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 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 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

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.

scholarly journals Significance of Mixed Convection and Arrhenius Activation Energy in a Non-Newtonian Third Grade Fluid Flow Containing Gyrotactic Microorganisms Towards Stretching Surface

2021 ◽  
Author(s):  
Abdullah Dawar ◽  
Saeed Islam ◽  
Zahir Shah ◽  
Poom Kumam
Keyword(s):  
Activation Energy ◽  
Numerical Solutions ◽  
Manufacturing Sector ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Stretching Surface ◽  
Arrhenius Activation Energy ◽  
Gyrotactic Microorganisms ◽  
Similarity Transformations ◽  
Grade Fluid

Abstract In most scenarios of concern, the bulk of fluids treated by researchers and engineers, such as air, water, and oils, can be considered as Newtonian. The inference of Newtonian action however is not true in many situations and the much more complicated non-Newtonian reaction should be superimposed. Such situations exist in the chemical manufacturing sector and the plastics processing plants. Here, we present the mixed convective flow of non-Newtonian third grade fluid containing gyrotactic microorganisms through a stretching surface. The flow is considered as unsteady, laminar, and incompressible. Furthermore, the flow is magnetized and electrically conducting with the help of applied magnetic field. Chemical reaction along with Arrhenius activation energy and viscous dissipation influences are taken into attention. The governing PDEs are transformed to ODEs through appropriate similarity transformations. Analytical and numerical solutions of the present analysis are done with the help of incorporated codes in MATHEMATICA 10.0. Convergence of HAM is presented through Figures. Also, the outcomes of the embedded factors on the nanofluid flow are displayed through Figures.

Parallel Plate Flow of a Third-Grade Fluid and a Newtonian Fluid With Variable Viscosity

2016 ◽  
Vol 71 (7) ◽  
pp. 595-606
Author(s):  
Volkan Yıldız ◽  
Mehmet Pakdemirli ◽  
Yiğit Aksoy
Keyword(s):  
Newtonian Fluid ◽  
Parallel Plate ◽  
Numerical Solutions ◽  
Variable Viscosity ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Regular Perturbation ◽  
Approximate Analytical Solutions ◽  
Grade Fluid ◽  
Perturbation Solutions

AbstractSteady-state parallel plate flow of a third-grade fluid and a Newtonian fluid with temperature-dependent viscosity is considered. Approximate analytical solutions are constructed using the newly developed perturbation-iteration algorithms. Two different perturbation-iteration algorithms are used. The velocity and temperature profiles obtained by the iteration algorithms are contrasted with the numerical solutions as well as with the regular perturbation solutions. It is found that the perturbation-iteration solutions converge better to the numerical solutions than the regular perturbation solutions, in particular when the validity criteria of the regular perturbation solution are not satisfied. The new analytical approach produces promising results in solving complex fluid problems.

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