Electro‐osmotic flow of fractional second‐grade fluid with fractional Cattaneo heat flux through a vertical microchannel

Heat Transfer ◽  
2021 ◽  
Author(s):  
Ahmed I. Abdellateef ◽  
Hashim M. Alshehri ◽  
Yasser Abd Elmaboud
Keyword(s):  
Heat Flux ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Osmotic Flow ◽  
Grade Fluid ◽  
Electro Osmotic Flow ◽  
Cattaneo Heat Flux ◽  
Vertical Microchannel

Exact Solutions of Electro-Osmotic Flow of Generalized Second-Grade Fluid with Fractional Derivative in a Straight Pipe of Circular Cross Section

2014 ◽  
Vol 69 (12) ◽  
pp. 697-704 ◽  
Author(s):  
Shaowei Wang ◽  
Moli Zhao ◽  
Xicheng Li ◽  
Xi Chen ◽  
Yanhui Ge
Keyword(s):  
Fractional Derivative ◽  
Integral Transform ◽  
Capillary Tube ◽  
Circular Cross Section ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Osmotic Flow ◽  
Grade Fluid ◽  
Generalized Second Grade Fluid ◽  
Electro Osmotic Flow

AbstractThe transient electro-osmotic flow of generalized second-grade fluid with fractional derivative in a narrow capillary tube is examined. With the help of the integral transform method, analytical expressions are derived for the electric potential and transient velocity profile by solving the linearized Poisson-Boltzmann equation and the Navier-Stokes equation. It was shown that the distribution and establishment of the velocity consists of two parts, the steady part and the unsteady one. The effects of retardation time, fractional derivative parameter, and the Debye-Hückel parameter on the generation of flow are shown graphically.

scholarly journals Transient electro-osmotic flow of generalized second-grade fluids under slip boundary conditions

2017 ◽  
Vol 95 (12) ◽  
pp. 1313-1320 ◽  
Author(s):  
Xiaoping Wang ◽  
Haitao Qi ◽  
Huanying Xu
Keyword(s):  
Boundary Conditions ◽  
Velocity Distribution ◽  
Fluid Velocity ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Osmotic Flow ◽  
Slip Boundary ◽  
Grade Fluid ◽  
Second Grade Fluids ◽  
Electro Osmotic Flow

This work investigates the transient slip flow of viscoelastic fluids in a slit micro-channel under the combined influences of electro-osmotic and pressure gradient forcings. We adopt the generalized second-grade fluid model with fractional derivative as the constitutive equation and the Navier linear slip model as the boundary conditions. The analytical solution for velocity distribution of the electro-osmotic flow is determined by employing the Debye–Hückel approximation and the integral transform methods. The corresponding expressions of classical Newtonian and second-grade fluids are obtained as the limiting cases of our general results. These solutions are presented as a sum of steady-state and transient parts. The combined effects of slip boundary conditions, fluid rheology, electro-osmotic, and pressure gradient forcings on the fluid velocity distribution are also discussed graphically in terms of the pertinent dimensionless parameters. By comparison with the two cases corresponding to the Newtonian fluid and the classical second-grade fluid, it is found that the fractional derivative parameter β has a significant effect on the fluid velocity distribution and the time when the fluid flow reaches the steady state. Additionally, the slip velocity at the wall increases in a noticeable manner the flow rate in an electro-osmotic flow.

SECOND‐GRADE FLUID FLOW WITH POWER‐LAW HEAT FLUX AND A HEAT SOURCE

2013 ◽  
Vol 44 (8) ◽  
pp. 687-702 ◽  
Author(s):  
Tasawar Hayat ◽  
Sabir A. Shehzad ◽  
Muhammad Qasim ◽  
F. Alsaadi ◽  
Ahmed Alsaedi
Keyword(s):  
Heat Flux ◽  
Fluid Flow ◽  
Heat Source ◽  
Power Law ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid ◽  
Power Law Heat Flux

The effect of slip on electro-osmotic flow of a second-grade fluid between two plates with Caputo–Fabrizio time fractional derivatives

2019 ◽  
Vol 97 (5) ◽  
pp. 509-516 ◽  
Author(s):  
Aziz Ullah Awan ◽  
Muhammad Danial Hisham ◽  
Nauman Raza
Keyword(s):  
Slip Flow ◽  
Second Grade ◽  
Parallel Plates ◽  
Second Grade Fluid ◽  
Thin Channel ◽  
Electro Osmosis ◽  
The Laplace Transform ◽  
Grade Fluid ◽  
Electro Osmotic Flow ◽  
Fractional Parameter

This work aims to probe the slip flow of second-grade fluid. The impetus of the flow is taken to be the electro-osmosis and the pressure gradient. The flow is considered to be in a thin channel-like passage formed by two parallel plates. The potential difference existing between the surface of the solid and fluid is taken to be non-symmetric. The governing equations are formed for the second-grade fluid with the Caputo–Fabrizio fractional derivative. The Laplace transform is used for transforming the problem into space parameters after introducing the dimensionless variables. Instead of developing an analytical expression for inverse Laplacian, the numerical Stehfest algorithm is used. A tabular comparison of the obtained results by two different methods (Stehfest and Tzou) is given and the conformity of the two ensures the validity of our obtained results. The results are also pictured in terms of graphs and carry the information of the slip flow effect. Furthermore, the effect of the fractional parameter on velocity has also been tabulated using different values of fractional parameter.

scholarly journals Heat and Mass Transfer in Hydromagnetic Second-Grade Fluid Past a Porous Inclined Cylinder under the Effects of Thermal Dissipation, Diffusion and Radiative Heat Flux

Energies ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 278 ◽  
Author(s):  
Sardar Bilal ◽  
Afraz Hussain Majeed ◽  
Rashid Mahmood ◽  
Ilyas Khan ◽  
Asiful H. Seikh ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Heat Flux ◽  
Differential Equations ◽  
Skin Friction ◽  
Heat And Mass Transfer ◽  
Radiative Heat ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Curvature Parameter ◽  
Grade Fluid

Current disquisition is presented to excogitate heat and mass transfer features of second grade fluid flow generated by an inclined cylinder under the appliance of diffusion, radiative heat flux, convective and Joule heating effects. Mathematical modelling containing constitutive expressions by obliging fundamental conservation laws are constructed in the form of partial differential equations. Afterwards, transformations are implemented to convert the attained partial differential system into ordinary differential equations. An implicit finite difference method known as the Keller Box was chosen to extract the solution. The impact of the flow-controlling variables on velocity, temperature and concentration profiles are evaluated through graphical visualizations. Variations in skin friction, heat transfer and mass flux coefficients against primitive variables are manipulated through numerical data. It is inferred from the analysis that velocity of fluid increases for incrementing magnitude of viscoelastic parameter and curvature parameter whereas it reduces for Darcy parameter whereas skin friction coefficient decreases against curvature parameter. Assurance of present work is manifested by constructing comparison with previous published literature.

Sign in / Sign up

Export Citation Format

Share Document