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.

scholarly journals A Note on the Solutions of Some Nonlinear Equations Arising in Third-Grade Fluid Flows: An Exact Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Taha Aziz ◽  
F. M. Mahomed
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Fluid Flows ◽  
Third Grade ◽  
Physical Parameters ◽  
Third Grade Fluid ◽  
Grade Fluid ◽  
Physical Boundary ◽  
Steady State Solutions

In this communication, we utilize some basic symmetry reductions to transform the governing nonlinear partial differential equations arising in the study of third-grade fluid flows into ordinary differential equations. We obtain some simple closed-form steady-state solutions of these reduced equations. Our solutions are valid for the whole domain [0,∞) and also satisfy the physical boundary conditions. We also present the numerical solutions for some of the underlying equations. The graphs corresponding to the essential physical parameters of the flow are presented and discussed.

scholarly journals Thermal Radiation and Chemical Reaction Effects on Unsteady Magnetohydrodynamic Third Grade Fluid Flow Between Stationary and Oscillating Plates

2019 ◽  
Vol 24 (2) ◽  
pp. 269-293
Author(s):  
A.S. Idowu ◽  
U. Sani
Keyword(s):  
Fluid Flow ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Nonlinear Partial Differential Equations ◽  
Mhd Flow ◽  
Third Grade ◽  
Physical Parameters ◽  
Parallel Plates ◽  
Third Grade Fluid ◽  
Grade Fluid

Abstract An analysis was carried out for an unsteady magnetohydrodynamic(MHD) flow of a generalized third grade fluid between two parallel plates. The fluid flow is a result of the plate oscillating, moving and pressure gradient. Three flow problems were investigated, namely: Couette, Poiseuille and Couette-Poiseuille flows and a number of nonlinear partial differential equations were obtained which were solved using the He-Laplace method. Expressions for the velocity field, temperature and concentration fields were given for each case and finally, effects of physical parameters on the fluid motion, temperature and concentration were plotted and discussed. It is found that an increase in the thermal radiation parameter increases the temperature of the fluid and hence reduces the viscosity of the fluid while the concentration of the fluid reduces as the chemical reaction parameter increases.

Thin Film Flow of a Third Grade Fluid with Variable Viscosity

2009 ◽  
Vol 64 (9-10) ◽  
pp. 553-558 ◽  
Author(s):  
Sohail Nadeem
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Variable Viscosity ◽  
Nonlinear Differential Equations ◽  
Third Grade ◽  
Outer Side ◽  
Physical Parameters ◽  
Third Grade Fluid ◽  
Thin Film Flow ◽  
Grade Fluid

The effects of variable viscosity on the flow and heat transfer in a thin film flow for a third grade fluid has been discussed. The thin film is considered on the outer side of an infinitely long vertical cylinder. The governing nonlinear differential equations of momentum and energy are solved analytically by using homotopy analysis method. The expression for the viscous dissipation and entropy generation are also defined. The graphical results are presented for various physical parameters appearing in the problem

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.

Nonlinear Flow of Third-Grade Fluid between Stretching-Shrinking Sheets

2016 ◽  
Vol 29 (3) ◽  
pp. 04015062 ◽  
Author(s):  
T. Hayat ◽  
Anum Shafiq ◽  
M. Nawaz ◽  
T. Barakat
Keyword(s):  
Nonlinear Flow ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Grade Fluid

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

Impact of nanoparticles on flow of a special non-Newtonian third-grade fluid over a porous heated shrinking sheet with nonlinear radiation

2018 ◽  
Vol 7 (2) ◽  
pp. 103-111 ◽  
Author(s):  
A. Zaib ◽  
A.J. Chamkha ◽  
M. M. Rashidi ◽  
K. Bhattacharyya
Keyword(s):  
Shooting Method ◽  
Third Grade ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
Third Grade Fluid ◽  
Suction Parameter ◽  
Grade Fluid ◽  
Buongiorno Model ◽  
Local Sherwood Number ◽  
Linear Radiation

Abstract This research peruses the characteristics of heat and mass transfern of a special non-Newtonian third-grade fluid over a porous convectively-heated shrinking sheet filled with nanoparticles. The Buongiorno model is used for the special non-Newtonian third-grade fluid that includes both the Brownian motion and the thermophoresis effects with non-linear radiation. The nonlinear system of ordinary differential equations are obtained using a suitable transformation. The converted system of equations are then numerically solved using shooting method. The numerically-obtained results for the skin friction, local Nusselt number and the local Sherwood number as well as velocity profile, temperature distribution and concentration of nanoparticle are illustrated for different physical parameters through graphs and tables. On the behalf of the whole studies, final conclusions are made and it is observed that multiple solutions are achieved for certain values of the suction parameter. Further, the non-Newtonian parameter reduces the velocity of the fluid and increases the temperature and the concentration profiles for the first solution while the reverse trend is seen for the second solution. Finally, a comparative analysis is made through previous studies in limiting cases and shown good correlation.

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