluid of second grade. - J. Math. Anal. Appl., vol.180, pp.122-137.
- Gupta G. and Massoudi M. (1993): Flow of a generalized second grade fluid between heated plates. - Acta Mech., vol.99, pp.21-33.
- Hayat T., Asghar S. and Siddiqui A.M. (1998): Periodic unsteady flows of a non-Newtonian fluid. - Acta Mech., vol.131, pp.169-175.
- Hayat T., Asghar S. and Siddiqui A.M. (1999): On the moment of a plane disk in a non-Newtonian fluid. - Acta Mech., vol.136, pp.125-131.
- Hayat T., Asghar S. and Siddiqui A.M. (2000): Some unsteady unidirectional flows of a non-Newtonian fluid. - Int. J. Eng. Sci., vol.38, pp.337-346.
- Liao S.J. (1992): The proposed homotopy analysis technique for the solution of nonlinear problems. - PhD Thesis, Shanghai Jiao Tong University.
- Liao S.J. (2003): On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet. - J. Fluid Mech., vol.488, pp.189-212.
- Liao S.J. (2003): Beyond perturbation: Introduction to homotopy analysis method. - Chapman and Hall/CRC Press, Boca Raton.
- Liao S.J. and Campo A. (2002): Analytic solutions of the temperature distribution in Blasius viscous flow problems. - J. Fluid Mech., vol.453, pp.411-425.
- Liao S.J. and Pop I. (2004): Explicit analytic solution for similarity boundary layer equations. - Int. J. Heat and Mass Trans., vol.47, pp.75-85.
- Man C.S. (1992): Nonsteady channel flow of ice as a modified second grade fluid with power law viscosity. - Arch. Rat. Mech. Anal., vol.119, pp.35-57.
- Maneschy C.E., Massoudi M. and Ghoneimy A. (1993): Heat transfer analysis of a non-Newtonian fluid past a porous plate. - Int. J. Non-Linear Mech., vol.28, pp.131-143.
- Massoudi M. and Phuoc T.X. (2001): Fully developed flow of a modified second grade fluid with temperature dependent viscosity. - Acta Mech., vol.150, pp.23-37.
- Rajagopal K.R. (1982): A note on unsteady unidirectional flows of a non-Newtonian fluid. - Int. J. Non-Linear Mech., vol.17, pp.369-373.
- Rajagopal K.R. (1983): Longitudinal and torsional oscillations of a rod in a non-Newtonian fluid. - Acta Mech., vol.49, pp.282-285.
- Rajagopal K.R. (1984): On the creeping flow of the second grade fluid. - J. Non-Newtonian Fluid Mech., vol.15, pp.239-246.
- Rajagopal K.R. and Gupta A.S. (1984): An exact solution for the flow of a non-Newtonian fluid past an infinite plate. - Meccanica, vol.19, pp.158-160.
- Rivilin R.S. and Ericksen J.L. (1995): Stress deformation relations for isotropic materials. - J. Rat. Mech. Anal., vol.4, pp.323-425.
- Siddiqui A.M., Hayat T. and Asghar S. (1999): Periodic flows of a non-Newtonian fluid between two parallel plates. - Int. J. Non-Linear Mech., vol.34, pp.895-899.
- Slattery J.C. (1999): Advanced transport phenomena. - New York: Cambridge University Press.
- Straughan B. (1983): Energy stability in the Benard problem for a fluid of second grade. - J. Appl. Math. Phys. (ZAMP), vol.34, pp.502-508.
- Straughan B. (1992): The energy method, stability and nonlinear convection. - New York, Springer.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ2-0035-0007