scholarly journals Application of Multi-Step Differential Transform Method on Flow of a Second-Grade Fluid over a Stretching or Shrinking Sheet

2011 ◽  
Vol 01 (02) ◽  
pp. 119-128 ◽  
Author(s):  
M.M Rashidi ◽  
Ali J. Chamkha ◽  
M Keimanesh
Keyword(s):  
Differential Transform Method ◽  
Second Grade ◽  
Shrinking Sheet ◽  
Second Grade Fluid ◽  
Transform Method ◽  
Differential Transform ◽  
Grade Fluid ◽  
Stretching Or Shrinking Sheet

scholarly journals Approximate Solutions of the Model Describing Fluid Flow Using Generalized ρ-Laplace Transform Method and Heat Balance Integral Method

Axioms ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 123 ◽  
Author(s):  
Mehmet Yavuz ◽  
Ndolane Sene
Keyword(s):  
Heat Balance ◽  
Integral Method ◽  
Fluid Model ◽  
Second Grade ◽  
Physical Analysis ◽  
Second Grade Fluid ◽  
Transform Method ◽  
Heat Balance Integral Method ◽  
Grade Fluid ◽  
The Impact

This paper addresses the solution of the incompressible second-grade fluid models. Fundamental qualitative properties of the solution are primarily studied for proving the adequacy of the physical interpretations of the proposed model. We use the Liouville-Caputo fractional derivative with its generalized version that gives more comprehensive physical results in the analysis and investigations. In this work, both the ρ-Laplace homotopy transform method (ρ-LHTM) and the heat balance integral method (HBIM) are successfully combined to solve the fractional incompressible second-grade fluid differential equations. Numerical simulations and their physical interpretations of the mentioned incompressible second-grade fluid model are ensured to illustrate the main findings. It is also proposed that one can recognize the differences in physical analysis of diffusions such as ballistic diffusion, super diffusion, and subdiffusion cases by considering the impact of the orders ρ and φ.

Series solutions for the stagnation flow of a second-grade fluid over a shrinking sheet

2009 ◽  
Vol 30 (10) ◽  
pp. 1255-1262 ◽  
Author(s):  
S. Nadeem ◽  
Anwar Hussain ◽  
M. Y. Malik ◽  
T. Hayat
Keyword(s):  
Second Grade ◽  
Shrinking Sheet ◽  
Series Solutions ◽  
Second Grade Fluid ◽  
Stagnation Flow ◽  
Grade Fluid

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.

scholarly journals Exact Solutions for Fractionalized Second Grade Fluid Flows with Boundary Slip Effects

2021 ◽  
Vol 26 (1) ◽  
pp. 88-103
Author(s):  
S. Dehraj ◽  
R.A. Malookani ◽  
S.K. Aasoori ◽  
G.M. Bhutto ◽  
L. Arain
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Exact Analytical Solution ◽  
Fluid Flows ◽  
Second Grade ◽  
Physical Parameters ◽  
Second Grade Fluid ◽  
Boundary Slip ◽  
Transform Method ◽  
Grade Fluid

AbstractIn this paper, an exact analytical solution for the motion of fractionalized second grade fluid flows moving over accelerating plate under the influence of slip has been obtained. A coupled system of partial differential equations representing the equation of motion has been re-written in terms of fractional derivatives form by using the Caputo fractional operator. The Discrete Laplace transform method has been employed for computing the expressions for the velocity field u(y, t) and the corresponding shear stress τ (y, t). The obtained solutions for the velocity field and the shear stress have been written in terms of Wright generalized hypergeometric function pψq and are expressed as a sum of the slip contribution and the corresponding no-slip contribution. In addition, the solutions for a fractionalized, ordinary second grade fluid and Newtonian fluid in the absence of slip effect have also been obtained as special case. Finally, the effect of different physical parameters has been demonstrated through graphical illustrations.

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