On Stokes' problem for the flow of a third-grade fluid induced bya variable shear stress

2006 ◽  
Vol 84 (11) ◽  
pp. 945-958 ◽  
Author(s):  
S Asghar ◽  
M R Mohyuddin ◽  
P D Ariel ◽  
T Hayat
Keyword(s):  
Shear Stress ◽  
Numerical Solutions ◽  
Stokes Problem ◽  
Nonlinear Partial Differential Equation ◽  
Momentum Equation ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Variable Shear ◽  
Grade Fluid ◽  
Grade Parameter

The flow of an incompressible third-grade fluid over an infinite wall is considered. The flow is due to a variable shear stress. Both the series and the numerical solutions of the nonlinear partial-differential equation resulting from the momentum equation are obtained. Effects of non-Newtonian parameters on the flow phenomena are analyzed. It is found that with an increase in second-grade parameter and third-grade parameter, the velocity decreases and thus, the boundary-layer thickness increases.PACS No.: 47.15.cb

Travelling Wave Solutions for the Unsteady Flow of a Third Grade Fluid Induced Due to Impulsive Motion of Flat Porous Plate Embedded in a Porous Medium

2014 ◽  
Vol 30 (5) ◽  
pp. 527-535 ◽  
Author(s):  
T. Aziz ◽  
F. M. Mahomed ◽  
A. Shahzad ◽  
R. Ali
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Nonlinear Partial Differential Equation ◽  
Porous Plate ◽  
Travelling Wave ◽  
Point Of View ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Physical Point ◽  
Grade Fluid

AbstractThis work describes the time-dependent flow of an incompressible third grade fluid filling the porous half space over an infinite porous plate. The flow is induced due to the motion of the porous plate in its own plane with an arbitrary velocityV(t). Translational type symmetries are employed to perform the travelling wave reduction into an ordinary differential equation of the governing nonlinear partial differential equation which arises from the laws of mass and momentum. The reduced ordinary differential equation is solved exactly, for a particular case, as well as by using the homotopy analysis method (HAM). The better solution from the physical point of view is argued to be the HAM solution. The essentials features of the various emerging parameters of the flow problem are presented and discussed.

scholarly journals Unsteady free convective heat transfer in third-grade fluid flow from an isothermal vertical plate: A thermodynamic analysis

2019 ◽  
Vol 33 (08) ◽  
pp. 1950060
Author(s):  
Ashwini Hiremath ◽  
G. Janardhana Reddy ◽  
Mahesh Kumar ◽  
O. Anwar Bég
Keyword(s):  
Heat Transfer ◽  
Entropy Generation ◽  
Vertical Plate ◽  
Third Grade ◽  
Dimensionless Temperature ◽  
Convection Flow ◽  
Bejan Number ◽  
Third Grade Fluid ◽  
Grade Fluid ◽  
Grade Parameter

The current study investigates theoretically and numerically the entropy generation in time-dependent free-convective third-grade viscoelastic fluid convection flow from a vertical plate. The nondimensional conservation equations for mass, momentum and energy are solved using a Crank–Nicolson finite difference method with suitable boundary conditions. Expressions for known values of flow-variables coefficients are also derived for the wall heat transfer and skin friction and numerically evaluated. The effect of Grashof number, Prandtl number, group parameter (product of dimensionless temperature difference and Brinkman number) and third-grade parameter on entropy heat generation is analyzed and shown graphically. Bejan line distributions are also presented for the influence of several control parameters. The computations reveal that with increasing third-grade parameter, the entropy generation decreases and Bejan number increases. Also, the comparison graph shows that contour lines for third-grade fluid vary considerably from the Newtonian fluid. The study is relevant to non-Newtonian thermal materials processing systems.

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.

scholarly journals Analysis of Electro-MHD of Third Grade Fuid Flow Through Porous Channel

2020 ◽  
Vol 13 (5) ◽  
pp. 1270-1284
Author(s):  
Sukanya Padhi ◽  
Itishree Nayak
Keyword(s):  
Magnetic Field ◽  
Nonlinear Partial Differential Equation ◽  
Mhd Flow ◽  
Elastic Parameter ◽  
Third Grade ◽  
Porous Channel ◽  
Third Grade Fluid ◽  
Fully Implicit ◽  
Contrasting Effect ◽  
Grade Fluid

This paper examines the Electro-MHD flow and heat transfer of a third grade fluid passing through a porous channel. An unidirectional and one-dimensional flow is propelled with the aid of lorentz force generated due to interaction of vertically applied magnetic field along with horizontally applied electric field. The equations of momentum and energy governing the third grade fluid flow are transformed to algebraic equation from nonlinear partial differential equation by implementing fully implicit finite difference scheme and solution is obtained by damped-Newton method. Lastly, the problem is simulated using MATLAB and the influence on velocity and temperature profiles with variation of non-dimensional parameters are depicted graphically. The noteworthy findings of this study is that the increasing values of elastic parameter α and non-Newtonian parameter γ diminishes the flow velocity and results in enhancement of temperature profile. A completely contrasting effect is observed for increasing values of strength of electric and magnetic field.

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.

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