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

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.

Download Full-text

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

Mathematical Problems in Engineering ◽

10.1155/2021/5539007 ◽

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.

Download Full-text

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

Mathematics ◽

10.3390/math9040334 ◽

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.

Download Full-text

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

Studia Universitatis Babes-Bolyai Matematica ◽

10.24193/subbmath.2021.1.16 ◽

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 ◽

Influence of an inclined magnetic field on the Poiseuille flow of immiscible micropolar–Newtonian fluids in a porous medium

Canadian Journal of Physics ◽

10.1139/cjp-2017-0998 ◽

2018 ◽

Vol 96 (9) ◽

pp. 1016-1028 ◽

Cited By ~ 6

Author(s):

Pramod Kumar Yadav ◽

Sneha Jaiswal

Keyword(s):

Magnetic Field ◽

Rotational Velocity ◽

Immiscible Fluids ◽

Newtonian Fluids ◽

Porous Channel ◽

Physical Parameters ◽

Inclined Magnetic Field ◽

Two Phase ◽

Flow Through ◽

Newtonian Viscous Fluid

The present problem is concerned with two-phase fluid flow through a horizontal porous channel in the presence of uniform inclined magnetic field. The micropolar fluid or Eringen fluid and Newtonian viscous fluid are flowing in the upper and lower regions of the horizontal porous channel, respectively. In this paper, the permeability of each region of the horizontal porous channel has been taken to be different. The effects of various physical parameters like angles of inclination of magnetic field, viscosity ratio, micropolarity parameter, etc., on the velocities, micro-rotational velocity of two immiscible fluids in horizontal porous channel, wall-shear stress, and flow rate have been discussed. The result obtained for immiscible micropolar–Newtonian fluids are compared with the results of two immiscible Newtonian fluids. The obtained result may be used in production of oil from oil reservoirs, purification of contaminated ground water, etc.

Download Full-text

Performance Indicators for Steady-State Heat Transfer Through Fin Assemblies

Journal of Heat Transfer ◽

10.1115/1.2825846 ◽

1996 ◽

Vol 118 (2) ◽

pp. 310-316 ◽

Cited By ~ 10

Author(s):

A. S. Wood ◽

G. E. Tupholme ◽

M. I. H. Bhatti ◽

P. J. Heggs

Keyword(s):

Heat Transfer ◽

Steady State ◽

Heat Flow ◽

Performance Indicators ◽

Physical Parameters ◽

State Heat ◽

Extended Surface ◽

Flow Through ◽

Steady State Heat ◽

Steady State Heat Transfer

A comparative study is presented of several models describing steady-state heat flow through an assembly consisting of a primary surface (wall) and attached extended surface (fin). Attention is focused on the validity of four performance indicators. The work shows that the augmentation factor is the only indicator capable of correctly predicting the behavioral trends of the rate of heat flow through the assembly as the influencing physical parameters are varied.

Download Full-text

Variable thermal conductivity and viscosity effects on non-Newtonian fluids flow through a vertical porous plate under Soret-Dufour influence

Mathematics and Computers in Simulation ◽

10.1016/j.matcom.2020.05.001 ◽

2020 ◽

Vol 177 ◽

pp. 358-384

Author(s):

A.S. Idowu ◽

B.O. Falodun

Keyword(s):

Thermal Conductivity ◽

Porous Plate ◽

Variable Thermal Conductivity ◽

Newtonian Fluids ◽

Vertical Porous Plate ◽

Viscosity Effects ◽

Flow Through

Download Full-text

Heat transfer and MHD flow of non-newtonian Maxwell fluid through a parallel plate channel: analytical and numerical solution

Mechanical Sciences ◽

10.5194/ms-9-61-2018 ◽

2018 ◽

Vol 9 (1) ◽

pp. 61-70 ◽

Cited By ~ 7

Author(s):

Alireza Rahbari ◽

Morteza Abbasi ◽

Iman Rahimipetroudi ◽

Bengt Sundén ◽

Davood Domiri Ganji ◽

...

Keyword(s):

Heat Transfer ◽

Parallel Plate ◽

Mhd Flow ◽

Maxwell Fluid ◽

Deborah Number ◽

Temperature Fields ◽

Physical Parameters ◽

Homotopy Analysis ◽

Velocity And Temperature Fields ◽

Plate Channel

Abstract. Analytical and numerical analyses have been performed to study the problem of magneto-hydrodynamic (MHD) flow and heat transfer of an upper-convected Maxwell fluid in a parallel plate channel. The governing equations of continuity, momentum and energy are reduced to two ordinary differential equation forms by introducing a similarity transformation. The Homotopy Analysis Method (HAM), Homotopy Perturbation Method (HPM) and fourth-order Runge-Kutta numerical method (NUM) are used to solve this problem. Also, velocity and temperature fields have been computed and shown graphically for various values of the physical parameters. The objectives of the present work are to investigate the effect of the Deborah numbers (De), Hartman electric number (Ha), Reynolds number (Rew) and Prandtl number (Pr) on the velocity and temperature fields. As an important outcome, it is observed that increasing the Hartman number leads to a reduction in the velocity values while increasing the Deborah number has negligible impact on the velocity increment.

Download Full-text

Slip Effects on Fractional Viscoelastic Fluids

International Journal of Differential Equations ◽

10.1155/2011/193813 ◽

2011 ◽

Vol 2011 ◽

pp. 1-19 ◽

Cited By ~ 13

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.

Download Full-text

Hall-current effects on unsteady MHD flow between stretching sheet and an oscillating porous upper parallel plate with constant suction

Thermal Science ◽

10.2298/tsci1102527c ◽

2011 ◽

Vol 15 (2) ◽

pp. 527-536 ◽

Cited By ~ 8

Author(s):

Raju Changal ◽

Reddy Ananda ◽

Kumar Vijaya

Keyword(s):

Stretching Sheet ◽

Hall Current ◽

Porous Plate ◽

Fluid Motion ◽

Mhd Flow ◽

Transverse Magnetic ◽

Physical Parameters ◽

Electrically Conducting ◽

Electrically Conducting Fluid ◽

Constant Suction

The unsteady MHD flow of an incompressible viscous electrically conducting fluid between two horizontal parallel non conducting plates, where the lower one is stretching sheet and the upper one is oscillating porous plate, is studied in the presence of a transverse magnetic field and the effects of Hall current. Fluid motion is caused by the stretching of the lower sheet and a constant suction is applied at the upper plate which is oscillating in its own plane. The stretching velocity of the sheet is assumed to be a linear function of distance along the channel. The expressions relating to the velocity distribution are obtained and effects of different values of various physical parameters are calculated numerically and shown graphically.

Download Full-text

MHD DOUBLE DIFFUSIVE AND CHEMICALLY REACTIVE FLUID FLOW THROUGH A ROTATING POROUS PLATE

International Journal of Research -GRANTHAALAYAH ◽

10.29121/granthaalayah.v5.i7.2017.2143 ◽

2017 ◽

Vol 5 (7) ◽

pp. 363-373

Author(s):

M. Umamaheswar ◽

Raju ◽

S.V. K. Varma ◽

C. Sucharitha

Keyword(s):

Fluid Flow ◽

Porous Plate ◽

Physical Parameters ◽

Heat Absorption ◽

Governing Equations ◽

Finite Difference Technique ◽

Reactive Fluid ◽

Flow Through ◽

Reactive Fluid Flow ◽

Double Diffusive

In this paper MHD rotating double diffusive and chemically reactive fluid flow past a vertical porous plate with thermal radiation and heat absorption/generation is studied. The non-dimensional governing equations involved in the present analysis are solved by using finite difference technique. The effects of various physical parameters on velocity, temperature and concentration along with skin friction, the rate of heat transfer in the form of Nusselt number and the rate of mass transfer in the form of Sherwood number are studied through the graphs and tables.

Download Full-text