Homotopy Perturbation Method for Flow of a Third-grade Fluid Through a Vertical Concentric Annulus

2012 ◽  
Vol 13 (3-4) ◽  
Author(s):  
Muhammad Zeb ◽  
Saeed Islam ◽  
Abdul Majeed Siddiqui ◽  
Tahira Haroon
Keyword(s):  
Perturbation Method ◽  
Incompressible Flow ◽  
Homotopy Perturbation Method ◽  
Theoretical Study ◽  
Longitudinal Velocity ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Concentric Annulus ◽  
Homotopy Perturbation ◽  
Grade Fluid

AbstractThis paper considers a theoretical study on steady incompressible flow of third grade fluid in helical screw rheometer (HSR) with zero flight angles (a vertical concentric annulus). The developed second order non linear coupled differential equations are solved by homotopy perturbation method. Expressions for torsional and longitudinal velocity components are derived. The effects of non-Newtonian parameter

Theoretical study of MHD electro-osmotically flow of third-grade fluid in micro channel

2022 ◽  
Vol 420 ◽  
pp. 126868
Author(s):  
Mubbashar Nazeer ◽  
Farooq Hussain ◽  
M. Ijaz Khan ◽  
Asad-ur-Rehman ◽  
Essam Roshdy El-Zahar ◽  
...  
Keyword(s):  
Theoretical Study ◽  
Third Grade ◽  
Micro Channel ◽  
Third Grade Fluid ◽  
Grade Fluid

scholarly journals Mathematical Model and Solution for an Unsteady MHD Fourth Grade Fluid Flow over a Vertical Plate in a Porous Medium with Magnetic Field and Suction/Injection Effects

2020 ◽  
Vol 12 (4) ◽  
pp. 485-498
Author(s):  
O. J. Fenuga ◽  
S. J. Aroloye ◽  
S. O. Salawu
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Fluid Flow ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Fourth Grade ◽  
Governing Equations ◽  
Homotopy Perturbation ◽  
Grade Fluid ◽  
Fourth Grade Fluid

This work investigates the mathematical model and solution for an unsteady MHD fourth grade fluid flow over a vertical plate in a porous medium with the effects of the magnetic field and suction/injection parameters using Homotopy Perturbation Method. The flow is considered to satisfy the constitutive equations of fourth grade fluid flow model and because of the Homotopy Perturbation Method used, only the momentum equation with initial and boundary conditions are solved as governing equations. After initializing stability test, the convergence of the governing equations are observed graphically using the results of Homotopy Perturbation Method with the new analytical method used by Yurusoy in literature and there is a perfect agreement in results. The impact of dimensionless second, third and fourth grade parameters with the effects of magnetic field and suction/injection parameters on the velocity field are displayed graphically and discussed. Increase in suction parameter decreases the momentum boundary layer thickness while injection parameter enhances velocity distribution in the boundary layer. Magnetic field reduces velocity throughout the boundary layer because the Lorentz force which acts as retarding force reduces the boundary layer thickness.

Analysis of Non-Newtonian Fluids in Microchannels With Different Wall Materials

2009 ◽  
Author(s):  
Masoud Darbandi ◽  
Mohammad Behshad Shafii ◽  
Salman SafariMohsenabad
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Perturbation Method ◽  
Power Law ◽  
Homotopy Perturbation Method ◽  
Newtonian Fluids ◽  
Homotopy Perturbation ◽  
Special Cases ◽  
Grade Fluid ◽  
Wall Shear

The behavior of non-Newtonian fluids is considered as an important subject in micro scale and microfluidic flow researches. Because of the complexity and cost in the numerical works and the experimental set-ups in some instances, the analytical approach can be taken into account as a robust alternative tool to solve the non-Newtonian microfluidic flows in some special cases benefiting from a few simplified assumptions. In this work, we analyze the flow of two non-Newtonian fluids including the power-law and grade-fluid models in microchannels. For the grade-fluid, the stress tensors are defined considering the Rivlin-Ericksen tensor definitions. To avoid the complexities in the entrance region, the flow is assumed to be hydrodynamically developed. The flow is steady and laminar and the fluid has constant properties independent of its temperature. We treat three different relations between slip velocity and wall shear stress as the slip boundary condition in our analysis. The Homotopy perturbation method is applied to solve the Navier-Stokes equations in case of grade fluid. To achieve the best slip coefficient, our power-law model solution is compared with available experimental data. Moreover, we compare the results of our Homotopy perturbation method with the numerical solutions. The current results show that the best slip relation is the one with a square of wall shear stress dependency.

Sign in / Sign up

Export Citation Format

Share Document