scholarly journals "Permanent solutions for some motions of UCM fluids with power-law dependence of viscosity on the pressure"

2021 ◽  
Vol 66 (1) ◽  
pp. 197-209
Author(s):  
Constantin Fetecau ◽  
Abdul Rauf
Keyword(s):  
Couette Flow ◽  
Power Law ◽  
Fluid Motion ◽  
Steady Motion ◽  
Physical Parameters ◽  
Parallel Plates ◽  
Maxwell Fluids ◽  
Gravity Effects ◽  
Starting Solutions ◽  
Similar Solutions

Steady motion of two types of incompressible Maxwell fluids with power-law dependence of viscosity on the pressure is analytically studied between infinite horizontal parallel plates when the gravity effects are taken into consideration. Simple and exact expressions are established for the permanent components of starting solutions corresponding to two oscillatory motions induced by the lower plate that oscillates in its plane. Such solutions are very important for the experimentalists who want to eliminate the transients from their experiments. The similar solutions for the simple Couette flow of the same fluids, as well as the permanent solutions corresponding to ordinary incompressible Maxwell fluids performing the same motions, are obtained as limiting cases of general solutions. The convergence of starting solutions to their permanent components as well as the influence of physical parameters on the fluid motion is graphically underlined and discussed.

Permanent solutions for some oscillatory motions of fluids with power-law dependence of viscosity on the pressure and shear stress on the boundary

2020 ◽  
Vol 75 (8) ◽  
pp. 757-769
Author(s):  
Constantin Fetecau ◽  
Abdul Rauf ◽  
Tahir Mushtaq Qureshi ◽  
Masood Khan
Keyword(s):  
Shear Stress ◽  
Power Law ◽  
Fluid Motion ◽  
Viscosity Coefficient ◽  
Shear Stresses ◽  
Parallel Plates ◽  
Constant Shear Stress ◽  
Starting Solutions ◽  
Similar Solutions ◽  
Oscillatory Shear Stress

AbstractIn this paper, we provide simple expressions for the permanent solutions corresponding to some oscillatory motions of two classes of Newtonian fluids with power-law dependence of viscosity on the pressure between two infinite horizontal parallel plates. The fluid motion is generated by the lower plate that applies an oscillatory shear stress to the fluid. Such solutions, which are lack in the existing literature, can be useful both for those who want to eliminate the transients from their experiments and as tests to verify numerical schemes that are developed to study complex unsteady flow problems of these fluids. The similar solutions corresponding to the motion due to a constant shear stress on the boundary are also determined and, contrary to our expectations, the shear stresses are constant on the whole flow domain although the associated velocity fields depend both of the spatial variable and the dimensionless pressure-viscosity coefficient. Finally, for validation, some comparative graphical illustrations are included and the convergence of starting solutions to the permanent solutions is graphically proved. Spatial profiles of starting solutions are also provided.

scholarly journals Analytical Solutions for Two Mixed Initial-Boundary Value Problems Corresponding to Unsteady Motions of Maxwell Fluids through a Porous Plate Channel

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Constantin Fetecau ◽  
Dumitru Vieru ◽  
Ahmed Zeeshan
Keyword(s):  
Steady State ◽  
Porous Plate ◽  
Fluid Motion ◽  
Initial Boundary ◽  
Newtonian Fluids ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Parallel Plates ◽  
Fourier Cosine ◽  
Maxwell Fluids

Two unsteady motions of incompressible Maxwell fluids between infinite horizontal parallel plates embedded in a porous medium are analytically studied to get exact solutions using the finite Fourier cosine transform. The motion is induced by the lower plate that applies time-dependent shear stresses to the fluid. The solutions that have been obtained satisfy all imposed initial and boundary conditions. They can be easily reduced as limiting cases to known solutions for the incompressible Newtonian fluids. For a check of their correctness, the steady-state solutions are presented in different forms whose equivalence is graphically proved. The effects of physical parameters on the fluid motion are graphically emphasized and discussed. Required time to reach the steady-state is also determined. It is found that the steady-state is rather obtained for Newtonian fluids as compared with Maxwell fluids. Furthermore, the effect of the side walls on the fluid motion is more effective in the case of Newtonian fluids.

scholarly journals Mathematical Analysis of Maxwell Fluid Flow through a Porous Plate Channel Induced by a Constantly Accelerating or Oscillating Wall

Mathematics ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 90
Author(s):  
Constantin Fetecau ◽  
Rahmat Ellahi ◽  
Sadiq M. Sait
Keyword(s):  
Steady State ◽  
Porous Plate ◽  
Fluid Motion ◽  
Maxwell Fluid ◽  
Newtonian Fluids ◽  
Physical Parameters ◽  
Maxwell Fluids ◽  
Flow Through ◽  
Starting Solutions ◽  
Plate Channel

Exact expressions for dimensionless velocity and shear stress fields corresponding to two unsteady motions of incompressible upper-convected Maxwell (UCM) fluids through a plate channel are analytically established. The porous effects are taken into consideration. The fluid motion is generated by one of the plates which is moving in its plane and the obtained solutions satisfy all imposed initial and boundary conditions. The starting solutions corresponding to the oscillatory motion are presented as sum of their steady-state and transient components. They can be useful for those who want to eliminate the transients from their experiments. For a check of the obtained results, their steady-state components are presented in different forms whose equivalence is graphically illustrated. Analytical solutions for the incompressible Newtonian fluids performing the same motions are recovered as limiting cases of the presented results. The influence of physical parameters on the fluid motion is graphically shown and discussed. It is found that the Maxwell fluids flow slower as compared to Newtonian fluids. The required time to reach the steady-state is also presented. It is found that the presence of porous medium delays the appearance of the steady-state.

scholarly journals Analytical Solutions of Upper Convected Maxwell Fluid with Exponential Dependence of Viscosity under the Influence of Pressure

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 334
Author(s):  
Constantin Fetecau ◽  
Dumitru Vieru ◽  
Tehseen Abbas ◽  
Rahmat Ellahi
Keyword(s):  
Fluid Motion ◽  
Maxwell Fluid ◽  
Newtonian Fluids ◽  
Exponential Dependence ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Parallel Plates ◽  
Pressure Dependent Viscosity ◽  
Laplace Transform Technique ◽  
Dependent Viscosity

Some unsteady motions of incompressible upper-convected Maxwell (UCM) fluids with exponential dependence of viscosity on the pressure are analytically studied. The fluid motion between two infinite horizontal parallel plates is generated by the lower plate, which applies time-dependent shear stresses to the fluid. Exact expressions, in terms of standard Bessel functions, are established both for the dimensionless velocity fields and the corresponding non-trivial shear stresses using the Laplace transform technique and suitable changes of the unknown function and the spatial variable in the transform domain. They represent the first exact solutions for unsteady motions of non-Newtonian fluids with pressure-dependent viscosity. The similar solutions corresponding to the flow of the same fluids due to an exponential shear stress on the boundary as well as the solutions of ordinary UCM fluids performing the same motions are obtained as limiting cases of present results. Furthermore, known solutions for unsteady motions of the incompressible Newtonian fluids with/without pressure-dependent viscosity induced by oscillatory or constant shear stresses on the boundary are also obtained as limiting cases. Finally, the influence of physical parameters on the fluid motion is graphically illustrated and discussed. It is found that fluids with pressure-dependent viscosity flow are slower when compared to ordinary fluids.

scholarly journals Jeffrey Fluid Behaviour on Oscillatory Couette Flow past Two Horizontal Parallel Plates in Presence of MHD and Radioactive Heat Transfer

2019 ◽  
Vol 8 (11) ◽  
pp. 3252-3257
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Couette Flow ◽  
Jeffrey Fluid ◽  
Physical Parameters ◽  
Parallel Plates ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Fluid Behaviour ◽  
Non Linear System

The aim of this study carry out on an unsteady MHD at no cost convective oscillatory Couette flow of a wellknown non-Newtonian Jeffrey fluid of an optically thin fluid bounded by two horizontal porous parallel walls in a channel embedded in porous medium in the presence of thermal radiation and angle of inclination. Design and Method is the flow is governed by a coupled non-linear system of partial differential equations which are solved numerically by using finite difference method. Results are the impacts of various physical parameters on the flow quantities viz. velocity and temperature reports, skinfriction and rate of heat transfer coefficients are studied numerically. The results are discussed with the help of graphs and tables. Conclusion is the finite difference results are compared favourably with already established results in literatures.

scholarly journals Free Convection MHD Couette Flow with Application of Periodic Temperature and Constant Heat Flux on Walls

2019 ◽  
Vol 9 (2) ◽  
pp. 4007-4011
Author(s):  
M. R. Abdullah ◽  
N. Saada
Keyword(s):  
Heat Flux ◽  
Analytical Solution ◽  
Free Convection ◽  
Couette Flow ◽  
Constant Heat Flux ◽  
Physical Parameters ◽  
Parallel Plates ◽  
Constant Heat ◽  
Plate Temperature ◽  
Periodic Temperature

Numerical analysis and analytical solution were performed to study the free convection in transient Couette flow of an electrically conducting fluid confined between two vertical parallel plates. Constant heat flux on the wall with uniform vertical motion in its own plane and periodic temperature on the stationary wall were applied. The dimensionless governing momentum and energy equations are solved numerically using a fully implicit finite difference method. An analytical solution using eigenfunction expansion method is carried out for temperature profile in case of constant plate temperature. Analytical and numerical results converge at a satisfactory degree. The effect of different physical parameters on the transient velocity and temperature, such as Grashof’s number (Gr), magnetic parameter (M), Prandtl number (Pr) and temperature frequency are also studied. It is found that the velocity increases with an increase in Gr and temperature frequency, while it decreases with an increase in Pr and M.

Onset of Instability of Power-Law Fluid in Couette Flow

1971 ◽  
Vol 97 (1) ◽  
pp. 1-12
Author(s):  
Yun-Sheng Yu ◽  
Dan B. McVickar
Keyword(s):  
Couette Flow ◽  
Power Law ◽  
Power Law Fluid

Numerical study of unsteady MHD Couette flow and heat transfer of nanofluids in a rotating system with convective cooling

2016 ◽  
Vol 26 (5) ◽  
pp. 1567-1579 ◽  
Author(s):  
Ahmada Omar Ali ◽  
Oluwole Daniel Makinde ◽  
Yaw Nkansah-Gyekye
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Couette Flow ◽  
Numerical Study ◽  
Integration Scheme ◽  
Parallel Plates ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Mhd Couette Flow ◽  
Rotating Channel

Purpose – The purpose of this paper is to investigate numerically the unsteady MHD Couette flow and heat transfer of viscous, incompressible and electrically conducting nanofluids between two parallel plates in a rotating channel. Design/methodology/approach – The nanofluid is set in motion by the combined action of moving upper plate, Coriolis force and the constant pressure gradient. The channel rotates in unison about an axis normal to the plates. The nonlinear governing equations for velocity and heat transfer are obtained and solved numerically using semi-discretization, shooting and collocation (bvp4c) techniques together with Runge-Kutta Fehlberg integration scheme. Findings – Results show that both magnetic field and rotation rate demonstrate significant effect on velocity and heat transfer profiles in the system with Cu-water nanofluid demonstrating the highest velocity and heat transfer efficiency. These numerical results are in excellent agreements with the results obtained by other methods. Practical implications – This paper provides a very useful source of information for researchers on the subject of hydromagnetic nanofluid flow in rotating systems. Originality/value – Couette flow of nanofluid in the presence of applied magnetic field in a rotating channel is investigated.

The stability of elastico-viscous flow between rotating cylinders Part 3. Overstability in viscous and Maxwell fluids

1966 ◽  
Vol 24 (2) ◽  
pp. 321-334 ◽  
Author(s):  
D. W. Beard ◽  
M. H. Davies ◽  
K. Walters
Keyword(s):  
Viscous Flow ◽  
Couette Flow ◽  
Taylor Number ◽  
Linear Perturbation ◽  
Rotating Cylinders ◽  
Initial Value ◽  
Viscous Liquids ◽  
Maxwell Fluids ◽  
Newtonian Liquids ◽  
The Stability

Consideration is given to the possibility of overstability in the Couette flow of viscous and elastico-viscous liquids. The relevant linear perturbation equations are solved numerically using an initial-value technique. It is shown that over-stability is not possible in the case of Newtonian liquids for the cases considered. In contrast, overstability is to be expected in the case of moderately-elastic Maxwell liquids. The Taylor number associated with the overstable mode decreases steadily as the amount of elasticity in the liquid increases, and it is concluded that highly elastic Maxwell liquids can be very unstable indeed.

Sign in / Sign up

Export Citation Format

Share Document