Comment on “Series solution for flow of a second grade fluid in a divergent – convergent channel” by T. Hayat, M. Nawaz, S. Asghar, and Awatif A. Hendi [Can. J. Phys. 88: 911–917 (2010)]

2017 ◽  
Vol 95 (6) ◽  
pp. 641-641
Author(s):  
Asterios Pantokratoras
Keyword(s):  
Series Solution ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Convergent Channel ◽  
Grade Fluid

Series solution for flow of a second-grade fluid in a divergent–convergent channel

2010 ◽  
Vol 88 (12) ◽  
pp. 911-917 ◽  
Author(s):  
T. Hayat ◽  
M. Nawaz ◽  
S. Asghar ◽  
Awatif A. Hendi
Keyword(s):  
Series Solution ◽  
Problem Formulation ◽  
Skin Friction Coefficient ◽  
Second Grade ◽  
Physical Parameters ◽  
Analysis Method ◽  
Second Grade Fluid ◽  
Convergent Channel ◽  
Homotopy Analysis ◽  
Grade Fluid

This study explores the flow of a second-grade fluid in divergent–convergent channel. The problem formulation is first developed, and then the corresponding nonlinear problem is solved by homotopy analysis method (HAM). The effects of different physical parameters on the velocity profile are shown. The numerical values of the skin friction coefficient for different values of parameters are tabulated.

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”

Open Physics ◽  
2010 ◽  
Vol 8 (3) ◽  
Author(s):  
Haider Zaman ◽  
Muhammad Ayub
Keyword(s):  
Heat Transfer ◽  
Hall Effect ◽  
Series Solution ◽  
Stretching Sheet ◽  
Second Grade ◽  
Hydromagnetic Flow ◽  
Second Grade Fluid ◽  
Flow And Heat Transfer ◽  
Grade Fluid

AbstractIn this reply to comment on ”Series solution of hydromagnetic flow and heat transfer with Hall effect in a second grade fluid over a stretching sheet” by R. A. Van Gorder and K. Vajravelu manuscript [R. A. Van Gorder, K. Vajravelu, Cent. Eur. J. Phys., DOI:10. 2478/s11534-009-0145-2], we once again claim that the governing similarity equations of Vajravelu and Roper [K. Vajravelu, T. Roper, Int. J. Nonlin. Mech. 34, 1031 (1999)] are incorrect and our claim in [M. Ayub, H. Zaman, M. Ahmad, Cent. Eur. J. Phys. 8, 135 (2010)] is true. For the literature providing justification regarding this issue is discussed in detail.

On the Analytic Solution of Magnetohydrodynamic Flow of a Second Grade Fluid Over a Shrinking Sheet

2007 ◽  
Vol 74 (6) ◽  
pp. 1165-1171 ◽  
Author(s):  
T. Hayat ◽  
Z. Abbas ◽  
M. Sajid
Keyword(s):  
Series Solution ◽  
Analytic Solution ◽  
Second Grade ◽  
Shrinking Sheet ◽  
Series Solutions ◽  
Analysis Method ◽  
Second Grade Fluid ◽  
Homotopy Analysis ◽  
Grade Fluid ◽  
Layer Flow

In this study, we derive an analytical solution describing the magnetohydrodynamic boundary layer flow of a second grade fluid over a shrinking sheet. Both exact and series solutions have been determined. For the series solution, the governing nonlinear problem is solved using the homotopy analysis method. The convergence of the obtained solution is analyzed explicitly. Graphical results have been presented and discussed for the pertinent parameters.

Comment on “Series solution of hydromagnetic flow and heat transfer with hall effect in a second grade fluid over a stretching sheet”

Open Physics ◽  
2010 ◽  
Vol 8 (3) ◽  
Author(s):  
Robert Gorder ◽  
Kuppalapalle Vajravelu
Keyword(s):  
Heat Transfer ◽  
Hall Effect ◽  
Series Solution ◽  
Stretching Sheet ◽  
Second Grade ◽  
Hydromagnetic Flow ◽  
Second Grade Fluid ◽  
Similarity Equation ◽  
Flow And Heat Transfer ◽  
Grade Fluid

AbstractIn a recently accepted paper of M. Ayub, H. Zaman and M. Ahmad [Cent. Eur. J. Phys. 8, 135 (2010)] the authors claim that the governing similarity equations of Vajravelu and Roper [Int. J. Nonlin. Mech. 34, 1031 (1999)] are incorrect; without any justification, the authors Ayub et al. simply mention that the equation is “found to be incorrect in the literature” (though no reference supporting this assertion is provided in the citations). We show that this assertion of Ayub et al. is wrong, and that the similarity equation of Vajravelu and Roper is indeed correct.

SECOND‐GRADE FLUID FLOW WITH POWER‐LAW HEAT FLUX AND A HEAT SOURCE

2013 ◽  
Vol 44 (8) ◽  
pp. 687-702 ◽  
Author(s):  
Tasawar Hayat ◽  
Sabir A. Shehzad ◽  
Muhammad Qasim ◽  
F. Alsaadi ◽  
Ahmed Alsaedi
Keyword(s):  
Heat Flux ◽  
Fluid Flow ◽  
Heat Source ◽  
Power Law ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid ◽  
Power Law Heat Flux

scholarly journals A new fourth-order explicit group method in the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Asim Khan ◽  
Norhashidah Hj. Mohd Ali ◽  
Nur Nadiah Abd Hamid
Keyword(s):  
Finite Difference ◽  
Stokes Problem ◽  
Stability And Convergence ◽  
Second Grade ◽  
Group Method ◽  
Two Dimensional ◽  
Second Grade Fluid ◽  
The Matrix ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid

Abstract In this article, a new explicit group iterative scheme is developed for the solution of two-dimensional fractional Rayleigh–Stokes problem for a heated generalized second-grade fluid. The proposed scheme is based on the high-order compact Crank–Nicolson finite difference method. The resulting scheme consists of three-level finite difference approximations. The stability and convergence of the proposed method are studied using the matrix energy method. Finally, some numerical examples are provided to show the accuracy of the proposed method.

Flow of Second Grade Fluid in a Scraped Surface Heat Exchanger

2016 ◽  
Vol 40 (2) ◽  
pp. e12393 ◽  
Author(s):  
A. Imran ◽  
M.A. Rana ◽  
A.M. Siddiqui ◽  
M. Shoaib
Keyword(s):  
Heat Exchanger ◽  
Surface Heat ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Scraped Surface Heat Exchanger ◽  
Grade Fluid ◽  
Surface Heat Exchanger

scholarly journals Three dimensional flow and mass transfer analysis of a second grade fluid in a porous channel with a lower stretching wall

2016 ◽  
Vol 21 (2) ◽  
pp. 359-376
Author(s):  
N.A. Khan ◽  
F. Naz
Keyword(s):  
Mass Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Three Dimensional ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Grade Fluid ◽  
Suction Or Injection

AbstractThis investigation analyses a three dimensional flow and mass transfer of a second grade fluid over a porous stretching wall in the presence of suction or injection. The equations governing the flow are attained in terms of partial differential equations. A similarity transformation has been utilized for the transformation of partial differential equations into the ordinary differential equations. The solutions of the nonlinear systems are given by the homotopy analysis method (HAM). A comparative study with the previous results of a viscous fluid has been made. The convergence of the series solution has also been considered explicitly. The influence of admissible parameters on the flows is delineated through graphs and appropriate results are presented. In addition, it is found that instantaneous suction and injection reduce viscous drag on the stretching sheet. It is also shown that suction or injection of a fluid through the surface is an example of mass transfer and it can change the flow field.

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