scholarly journals Flow of a Dense Suspension Modeled as a Modified Second Grade Fluid

Fluids ◽  
2018 ◽  
Vol 3 (3) ◽  
pp. 55 ◽  
Author(s):  
Wei-Tao Wu ◽  
Nadine Aubry ◽  
James Antaki ◽  
Mehrdad Massoudi
Keyword(s):  
Normal Stress ◽  
Volume Fraction ◽  
Variable Viscosity ◽  
Fluid Model ◽  
Constitutive Relationship ◽  
Second Grade ◽  
Simple Shear Flow ◽  
Second Grade Fluid ◽  
Dense Suspension ◽  
Grade Fluid

In this paper, a simple shear flow of a dense suspension is studied. We propose a new constitutive relationship based on the second grade fluid model for the suspension, capable of exhibiting non-linear effects, where the normal stress coefficients are assumed to depend on the volume fraction of the particles and the shear viscosity depends on the shear rate and the volume fraction. After non-dimensionalizing the equations, we perform a parametric study looking at the effects of the normal stress coefficients and the variable viscosity. The numerical results show that for a certain range of parameters, the particles tend to form a region of high and uniform volume fraction, near the lower half of the flow.

scholarly journals Entropy Generation in MHD Second-Grade Nanofluid Thin Film Flow Containing CNTs with Cattaneo-Christov Heat Flux Model Past an Unsteady Stretching Sheet

2020 ◽  
Vol 10 (8) ◽  
pp. 2720 ◽  
Author(s):  
Zahir Shah ◽  
Ebraheem O. Alzahrani ◽  
Abdullah Dawar ◽  
Wajdi Alghamdi ◽  
Malik Zaka Ullah
Keyword(s):  
Entropy Generation ◽  
Volume Fraction ◽  
Second Grade ◽  
Thin Film Flow ◽  
Second Grade Fluid ◽  
Fluid Parameter ◽  
Grade Fluid ◽  
Flux Model ◽  
Walled Carbon Nanotubes ◽  
Heat Flux Model

Entropy generation plays a significant role in several complex processes, extending from cosmology to biology. The entropy generation minimization procedure can be applied for the optimization of mechanical systems including heat exchangers, elements of nuclear and thermal power plants, ventilation and air-conditioning systems. In order to present our analysis, entropy generation in a thin film flow of second grade nanofluid holding single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) with a Cattaneo–Christov heat flux model is studied in this article. The flow is considered passing a linearly extending surface. A variable magnetic field with aligned angle ε is functioned along the extending sheet. With the aid of the homotopy analysis method (HAM), the fluid flow model is elucidated. The impressions of embedded factors on the flow are obtainable through figures and discussed in detail. It is observed that the velocity profile escalated with the increasing values of volume fraction of nanoparticles and second grade fluid parameter. The higher values of volume fraction of nanoparticles, second grade fluid parameter, non-linear heat source/sink, and thermal radiation parameter intensified the temperature profile. Surface drag force escalated with heightening values of nanoparticles volume fraction, unsteadiness, film thickness, magnetic, and second grade fluid parameters. Entropy generation increased with enhancing values of magnetic parameter, Brinkman number, and Reynolds number.

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.

On some generalizations of the second grade fluid model

2008 ◽  
Vol 9 (3) ◽  
pp. 1169-1183 ◽  
Author(s):  
Mehrdad Massoudi ◽  
Ashwin Vaidya
Keyword(s):  
Fluid Model ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid

scholarly journals MHD nonaligned stagnation point flow of second grade fluid towards a porous rotating disk

2019 ◽  
Vol 8 (1) ◽  
pp. 231-249
Author(s):  
Najeeb Alam Khan ◽  
Farah Naz ◽  
Nadeem Alam Khan ◽  
Saif Ullah
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Fluid Model ◽  
Mathematical Formulation ◽  
Rotating Disk ◽  
Stagnation Point Flow ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Nonlinear Odes ◽  
Grade Fluid

Abstract This paper provides analytical solution of the non-aligned stagnation point flow of second grade fluid over a porous rotating disk in the presence of a magnetic field and suction/injection at the disk surface. The mathematical formulation of the fluid model is obtained in terms of partial differential equations (PDEs). The PDEs governing the motion are transformed into a system of ordinary differential equations (ODEs) by means of a similarity transformation and these corresponding nonlinear ODEs are solved by employing the homotopy analysis method (HAM) and the convergence analysis of the presented method is also performed graphically. An inclusion of the influences of various admissible parameters has been shown numerically and graphically on the flow field. Furthermore, comparison is made and it concedes that the obtained results are found to be in good agreement with results existing in literature.

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