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 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.

Thermally Developing Heat Transfer With Nonlinear Viscoelastic and Newtonian Fluids With Pressure-Dependent Viscosity

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
Dennis A. Siginer ◽  
F. Talay Akyildiz ◽  
Mhamed Boutaous
Keyword(s):  
Nusselt Number ◽  
Local Nusselt Number ◽  
Pressure Coefficient ◽  
Maxwell Fluid ◽  
Weissenberg Number ◽  
Newtonian Fluids ◽  
Bulk Temperature ◽  
Constant Wall Temperature ◽  
Pressure Dependent Viscosity ◽  
Dependent Viscosity

A semi-analytical solution of the thermal entrance problem with constant wall temperature for channel flow of Maxwell type viscoelastic fluids and Newtonian fluids, both with pressure dependent viscosity, is derived. A Fourier–Gauss pseudo-spectral scheme is developed and used to solve the variable coefficient parabolic partial differential energy equation. The dependence of the Nusselt number and the bulk temperature on the pressure coefficient is investigated for the Newtonian case including viscous dissipation. These effects are found to be closely interactive. The effect of the Weissenberg number on the local Nusselt number is explored for the Maxwell fluid with pressure-dependent viscosity. Local Nusselt number decreases with increasing pressure coefficient for both fluids. The local Nusselt number Nu for Newtonian fluid with pressure-dependent viscosity is always greater than Nu related to the viscoelastic Maxwell fluid with pressure-dependent viscosity.

scholarly journals Effect of Pressure Dependent Viscosity on Couple Stress Squeeze Film Lubrication between Rough Parallel Plates

2015 ◽  
Vol 10 (1) ◽  
pp. 76-83 ◽  
Author(s):  
Neminath Bujappa Naduvinamani ◽  
Siddangouda Apparao ◽  
Hiremath Ayyappa Gundayya ◽  
Shivraj Nagshetty Biradar
Keyword(s):  
Couple Stress ◽  
Squeeze Film ◽  
Parallel Plates ◽  
Effect Of Pressure ◽  
Pressure Dependent Viscosity ◽  
Dependent Viscosity ◽  
Film Lubrication

scholarly journals Unsteady Hartmann Two-Phase Flow: The Riemann-Sum Approximation Approach

2016 ◽  
Vol 21 (4) ◽  
pp. 891-904
Author(s):  
B.K. Jha ◽  
C.T. Babila ◽  
S. Isa
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Sudden Change ◽  
Conducting Fluid ◽  
Physical Parameters ◽  
Physical Situation ◽  
Parallel Plates ◽  
Riemann Sum ◽  
Flow Formation ◽  
Laplace Transform Technique

Abstract We consider the time dependent Hartmann flow of a conducting fluid in a channel formed by two horizontal parallel plates of infinite extent, there being a layer of a non-conducting fluid between the conducting fluid and the upper channel wall. The flow formation of conducting and non-conducting fluids is coupled by equating the velocity and shear stress at the interface. The unsteady flow formation inside the channel is caused by a sudden change in the pressure gradient. The relevant partial differential equations capturing the present physical situation are transformed into ordinary differential equations using the Laplace transform technique. The ordinary differential equations are then solved analytically and the Riemann-sum approximation method is used to invert the Laplace domain into time domain. The solution obtained is validated by comparisons with the closed form solutions obtained for steady states which have been derived separately and also by the implicit finite difference method. The variation of velocity, mass flow rate and skin-friction on both plates for various physical parameters involved in the problem are reported and discussed with the help of line graphs. It was found that the effect of changes of the electric load parameter is to aid or oppose the flow as compared to the short-circuited case.

scholarly journals Analytical Solutions for a General Mixed Boundary Value Problem Associated with Motions of Fluids with Linear Dependence of Viscosity on the Pressure

2020 ◽  
Vol 25 (3) ◽  
pp. 181-197
Author(s):  
D. Vieru ◽  
C. Fetecau ◽  
C. Bridges
Keyword(s):  
Shear Stress ◽  
Linear Dependence ◽  
Mixed Boundary ◽  
Fluid Motion ◽  
Hankel Transform ◽  
Shear Stresses ◽  
Parallel Plates ◽  
Special Cases ◽  
Independent Variable ◽  
Suitable Change

AbstractAn unsteady flow of incompressible Newtonian fluids with linear dependence of viscosity on the pressure between two infinite horizontal parallel plates is analytically studied. The fluid motion is induced by the upper plate that applies an arbitrary time-dependent shear stress to the fluid. General expressions for the dimensionless velocity and shear stress fields are established using a suitable change of independent variable and the finite Hankel transform. These expressions, that satisfy all imposed initial and boundary conditions, can generate exact solutions for any motion of this type of the respective fluids. For illustration, three special cases with technical relevance are considered and some important observations and graphical representations are provided. An interesting relationship is found between the solutions corresponding to motions induced by constant or ramptype shear stresses on the boundary. Furthermore, for validation of the results, the steady-state solutions corresponding to oscillatory motions are presented in different forms whose equivalence is graphically proved.

scholarly journals Slip Effects on Fractional Viscoelastic Fluids

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Muhammad Jamil ◽  
Najeeb Alam Khan
Keyword(s):  
Hypergeometric Functions ◽  
Fractional Derivatives ◽  
Fluid Motion ◽  
Maxwell Fluid ◽  
Newtonian Fluids ◽  
Generalized Hypergeometric Functions ◽  
General Solutions ◽  
Slip Effects ◽  
Special Cases ◽  
Wright Generalized Hypergeometric Functions

Unsteady flow of an incompressible Maxwell fluid with fractional derivative induced by a sudden moved plate has been studied, where the no-slip assumption between the wall and the fluid is no longer valid. The solutions obtained for the velocity field and shear stress, written in terms of Wright generalized hypergeometric functions , by using discrete Laplace transform of the sequential fractional derivatives, satisfy all imposed initial and boundary conditions. The no-slip contributions, that appeared in the general solutions, as expected, tend to zero when slip parameter is . Furthermore, the solutions for ordinary Maxwell and Newtonian fluids, performing the same motion, are obtained as special cases of general solutions. The solutions for fractional and ordinary Maxwell fluid for no-slip condition also obtained as limiting cases, and they are equivalent to the previously known results. Finally, the influence of the material, slip, and the fractional parameters on the fluid motion as well as a comparison among fractional Maxwell, ordinary Maxwell, and Newtonian fluids is also discussed by graphical illustrations.

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