Complete Derivation of the Momentum Equation for the Second Grade Fluid
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Authors
Muhammad Ayub
- Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 44000, Pakistan
Haider Zaman
- Department of Mathematics, Islamia College Chartered University 25120, Peshawar 25000, Pakistan
Abstract
In a recently accepted paper of R. A. Van Gorder and K. Vajravelu [1] (Comments on "Series solution of hydromagnetic flow and heat transfer with Hall effect in a second grade fluid over a stretching sheet") Central European Journal of Physics, DOI:10.2478/s11534-009-0145-2 (online), the authors have made momentum equation for the second grade fluid very controversial. The aim of our this communication is to give complete exact derivation of the momentum equation for second grade fluid and remedy this confusion.
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ISRP Style
Muhammad Ayub, Haider Zaman, Complete Derivation of the Momentum Equation for the Second Grade Fluid, Journal of Mathematics and Computer Science, 1 (2010), no. 1, 33--39
AMA Style
Ayub Muhammad, Zaman Haider, Complete Derivation of the Momentum Equation for the Second Grade Fluid. J Math Comput SCI-JM. (2010); 1(1):33--39
Chicago/Turabian Style
Ayub, Muhammad, Zaman, Haider. " Complete Derivation of the Momentum Equation for the Second Grade Fluid." Journal of Mathematics and Computer Science, 1, no. 1 (2010): 33--39
Keywords
- Second grade fluid
- Boundary layer approxmations
- Thermodynamical compatibility for second grade fluid model
MSC
References
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[1]
R. A. Van Gorder, K. Vajravelu, Comment on “Series solution of hydromagnetic flow and heat transfer with hall effect in a second grade fluid over a stretching sheet”, Centr. Eur. J. Phys., 8 (2010), 514--515
-
[2]
S. K. Khan, E. Sanjayanand, Viscoelastic boundary layer MHD flow through a porous medium over a porous quadratic stretching sheet, Archives of Mechanics, 56 (2004), 191--204
-
[3]
S. Abdel, P. H. Veena, K. Rajgopal, V. K. Parvin, Non-Newtonian magnetohydrodynamic flow over a stretching surface with heat and mass transfer, Int. J. Non-Linear Mech., 39 (2004), 1067--1078
-
[4]
M. S. Abdel, M. M. Nandeppanavar, Heat transfer in MHD viscoelastic boundary layer flow over a stretching sheet with non-uniform heat source/sink, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 2120--2131
-
[5]
J. E. Dunn, K. R. Rajagopal, Fluids of differential type: Critical review and thermodynamic analysis, Int. J. Eng. Sci., 33 (1995), 689--729
-
[6]
H. Zaman, M. Ayub, Reply to the comments on: ”Series solution of hydromagnetic flow and heat transfer with Hall effect in a second grade fluid over a stretching sheet”, Centr. Eur. J. Phys., 8 (2010), 516--518
-
[7]
K. Vajravelu, D. Rollins, Hydromagnetic flow of a second grade fluid over a stretching sheet, Appl. Math. Comput., 148 (2004), 783--791
-
[8]
M. Sajid, T. Hayat, S. Asghar, Non-similar analytic solution for MHD flow and heat transfer in a third-order fluid over a stretching sheet, Int. J. Heat Mass Transfer, 50 (2007), 1723--1736
-
[9]
T. Hayat, Z. Abbas, I. Pop, Momentum and heat transfer over a continuously moving surface with a parallel free stream in a viscoelastic fluid, Numer. Methods Partial Differential Equations, 26 (2010), 305--319
-
[10]
F. M. Hady, R. S. R Gorla, Heat transfer from a continuous surface in a parallel free stream of viscoelastic fluid, Acta Mechanica, 128 (1998), 201--208
-
[11]
K. Sadeghy, M. Sharifi, Local similarity solution for the flow of a “second-grade” viscoelastic fluid above a moving plate, Int. J. Non-linear Mech., 39 (2004), 1265--1273
-
[12]
R. S. Rivilin, J. L. Ericksen, Stress-Deformation Relations for Isotropic Materials, J. Rational Mech. Anal., 4 (1955), 323--425
-
[13]
R. L. Fosdick, K. R. Rajagopal, Anomalous features in the model of “second order fluids”, Arch. Rational Mech. Anal., 70 (1979), 145--152
-
[14]
J. E. Dunn, R. L. Fosdick, Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade, Arch. Rational Mech. Anal., 56 (1974), 191--252
-
[15]
H. Schlichting, K. Gersten, Boundary-layer theory, Springer-Verlag, Berlin (2000)