scholarly journals Decay of Potential Vortex and Diffusion of Temperature in a Generalized Oldroyd-B Fluid through a Porous Medium

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaoyi Guo
Keyword(s):  
Porous Medium ◽  
Fractional Derivatives ◽  
Maxwell Fluid ◽  
Hankel Transform ◽  
Temperature Fields ◽  
Darcy Law ◽  
Porous Space ◽  
Maxwell Fluids ◽  
Potential Vortex ◽  
And Diffusion

Based on a modified Darcy law, the decay of potential vortex and diffusion of temperature in a generalized Oldroyd-B fluid with fractional derivatives through a porous medium is studied. Exact solutions of the velocity and temperature fields are obtained in terms of the generalized Mittag-Leffler function by using the Hankel transform and discrete Laplace transform of the sequential fractional derivatives. One of the solutions is the sum of the Newtonian solutions and the non-Newtonian contributions. As limiting cases of the present solutions, the corresponding solutions of the fractional Maxwell fluid and classical Maxwell fluids are given. The influences of the fractional parameters, material parameters, and the porous space on the decay of the vortex are interpreted by graphical results.

Exact Solution of the Start-Up Electroosmotic Flow of Generalized Maxwell Fluids in Triangular Microducts

2021 ◽  
Author(s):  
F.Talay Akyildiz ◽  
Dennis A. Siginer
Keyword(s):  
Exact Solution ◽  
Electroosmotic Flow ◽  
Fractional Derivatives ◽  
Maxwell Fluid ◽  
Solution Technique ◽  
Maxwell Fluids ◽  
Start Up ◽  
Triangular Region ◽  
Overshoot Phenomenon ◽  
Poisson Boltzmann

Abstract Unsteady electroosmotic flow of generalized Maxwell fluids in triangular microducts is investigated. The governing equation is formulated with Caputo-Fabrizio time-fractional derivatives whose orders are distributed in the interval [0, 1). The linear momentum and the Poisson-Boltzmann equations are solved analytically in tandem in the triangular region with the help of the Helmholtz eigenvalue problem and Laplace transforms. The analytical solution developed is exact. The solution technique we use is new, leads to exact solutions, is completely different from those available in the literature and is applicable to other similar problems. The new expression for the velocity field displays experimentally observed 'velocity overshoot' as opposed to existing analytical studies none of which can predict the overshoot phenomenon. We show that when Caputo-Fabrizio time-fractional derivatives approach unity the exact solution for the classical upper convected Maxwell fluid is obtained. The presence of elasticity in the constitutive structure alters the Newtonian velocity profiles drastically. The influence of pertinent parameters on the flow field is explored.

scholarly journals Influence of Inclined MHD on Unsteady Flow of Generalized Maxwell Fluid with Fractional Derivative between Two Inclined Coaxial Cylinders through a Porous Medium

2020 ◽  
pp. 1705-1714
Author(s):  
Sundos Bader ◽  
Suad Naji Kadhim ◽  
Ahmed. M. Abdulhadi
Keyword(s):  
Porous Medium ◽  
Velocity Field ◽  
Fractional Derivative ◽  
Maxwell Fluid ◽  
Hankel Transform ◽  
Analytic Solutions ◽  
Circular Cylinders ◽  
Physical Parameters ◽  
The Laplace Transform ◽  
Generalized Maxwell Fluid

"This paper presents a study of inclined magnetic field on the unsteady rotating flow of a generalized Maxwell fluid with fractional derivative between two inclined infinite circular cylinders through a porous medium. The analytic solutions for velocity field and shear stress are derived by using the Laplace transform and finite Hankel transform in terms of the generalized G functions. The effect of the physical parameters of the problem on the velocity field is discussed and illustrated graphically.

Mixed Convection Three-Dimensional Flow of an Upper-Convected Maxwell Fluid Under Magnetic Field, Thermal-Diffusion, and Diffusion-Thermo Effects

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
T. Hayat ◽  
M. Awais ◽  
S. Obaidat
Keyword(s):  
Mixed Convection ◽  
Three Dimensional ◽  
Maxwell Fluid ◽  
Temperature Fields ◽  
Analysis Method ◽  
Soret And Dufour Effects ◽  
Homotopy Analysis ◽  
Dimensional Boundary ◽  
Layer Flow ◽  
And Diffusion

This paper discusses the mixed convection three-dimensional boundary layer flow of upper-convected Maxwell fluid over a stretching surface. Magnetohydrodynamic (MHD) combined with Soret and Dufour effects are also taken into account. The governing problems are first modeled and then solved by a homotopy analysis method (HAM). The variations of several parameters of interest on the velocity, concentration, and temperature fields are analyzed by the presentation of graphs. Several known results have been pointed out as the particular cases of the present analysis.

Melting of ice in a porous medium saturated with ice and gas while injecting warm water

2019 ◽  
Vol 13 (4) ◽  
pp. 112-117 ◽  
Author(s):  
V.Sh. Shagapov ◽  
M.N. Zapivakhina
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Low Temperature ◽  
Numerical Models ◽  
Warm Water ◽  
Temperature Fields ◽  
Initial State ◽  
Simplified Models ◽  
Frozen Soils ◽  
Porous Formation

The numerical models for the injection of warm water (in the temperature range from 300 to 340 K) into a cold porous formation are considered. Simplified models describing the processes of heat and mass transfer are proposed. The influence of the parameters determining the initial state of the porous medium, the boundary pressure, temperature and moisture content on the rate of propagation of hydrodynamic and temperature fields in the porous medium is investigated. It has been established that it is economically feasible to melt frozen soils saturated with ice and gas (air) at a sufficiently low temperature of the injected water (about 300 K).

scholarly journals MHD Peristaltic Flow of Fractional Jeffrey Model through Porous Medium

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Xiaoyi Guo ◽  
Jianwei Zhou ◽  
Huantian Xie ◽  
Ziwu Jiang
Keyword(s):  
Porous Medium ◽  
Pressure Rise ◽  
Maxwell Fluid ◽  
Peristaltic Flow ◽  
Constitutive Relationship ◽  
Second Grade ◽  
Jeffrey Fluid ◽  
Viscoelastic Parameters ◽  
Special Cases ◽  
Generalized Second Grade Fluid

The magnetohydrodynamic (MHD) peristaltic flow of the fractional Jeffrey fluid through porous medium in a nonuniform channel is presented. The fractional calculus is considered in Darcy’s law and the constitutive relationship which included the relaxation and retardation behavior. Under the assumptions of long wavelength and low Reynolds number, the analysis solutions of velocity distribution, pressure gradient, and pressure rise are investigated. The effects of fractional viscoelastic parameters of the generalized Jeffrey fluid on the peristaltic flow and the influence of magnetic field, porous medium, and geometric parameter of the nonuniform channel are presented through graphical illustration. The results of the analogous flow for the generalized second grade fluid, the fractional Maxwell fluid, are also deduced as special cases. The comparison among them is presented graphically.

Nonlinear thermal radiation and chemical reaction effects on Maxwell fluid flow with convectively heated plate in a porous medium

2018 ◽  
Vol 48 (2) ◽  
pp. 744-759 ◽  
Author(s):  
Kh. Hosseinzadeh ◽  
M. Gholinia ◽  
B. Jafari ◽  
A. Ghanbarpour ◽  
H. Olfian ◽  
...  
Keyword(s):  
Porous Medium ◽  
Fluid Flow ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Maxwell Fluid ◽  
Nonlinear Thermal Radiation ◽  
Heated Plate

The MHD Flows for a Heated Generalized Oldroyd-B Fluid With Fractional Derivative

2010 ◽  
Author(s):  
Yaqing Liu ◽  
Liancun Zheng ◽  
Xinxin Zhang ◽  
Fenglei Zong
Keyword(s):  
Fractional Calculus ◽  
Viscoelastic Fluid ◽  
Mhd Flow ◽  
Hankel Transform ◽  
Constitutive Relationship ◽  
Temperature Fields ◽  
Fractional Partial Differential Equations ◽  
Relation Model ◽  
Velocity And Temperature Fields ◽  
Relationship Of

In this paper, we present a circular motion of magnetohydrodynamic (MHD) flow for a heated generalized Oldroyd-B fluid. The fractional calculus approach is introduced to establish the constitutive relationship of a viscoelastic fluid. The velocity and temperature fields of the flow are described by fractional partial differential equations. Exact analytical solutions of velocity and temperature fields are obtained by using Hankel transform and Laplace transform for fractional calculus. Results for ordinary viscous flow are deduced by making the fractional order of differential tend to one and zero. It is shown that the fractional constitutive relation model is more useful than the conventional model for describing the properties of viscoelastic fluid.

scholarly journals Effects of Anisotropy on Natural Convection in a Vertical Porous Cavity Filled with a Heat Generation

2020 ◽  
pp. 12-27
Author(s):  
Degan Gerard ◽  
Sokpoli Amavi Ernest ◽  
Akowanou Djidjoho Christian ◽  
Vodounnou Edmond Claude
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Temperature Fields ◽  
Poisson Equations ◽  
Gravitational Vector ◽  
Side Walls ◽  
Rayleigh Numbers ◽  
Vertical Cavity

This research was devoted to the analytical study of heat transfer by natural convection in a vertical cavity, confining a porous medium, and containing a heat source. The porous medium is hydrodynamically anisotropic in permeability whose axes of permeability tensor are obliquely oriented relative to the gravitational vector and saturated with a Newtonian fluid. The side walls are cooled to the temperature  and the horizontal walls are kept adiabatic. An analytical solution to this problem is found for low Rayleigh numbers by writing the solutions of mathematical model in polynomial form of degree n of the Rayleigh number. Poisson equations obtained are solved by the modified Galerkin method. The results are presented in term of streamlines and isotherms. The distribution of the streamlines and the temperature fields are greatly influenced by the permeability anisotropy parameters and the thermal conductivity. The heat transfer decreases considerably when the Rayleigh number increases.

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