scholarly journals Time Fractional Analysis of Channel Flow of Couple Stress Casson Fluid using Fick’s and Fourier’s Laws

2021 ◽  
Author(s):  
Shafiq Ahmad ◽  
Sami Ul Haq ◽  
Farhad Ali ◽  
Ilyas Khan ◽  
Kottakkaran Sooppy Nisar
Keyword(s):  
Channel Flow ◽  
Couple Stress ◽  
Integral Transformation ◽  
Physical Phenomenon ◽  
Classical Model ◽  
Fourier Integral ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Fractional Model ◽  
Stress Parameter

Abstract This study aim to examine the channel flow of a couple stress Casson fluid. The flow is generated due to the motion of the plate at y = o, while the plate at y = d is at rest. This physical phenomenon is derived in terms of partial differential equations. The subjected governing PDE’s are non-dimensionalized with the help of dimensionless variables. The dimensionless classical model is generalized by transforming it to the time fractional model using Fick’s and Fourier’s Laws. The general fractional model is solved by applying the Laplace and Fourier integral transformation. Furthermore, the parametric influence of various physical parameters like Casson parameter, couple stress parameter, Grashof number, Schmidt number and Prandtl number on velocity, temperature, and concentration distributions is shown graphically and discussed. The heat transfer rate, skin friction, and Sherwood number are calculated and presented in tabular form. It is worth noting that the increasing values of the couple stress parameter λ deaccelerate the velocity of Couple stress Casson fluid.

scholarly journals Fractional model for MHD flow of Casson fluid with cadmium telluride nanoparticles using the generalized Fourier’s law

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Nadeem Ahmad Sheikh ◽  
Dennis Ling Chuan Ching ◽  
Ilyas Khan ◽  
Hamzah Bin Sakidin ◽  
Muhammad Jamil ◽  
...  
Keyword(s):  
Energy Equation ◽  
Volume Fraction ◽  
Mhd Flow ◽  
Integral Transforms ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Fourier’S Law ◽  
Fractional Model ◽  
Laplace Transformations ◽  
Fourier's Law

AbstractThe present work used fractional model of Casson fluid by utilizing a generalized Fourier’s Law to construct Caputo Fractional model. A porous medium containing nanofluid flowing in a channel is considered with free convection and electrical conduction. A novel transformation is applied for energy equation and then solved by using integral transforms, combinedly, the Fourier and Laplace transformations. The results are shown in form of Mittag-Leffler function. The influence of physical parameters have been presented in graphs and values in tables are discussed in this work. The results reveal that heat transfer increases with increasing values of the volume fraction of nanoparticles, while the velocity of the nanofluid decreases with the increasing values of volume fraction of these particles.

Numerical simulation of nonlinear thermal radiation on the 3D flow of a couple stress Casson nanofluid due to a stretching sheet

2020 ◽  
pp. 1-28
Author(s):  
P. V. Satya Narayana ◽  
Tarakaramu Nainaru ◽  
G. Sarojamma ◽  
Isaac Lare Animasaun
Keyword(s):  
Heat Transfer ◽  
Couple Stress ◽  
Three Dimensional ◽  
Casson Fluid ◽  
Industrial Applications ◽  
Physical Parameters ◽  
Nonlinear Thermal Radiation ◽  
Scaling Analysis ◽  
Nonlinear Odes ◽  
Limiting Case

Abstract Little is known on the three-dimensional flow of couple stress Casson fluid conveying nanoparticles when the significance of Lorentz force, chaotic gesture of those minute particles and thermophoresis are significant. The intent of this investigation is to focus on the flow of such fluid along a horizontal surface due to dual stretching and internal heating. The dimensional nonlinear equations are reduced into a system of coupled nonlinear ODEs employing scaling analysis and later they are solved numerically. The results are discussed graphically for various emerged physical parameters through different plots. The results in the absence of stretching ratio factor indicate that the heat absorption parameter and Prandtl number accelerate the heat transfer rate. The temperature of the non- Newtonian couple stress fluid is found to be bigger than that of viscous case. It may be suggested that Casson couple stress nanofluid can be substituted for the corresponding viscous fluid in industrial applications for greater heat transfer. The outcomes are closely matched with the studies available in the literature as a limiting case.

scholarly journals Free convective flow of a couple stress fluid through a vertical porous channel in the presence of a transverse magnetic field

2018 ◽  
Vol 12 (1) ◽  
pp. 49-62
Author(s):  
M. Prasad Siddalinga ◽  
B. S. Shashikala
Keyword(s):  
Magnetic Field ◽  
Transverse Magnetic Field ◽  
Couple Stress ◽  
Hartmann Number ◽  
Transverse Magnetic ◽  
Porous Channel ◽  
Couple Stress Fluid ◽  
Physical Parameters ◽  
Stress Parameter ◽  
Buoyancy Parameter

Nonlinear oberbeck convection of a couple stress fluid in a vertical porous channel in the presence of transverse magnetic field is investigated in this paper. Analytical solution is obtained using the perturbation technique for vanishing values of the buoyancy parameter. Numerical solution of the nonlinear governing equations is obtained using the finite difference technique to validate the results obtained from the analytical solutions. The influence of the physical parameters on the flow, such as couple stress parameter, Hartmann number, temperature parameter, porous parameter and buoyancy parameter are evaluated and presented graphically. A new approach is used to analyse the flow for strong, weak and comparable porosity cases. It is found that increase in porous parameter, couple stress parameter, Hartmann number and temperature parameters decrease the velocity considerably.Kathmandu University Journal of Science, Engineering and Technology Vol. 12, No. I, June, 2016, Page: 49-62

scholarly journals Exact Solutions of Brinkman Type Fluid Between Side Walls Over an Infinite Plate

2018 ◽  
Author(s):  
Saeed Islam ◽  
Muhammad Asif ◽  
Samiul Haq
Keyword(s):  
Integral Transformation ◽  
Infinite Plate ◽  
Fourier Integral ◽  
Bottom Plate ◽  
Physical Parameters ◽  
Shear Stresses ◽  
Special Cases ◽  
Depth Analysis ◽  
Side Walls ◽  
Oscillating Shear Stress

In this paper Brinkman type fluid over an infinite plate between side walls is being investigated. The flow is generated by oscillating shear stress of the bottom plate and the solutions are obtained by using Fourier integral transformation. The obtained results are presented in steady and transient states for both sin and cos shear stresses. The general solutions are reduced to some special cases corresponding, namely to the Brinkman type fluid over an infinite plate and flow of a Newtonian viscous fluid. Graphical illustrations are carried out to have in depth analysis of the involved physical parameters

Flow and heat transfer of a couple-stress fluid sandwiched between viscous fluid layers

2005 ◽  
Vol 83 (7) ◽  
pp. 705-720 ◽  
Author(s):  
J C Umavathi ◽  
A J Chamkha ◽  
M H Manjula ◽  
A Al-Mudhaf
Keyword(s):  
Heat Transfer ◽  
Couple Stress ◽  
Temperature Fields ◽  
Couple Stress Fluid ◽  
Physical Parameters ◽  
Linear Ordinary Differential Equations ◽  
Closed Form Solutions ◽  
Stress Parameter ◽  
Flow And Heat Transfer ◽  
Fluid Layers

The problem of steady laminar fully developed flow and heat transfer in a horizontal channel consisting of a couple-stress fluid sandwiched between two clear viscous fluids is analyzed analytically. The fluids in all regions are assumed to be incompressible, immiscible, and the transport properties of the fluids in all regions are assumed to be constant. Under these assumptions, the resulting governing equations constitute a set of coupled linear ordinary differential equations that is solved analytically. The closed form solutions obtained for the velocity and temperature fields in the channel are evaluated numerically for various parametric conditions. These results are illustrated graphically to illustrate the effects of the physical parameters governing the flow such as the viscosity ratio, conductivity ratio, couple-stress parameter, Eckert number, and the Prandtl number on the velocity and temperature profiles. In addition, results for the rate of heat transfer are computed for different values of the physical parameters and presented in tabular form. It is found that the effect of the couple stress parameter is to promote the motion of the fluid.PACS Nos.: 44.15.+a

scholarly journals Couple stress fluid flow due to slow steady oscillations of a permeable sphere

2020 ◽  
Vol 9 (1) ◽  
pp. 352-360
Author(s):  
P. Aparna ◽  
P. Padmaja ◽  
N. Pothanna ◽  
J.V. Ramana Murthy
Keyword(s):  
Fluid Flow ◽  
Couple Stress ◽  
Bessel Functions ◽  
Pressure Field ◽  
Flow Region ◽  
Couple Stress Fluid ◽  
Physical Parameters ◽  
External Flows ◽  
Steady Oscillations ◽  
Permeable Sphere

AbstractThe study of oscillating flow of a Couple Stress fluid past a permeable sphere is considered. Analytical solution for the flow field in terms of stream function is obtained using modified Bessel functions. The formula for Drag acting on the sphere due external flow is evaluated. Pressure field for the flow region past and inside the sphere is obtained. Effects of physical parameters like couple stress parameter, permeability, frequency and geometric parameters on the drag due to internal and external flows are represented graphically. It is observed that the drag for viscous fluid flow will be less than the case of couple-stress fluid flow and hence couple stress fluids offer resistance for flow.

PERISTALTIC FLOW OF COUPLE-STRESS CONDUCTING FLUIDS THROUGH A POROUS CHANNEL: APPLICATIONS TO BLOOD FLOW IN THE MICRO-CIRCULATORY SYSTEM

2011 ◽  
Vol 19 (03) ◽  
pp. 461-477 ◽  
Author(s):  
DHARMENDRA TRIPATHI
Keyword(s):  
Frictional Force ◽  
Couple Stress ◽  
Amplitude Ratio ◽  
Circulatory System ◽  
Mechanical Efficiency ◽  
Peristaltic Flow ◽  
Porous Channel ◽  
Stress Parameter ◽  
Permeability Parameter ◽  
Conducting Fluids

The present investigation is devoted to study a theoretical investigation of the peristaltic flow of a couple-stress conducting fluids in a porous channel under the influence of slip boundary condition. This study is applicable to the physiological flow of blood in the micro-circulatory system, by taking account of the particle size effect. The expressions for axial velocity, pressure gradient, stream function, frictional force and mechanical efficiency are obtained under the small Reynolds number and the large wavelength approximations. Effects of different physical parameters reflecting permeability parameter, couple-stress parameter, Hartmann number as well as amplitude ratio on pumping characteristics, frictional force, mechanical efficiency and trapping of peristaltic flow pattern are studied. The computational and numerical results are presented in graphical form. On the basis of our discussion, it is concluded that pressure reduces by increasing the magnitude of couple-stress parameter, permeability parameter, slip parameter, whereas it enhances by increasing the magnitude of magnetic field and amplitude ratio.

On the Modeling and Simulation of Friction

1991 ◽  
Vol 113 (3) ◽  
pp. 354-362 ◽  
Author(s):  
D. A. Haessig ◽  
B. Friedland
Keyword(s):  
Modeling And Simulation ◽  
Experimental Observation ◽  
Friction Force ◽  
Closed Loop ◽  
Physical Phenomenon ◽  
Classical Model ◽  
The Other ◽  
Simulation Experiments ◽  
New Models ◽  
Integrator Model

Two new models for “slip-stick” friction are presented. One, called the “bristle model,” is an approximation designed to capture the physical phenomenon of sticking. This model is relatively inefficient numerically. The other model, called the “reset integrator model,” does not capture the details of the sticking phenomenon, but is numerically efficient and exhibits behavior similar to the model proposed by Karnopp in 1985. All three of these models and the Dahl model are preferable to the classical model, which poorly represents the friction force at zero velocity. Simulation experiments show that the Karnopp model, the Dahl model, and the new models give similar results in two examples. In a closed-loop example, the classical model predicts a limit cycle which is not observed in the laboratory. The Karnopp model, the Dahl model, and the new models, on the other hand, agree with the experimental observation.

scholarly journals Memory effects on the proliferative function in the cycle-specific of chemotherapy

2021 ◽  
Author(s):  
Najma Ahmed ◽  
Dumitru Vieru ◽  
Fiazud Din Zaman
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Numerical Solutions ◽  
Classical Model ◽  
Cell Mass ◽  
Time Derivative ◽  
Fractional Model ◽  
Fractional Differential ◽  
Mathcad Software

A generalized mathematical model of the breast and ovarian cancer is developed by considering the fractional differential equations with Caputo time-fractional derivatives. The use of the fractional model shows that the time-evolution of the proliferating cell mass, the quiescent cell mass, and the proliferative function are significantly influenced by their history. Even if the classical model, based on the derivative of integer order has been studied in many papers, its analytical solutions are presented in order to make the comparison between the classical model and the fractional model. Using the finite difference method, numerical schemes to the Caputo derivative operator and Riemann-Liouville fractional integral operator are obtained. Numerical solutions to the fractional differential equations of the generalized mathematical model are determined for the chemotherapy scheme based on the function of "on-off" type. Numerical results, obtained with the Mathcad software, are discussed and presented in graphical illustrations. The presence of the fractional order of the time-derivative as a parameter of solutions gives important information regarding the proliferative function, therefore, could give the possible rules for more efficient chemotherapy.

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