Specific shear-dependent viscoelastic third-grade fluid model

2016 ◽  
Author(s):  
Fernando Carapau ◽  
Paulo Correia ◽  
Luis M. Grilo
Keyword(s):  
Fluid Model ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Grade Fluid

Electro-magnetohydrodynamic flow and heat transfer of a third-grade fluid using a Darcy-Brinkman-Forchheimer model

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Lijun Zhang ◽  
Muhammad Mubashir Bhatti ◽  
Efstathios E. Michaelides
Keyword(s):  
Temperature Profile ◽  
Fluid Model ◽  
Nonlinear Problems ◽  
Third Grade ◽  
Solution Technique ◽  
Parallel Plates ◽  
Third Grade Fluid ◽  
Transform Method ◽  
Content Type ◽  
Grade Fluid

Purpose The purpose of this paper is to examine the electro-magnetohydrodynamic behavior of a third-grade non-Newtonian fluid, flowing between a pair of parallel plates in the presence of electric and magnetic fields. The flow medium between the plates is porous. The effects of Joule heating and viscous energy dissipation are studied in the present study. Design/methodology/approach A semi-analytical/numerical method, the differential transform method, is used to obtain solutions for the system of the nonlinear differential governing equations. This solution technique is efficient and may be adapted to solve a variety of nonlinear problems in simple geometries, as it was confirmed by comparisons between the results using this method and those of a fully numerical scheme. Findings The results of the computations show that the Darcy–Brinkman–Forchheimer parameter and the third-grade fluid model parameter retards, whereas both parameters have an inverse effect on the temperature profile because the viscous dissipation increases. The presence of the magnetic field also enhances the temperature profile between the two plates but retards the velocity profile because it generates the opposing Lorenz force. A graphical comparison with previously published results is also presented as a special case of this study. Originality/value The obtained results are new and presented for the first time in the literature.

scholarly journals Shock Wave Solutions for Some Nonlinear Flow Models Arising in the Study of a Non-Newtonian Third Grade Fluid

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Taha Aziz ◽  
R. J. Moitsheki ◽  
A. Fatima ◽  
F. M. Mahomed
Keyword(s):  
Shock Wave ◽  
Differential Equations ◽  
Fluid Model ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Flow ◽  
Third Grade ◽  
Physical Parameters ◽  
Third Grade Fluid ◽  
Wave Solutions ◽  
Grade Fluid

This study is based upon constructing a new class of closed-form shock wave solutions for some nonlinear problems arising in the study of a third grade fluid model. The Lie symmetry reduction technique has been employed to reduce the governing nonlinear partial differential equations into nonlinear ordinary differential equations. The reduced equations are then solved analytically, and the shock wave solutions are constructed. The conditions on the physical parameters of the flow problems also fall out naturally in the process of the derivation of the solutions.

A Note on Oscillatory Flow of a Third Grade Fluid in a Porous Medium

2008 ◽  
Vol 11 (5) ◽  
pp. 467-473
Author(s):  
Tasawar Hayat ◽  
F. Shahzad ◽  
S. Asghar
Keyword(s):  
Porous Medium ◽  
Oscillatory Flow ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Grade Fluid
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