scholarly journals Semi-analytical technique for the solution of fractional Maxwell fluid

2017 ◽  
Vol 95 (5) ◽  
pp. 472-478 ◽  
Author(s):  
M. Abdullah ◽  
Asma Rashid Butt ◽  
Nauman Raza ◽  
Ehsan Ul Haque
Keyword(s):  
Circular Cylinder ◽  
Fractional Derivatives ◽  
Bessel Functions ◽  
Maxwell Fluid ◽  
Inverse Transformation ◽  
Physical Parameters ◽  
Time Dynamic ◽  
Analytical Technique ◽  
In Series ◽  
The Impact

In this work, the flow of a fractional Maxwell fluid is discussed. The velocity function and time-dependent shear stress of a Maxwell fluid with fractional derivatives are calculated. It is considered that the fluid in the infinitely long circular cylinder is moving with a velocity ft. The fluid in the infinitely long circular cylinder of radius R is initially at rest and at t = 0+, because of shear, it instantly starts to move longitudinally. To obtain the solutions, we have employed Laplace transformation and modified Bessel equation. The solutions are in series form, which are expressed in terms of modified Bessel functions [Formula: see text] and [Formula: see text], and satisfy all given conditions. In this paper, Laplace inverse transformation has been calculated numerically by using MATLAB. The behavior of the following physical parameters on the flow are investigated: relaxation time, dynamic viscosity, kinematics viscosity, similarity parameters of fractional derivatives and radius of the circular cylinder. Finally, the impact of the fractional parameter and material elements is shown by graphical demonstration.

Helices of fractionalized Maxwell fluid

2015 ◽  
Vol 4 (4) ◽  
Author(s):  
Muhammad Jamil ◽  
Kashif Ali Abro ◽  
Najeeb Alam Khan
Keyword(s):  
Angular Velocity ◽  
General Solution ◽  
Circular Cylinder ◽  
Special Function ◽  
Fluid Model ◽  
Fluid Motion ◽  
Maxwell Fluid ◽  
Initial Moment ◽  
Special Cases ◽  
In Series

AbstractIn this paper the helical flows of fractionalized Maxwell fluid model, through a circular cylinder, is studied. The motion is produced by the cylinder that at the initial moment begins to rotate around its axis with an angular velocity Omegatp, and to slide along the same axis with linear velocity Utp. The solutions that have been obtained using Laplace and finite Hankel transforms and presented in series form in terms of the newly defined special function M(z), satisfy all imposed initial and boundary conditions. Moreover, the corresponding solutions for ordinary Maxwell and Newtonian fluid obtained as special cases of the present general solution. Finally, the influence of various pertinent parameters on fluid motion as well as the comparison among different fluids models is analyzed by graphical illustrations.

scholarly journals Role of Newtonian heating on a Maxwell fluid via special functions: memory impact of local and nonlocal kernels

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nazish Iftikhar ◽  
Fatima Javed ◽  
Muhammad Bilal Riaz ◽  
Muhammad Abbas ◽  
Abdullah M. Alsharif ◽  
...  
Keyword(s):  
Memory Effect ◽  
Fractional Derivatives ◽  
Special Functions ◽  
Maxwell Fluid ◽  
Laplace Transforms ◽  
Time Dependent ◽  
Abc Model ◽  
Newtonian Heating ◽  
The Impact

AbstractThe impact of Newtonian heating on a time-dependent fractional magnetohydrodynamic (MHD) Maxwell fluid over an unbounded upright plate is investigated. The equations for heat, mass and momentum are established in terms of Caputo (C), Caputo–Fabrizio (CF) and Atangana–Baleanu (ABC) fractional derivatives. The solutions are evaluated by employing Laplace transforms. The change in the momentum profile due to variability in the values of parameters is graphically illustrated for all three C, CF and ABC models. The ABC model has proficiently revealed a memory effect.

scholarly journals Hydrodynamical Study of Creeping Maxwell Fluid Flow through a Porous Slit with Uniform Reabsorption and Wall Slip

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1852
Author(s):  
Hameed Ullah ◽  
Dianchen Lu ◽  
Abdul Majeed Siddiqui ◽  
Tahira Haroon ◽  
Khadija Maqbool
Keyword(s):  
Fluid Flow ◽  
Physical Phenomenon ◽  
Fluid Velocity ◽  
Axial Flow ◽  
Maximum Velocity ◽  
Maxwell Fluid ◽  
Two Dimensional ◽  
Mathematical Basis ◽  
Analytical Technique ◽  
The Impact

The present theoretical study investigates the influence of velocity slip characteristics on the plane steady two-dimensional incompressible creeping Maxwell fluid flow passing through a porous slit with uniform reabsorption. This two-dimensional flow phenomenon is governed by the mathematical model having nonlinear partial differential equations together with non-homogeneous boundary conditions. An analytical technique, namely the recursive approach, is used successfully to find the solutions of the problem. The explicit expressions for stream function, velocity components, pressure distribution, wall shear stress and normal stress difference have been derived. The axial flow rate, leakage flux and fractional reabsorption are also found out. The points of maximum velocity are identified. Non-dimensionalization is carried out and graphs are portrayed at different positions of the channel to show the impact of pertinent parameters: slip parameter, Maxwell fluid parameter and absorption parameter, on flow variables and found that the fluid velocity is affected significantly due to these parameters. This study provides a mathematical basis to understand the physical phenomenon for fluid flows through permeable boundaries which exists in different problems like gaseous diffusion, filtration and biological mechanisms.

scholarly journals On the flow of MHD generalized maxwell fluid via porous rectangular duct

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 989-1002
Author(s):  
Aamir Farooq ◽  
Muhammad Kamran ◽  
Yasir Bashir ◽  
Hijaz Ahmad ◽  
Azeem Shahzad ◽  
...  
Keyword(s):  
Fluid Model ◽  
Maxwell Fluid ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Rectangular Duct ◽  
Modified Darcy’S Law ◽  
Initial Boundary Value ◽  
Generalized Maxwell Fluid ◽  
Limiting Case ◽  
The Impact

Abstract The purpose of this proposed investigation is to study unsteady magneto hydrodynamic (MHD) mixed initial-boundary value problem for incompressible fractional Maxwell fluid model via oscillatory porous rectangular duct. Considering the modified Darcy’s law, the problem is simplified by using the method of the double finite Fourier sine and Laplace transforms. As a limiting case of the general solutions, the same results can be obtained for the classical Maxwell fluid. Also, the impact of magnetic parameter, porosity of medium, and the impact of various material parameters on the velocity profile and the corresponding tangential tensions are illuminated graphically. At the end, we will give the conclusion of the whole paper.

scholarly journals Damage Evolution of Granodiorite after Heating and Cooling Treatments

Minerals ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 779
Author(s):  
Mohamed Gomah ◽  
Guichen Li ◽  
Salah Bader ◽  
Mohamed Elkarmoty ◽  
Mohamed Ismael
Keyword(s):  
Mechanical Properties ◽  
Tensile Strength ◽  
Failure Mode ◽  
Physical And Mechanical Properties ◽  
P Wave ◽  
Physical Parameters ◽  
Slow Cooling ◽  
Heating And Cooling ◽  
Natural Rock ◽  
The Impact

The awareness of the impact of high temperatures on rock properties is essential to the design of deep geotechnical applications. The purpose of this research is to assess the influence of heating and cooling treatments on the physical and mechanical properties of Egyptian granodiorite as a degrading factor. The samples were heated to various temperatures (200, 400, 600, and 800 °C) and then cooled at different rates, either slowly cooled in the oven and air or quickly cooled in water. The porosity, water absorption, P-wave velocity, tensile strength, failure mode, and associated microstructural alterations due to thermal effect have been studied. The study revealed that the granodiorite has a slight drop in tensile strength, up to 400 °C, for slow cooling routes and that most of the physical attributes are comparable to natural rock. Despite this, granodiorite thermal deterioration is substantially higher for quick cooling than for slow cooling. Between 400:600 °C is ‘the transitional stage’, where the physical and mechanical characteristics degraded exponentially for all cooling pathways. Independent of the cooling method, the granodiorite showed a ductile failure mode associated with reduced peak tensile strengths. Additionally, the microstructure altered from predominantly intergranular cracking to more trans-granular cracking at 600 °C. The integrity of the granodiorite structure was compromised at 800 °C, the physical parameters deteriorated, and the rock tensile strength was negligible. In this research, the temperatures of 400, 600, and 800 °C were remarked to be typical of three divergent phases of granodiorite mechanical and physical properties evolution. Furthermore, 400 °C could be considered as the threshold limit for Egyptian granodiorite physical and mechanical properties for typical thermal underground applications.

scholarly journals A novel method for the analytical solution of fractional Zakharov–Kuznetsov equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Rasool Shah ◽  
Hassan Khan ◽  
Dumitru Baleanu ◽  
Poom Kumam ◽  
Muhammad Arif
Keyword(s):  
Present Method ◽  
Decomposition Method ◽  
Fractional Derivatives ◽  
Adomian Decomposition Method ◽  
Current Method ◽  
Analytical Technique ◽  
Suggested Technique ◽  
Adomian Decomposition ◽  
Novel Method ◽  
The Given

AbstractIn this article, an efficient analytical technique, called Laplace–Adomian decomposition method, is used to obtain the solution of fractional Zakharov– Kuznetsov equations. The fractional derivatives are described in terms of Caputo sense. The solution of the suggested technique is represented in a series form of Adomian components, which is convergent to the exact solution of the given problems. Furthermore, the results of the present method have shown close relations with the exact approaches of the investigated problems. Illustrative examples are discussed, showing the validity of the current method. The attractive and straightforward procedure of the present method suggests that this method can easily be extended for the solutions of other nonlinear fractional-order partial differential equations.

scholarly journals A Review of Photocatalytic Materials for Urban NOx Remediation

Catalysts ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 675
Author(s):  
Hugo Savill Russell ◽  
Louise Bøge Frederickson ◽  
Ole Hertel ◽  
Thomas Ellermann ◽  
Steen Solvang Jensen
Keyword(s):  
Photocatalytic Oxidation ◽  
Urban Air Pollution ◽  
Field Trials ◽  
Urban Environments ◽  
Physical Parameters ◽  
Nox Removal ◽  
Removal Efficiencies ◽  
The Impact ◽  
By Products ◽  
Photocatalytic Materials

NOx is a pervasive pollutant in urban environments. This review assesses the current state of the art of photocatalytic oxidation materials, designed for the abatement of nitrogen oxides (NOx) in the urban environment, and typically, but not exclusively based on titanium dioxide (TiO2). Field trials with existing commercial materials, such as paints, asphalt and concrete, in a range of environments including street canyons, car parks, tunnels, highways and open streets, are considered in-depth. Lab studies containing the most recent developments in the photocatalytic materials are also summarised, as well as studies investigating the impact of physical parameters on their efficiency. It is concluded that this technology may be useful as a part of the measures used to lower urban air pollution levels, yielding ∼2% NOx removal in the immediate area around the surface, for optimised TiO2, in some cases, but is not capable of the reported high NOx removal efficiencies >20% in outdoor urban environments, and can in some cases lower air quality by releasing hazardous by-products. However, research into new material is ongoing. The reason for the mixed results in the studies reviewed, and massive range of removal efficiencies reported (from negligible and up to >80%) is mainly the large range of testing practices used. Before deployment in individual environments site-specific testing should be performed, and new standards for lab and field testing should be developed. The longevity of the materials and their potential for producing hazardous by-products should also be considered.

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 Modelling H2 and its effects on star formation using a joint implementation of gadget-3 and KROME

2021 ◽  
Vol 504 (2) ◽  
pp. 2325-2345
Author(s):  
Emanuel Sillero ◽  
Patricia B Tissera ◽  
Diego G Lambas ◽  
Stefano Bovino ◽  
Dominik R Schleicher ◽  
...  
Keyword(s):  
Star Formation ◽  
Formation Rate ◽  
Physical Parameters ◽  
Density Profiles ◽  
Star Forming ◽  
Chemical Enrichment ◽  
Numerical Resolution ◽  
Stellar Radiation ◽  
Wide Range ◽  
The Impact

ABSTRACT We present p-gadget3-k, an updated version of gadget-3, that incorporates the chemistry package krome. p-gadget3-k follows the hydrodynamical and chemical evolution of cosmic structures, incorporating the chemistry and cooling of H2 and metal cooling in non-equilibrium. We performed different runs of the same ICs to assess the impact of various physical parameters and prescriptions, namely gas metallicity, molecular hydrogen formation on dust, star formation recipes including or not H2 dependence, and the effects of numerical resolution. We find that the characteristics of the simulated systems, both globally and at kpc-scales, are in good agreement with several observable properties of molecular gas in star-forming galaxies. The surface density profiles of star formation rate (SFR) and H2 are found to vary with the clumping factor and resolution. In agreement with previous results, the chemical enrichment of the gas component is found to be a key ingredient to model the formation and distribution of H2 as a function of gas density and temperature. A star formation algorithm that takes into account the H2 fraction together with a treatment for the local stellar radiation field improves the agreement with observed H2 abundances over a wide range of gas densities and with the molecular Kennicutt–Schmidt law, implying a more realistic modelling of the star formation process.

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