Fractional model for MHD flow of Casson fluid with cadmium telluride nanoparticles using the generalized 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.

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Slip Flow of a Nanofluid Over a Stretching Cylinder with Cattaneo-Christov Flux Model: Using SRM

International Journal of Engineering & Technology ◽

10.14419/ijet.v7i4.10.20901 ◽

2018 ◽

Vol 7 (4.10) ◽

pp. 225

Author(s):

Gangadhar K ◽

Venkata Ramana ◽

Dasaradha Ramaiah ◽

B. Rushi Kumar

Keyword(s):

Heat Transfer ◽

Differential Equations ◽

Volume Fraction ◽

Slip Flow ◽

Physical Parameters ◽

Stretching Cylinder ◽

Nanoparticle Volume Fraction ◽

Fourier’S Law ◽

Flux Model ◽

Fourier's Law

This article represents a numerical investigation of heat transfer and slip flow of a nanofluid over a stretching cylinder in magnetic field. In order to explore the heat transfer characteristics Cattaneo-Christov flux model is utilized in place of Fourier’s law. By using, suitable transformations, the governing partial differential equations are changed into non-linear ordinary differential equations. A numerical method, known as, spectral relaxation method is used to solve these equations. By using pictorial graphs, the relevant physical parameters that appear in temperature and velocity distributions are analytically discussed. Various types of nanoparticles like Alumina (Al2O3), Titanium oxide (TiO2), Copper (Cu) and Silver (Ag) with water as their base fluid has been assumed. It was identified that absolute value of skin friction coefficient and Nusselt number increases as each of nanoparticle volume fraction or Reynolds number increases. Temperature profile goes up in a faster way in Fourier’s law case than Cattaneo-Christov heat flux model. It is also found that the choice of copper (for large values of nanoparticle volume fraction) and alumina (for small nanoparticle volume fraction) leads to highest cooling performance in solving this problem. In order to examine the accuracy of the method, thorough comparison has been made with some previous results.

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Effect of Brownian Motion and External Magnetic Field on the Effective Heat Capacity of Ferrofluids

Volume 6: Fluids and Thermal Systems; Advances for Process Industries, Parts A and B ◽

10.1115/imece2011-63985 ◽

2011 ◽

Author(s):

Narges Susan Mousavi Kh. ◽

Sunil Kumar ◽

Arvind Narayanaswamy

Keyword(s):

Magnetic Field ◽

Heat Capacity ◽

Brownian Motion ◽

Energy Equation ◽

Volume Fraction ◽

Physical Parameters ◽

Effective Heat Capacity ◽

Effective Heat ◽

Negligible Contribution

An Eulerian formalism is used to derive the energy equation for a system of magnetic nanoparticles in a fluid (ferrofluid) in the presence of uniform magnetic field. The energy equation proposed here contains an effective heat capacity, which has contributions from: (1) Brownian motion of nanoparticles, (2) magnetic field, (3) temperature, and (4) volume fraction of particles. The modified term quantitatively shows the negligible contribution of the first three factors but the significant effect of concentration of particles in change in heat capacity of ferrofluid. In order to have a better understanding of the problem, the equation is converted to a non dimensional form from which the role of each of physical parameters can be inferred.

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Caputo Time Fractional Model Based on Generalized Fourier’s and Fick’s Laws for Jeffrey Nanofluid: Applications in Automobiles

Mathematical Problems in Engineering ◽

10.1155/2021/4611656 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Jawad Ahmad ◽

Farhad Ali ◽

Saqib Murtaza ◽

Ilyas Khan

Keyword(s):

Heat Transfer ◽

Transfer Rate ◽

Energy Equation ◽

Special Function ◽

Volume Fraction ◽

Classical Model ◽

Fractional Model ◽

Jeffrey Nanofluid ◽

Mass And Heat Transfer ◽

Jeffery Nanofluid

This article aims to examine Jeffery nanofluid with joint effects of mass and heat transfer in a horizontal channel. The classical model is transferred to the Caputo fractional model by using the generalized Fourier’s and Fick’s laws. The nanofluids are formed by dispersing two different nanoparticles, silver and copper, into a based fluid. A novel transformation has been applied to the mass and energy equation and then solved by using the sine Fourier and the Laplace transformation jointly. The exact solution is given in terms of a special function, that is, the Mittag-Leffler function. The Sherwood number and Nusselt number are calculated and displayed in the tabular form. The effect of embedded parameters on the velocity, concentration, and temperature profile is discussed graphically. It is noted that the heat transfer rate of EO is improved by 28.24% when the volume fraction of Ag nanoparticles is raised from 0.00 to 0.04.

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MHD Stagnation Point Flow and Heat Transfer Over a Stretching Sheet in a Blood-Based Casson Ferrofluid With Newtonian Heating

Journal of Advanced Research in Fluid Mechanics and Thermal Sciences ◽

10.37934/arfmts.82.1.111 ◽

2021 ◽

Vol 82 (1) ◽

pp. 1-11

Author(s):

Muhammad Khairul Anuar Mohamed ◽

Siti Hanani Mat Yasin ◽

Mohd Zuki Salleh ◽

Hamzeh Taha Alkasasbeh

Keyword(s):

Heat Transfer ◽

Stagnation Point ◽

Stretching Sheet ◽

Volume Fraction ◽

Mhd Flow ◽

Casson Fluid ◽

Skin Friction Coefficient ◽

Newtonian Heating ◽

Linear Partial Differential Equations ◽

Flow And Heat Transfer

The present study investigated the magnetohydrodynamic (MHD) flow and heat transfer on a stagnation point past a stretching sheet in a blood-based Casson ferrofluid with Newtonian heating boundary conditions. The ferrite Fe3O4 and cobalt ferrite CoFe2O4 ferroparticles suspended into Casson fluid represent by human blood to form blood-based Casson ferrofluid are numerically examined. The mathematical model for Casson ferrofluid which is in non-linear partial differential equations are first transformed to a more convenient form by similarity transformation approach then solved numerically by using the Runge-Kutta-Fehlberg (RKF45) method. The characteristics and effects of the stretching parameter, the magnetic parameter, the Casson parameter and the ferroparticle volume fraction for Fe3O4 and CoFe2O4 on the variation of surface temperature and the reduced skin friction coefficient are analyzed and discussed. It is found that the blood-based Casson ferrofluid provided up to 46% higher in temperature surface compared to blood-based fluid with the presence of magnetic effects.

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Study of Carbon Nanotubes with a Casson Fluid in a Vertical Channel of Porous Media under MHD and Dufour Effect

Journal of Scientific Research ◽

10.3329/jsr.v13i1.47458 ◽

2021 ◽

Vol 13 (1) ◽

pp. 31-45

Author(s):

S. Hazarika ◽

S. Ahmed

Keyword(s):

Carbon Nanotubes ◽

Volume Fraction ◽

Saturated Porous Medium ◽

Fluid Velocity ◽

Vertical Channel ◽

Casson Fluid ◽

Engine Oil ◽

Single Wall Carbon Nanotubes ◽

Physical Parameters ◽

The Impact

An analysis is conducted to investigate the problem of heat/mass transfer in MHD free convective flow of Casson-fluid in a vertical channel embedded with saturated porous medium past through carbon nanotubes in the form of single-wall carbon nanotubes (SWCNTs) and multiple-wall carbon nanotubes (MWCNTs) with engine oil as base fluid. In this article, the impact of CNT’s on velocity, temperature, shear stress and rate of heat transfer of the nanofluid has been investigated and studied graphically for the effects of different key physical parameters involved. The validity of this flow model is presented and is found satisfactory agreement with published results. The results state that, fluid velocity accelerates for greater values of Casson parameter and nanoparticles volume fraction, while thermal radiation (R) and heat generation (Q) assume a significant role in CNT's. Applications of this study arise in broad area of science and engineering such as thermal conductivity, energy storage, biomedical applications, air and water filtration, fibers and fabrics.

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MHD Flow and Heat Transfer in Sodium Alginate Fluid with Thermal Radiation and Porosity Effects: Fractional Model of Atangana–Baleanu Derivative of Non-Local and Non-Singular Kernel

Symmetry ◽

10.3390/sym11101295 ◽

2019 ◽

Vol 11 (10) ◽

pp. 1295 ◽

Cited By ~ 3

Author(s):

Arshad Khan ◽

Dolat Khan ◽

Ilyas Khan ◽

Muhammad Taj ◽

Imran Ullah ◽

...

Keyword(s):

Heat Transfer ◽

Temperature Profile ◽

Sodium Alginate ◽

Mhd Flow ◽

Casson Fluid ◽

Singular Kernel ◽

Heat Transfer Analysis ◽

Fractional Model ◽

The Laplace Transform ◽

Non Local

Heat transfer analysis in an unsteady magnetohydrodynamic (MHD) flow of generalized Casson fluid over a vertical plate is analyzed. The medium is porous, accepting Darcy’s resistance. The plate is oscillating in its plane with a cosine type of oscillation. Sodium alginate (SA–NaAlg) is taken as a specific example of Casson fluid. The fractional model of SA–NaAlg fluid using the Atangana–Baleanu fractional derivative (ABFD) of the non-local and non-singular kernel has been examined. The ABFD definition was based on the Mittag–Leffler function, and promises an improved description of the dynamics of the system with the memory effects. Exact solutions in the case of ABFD are obtained via the Laplace transform and compared graphically. The influence of embedded parameters on the velocity field is sketched and discussed. A comparison of the Atangana–Baleanu fractional model with an ordinary model is made. It is observed that the velocity and temperature profile for the Atangana–Baleanu fractional model are less than that of the ordinary model. The Atangana–Baleanu fractional model reduced the velocity profile up to 45.76% and temperature profile up to 13.74% compared to an ordinary model.

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A Novel Algorithm for Studying the Effects of Squeezing Flow of a Casson Fluid between Parallel Plates on Magnetic Field

Journal of Applied Mathematics ◽

10.1155/2019/3679373 ◽

2019 ◽

Vol 2019 ◽

pp. 1-19

Author(s):

Abdul-Sattar J. A. Al-Saif ◽

Abeer Majeed Jasim

Keyword(s):

Numerical Range ◽

Flow Behavior ◽

Analytical Techniques ◽

Mhd Flow ◽

Convergent Series ◽

Casson Fluid ◽

Squeezing Flow ◽

Physical Parameters ◽

Parallel Plates ◽

Novel Algorithm

In this paper, the magneto hydrodynamic (MHD) squeezing flow of a non-Newtonian, namely, Casson, fluid between parallel plates is studied. The suitable one of similarity transformation conversion laws is proposed to obtain the governing MHD flow nonlinear ordinary differential equation. The resulting equation has been solved by a novel algorithm. Comparisons between the results of the novel algorithm technique and other analytical techniques and one numerical Range-Kutta fourth-order algorithm are provided. The results are found to be in excellent agreement. Also, a novel convergence proof of the proposed algorithm based on properties of convergent series is introduced. Flow behavior under the changing involved physical parameters such as squeeze number, Casson fluid parameter, and magnetic number is discussed and explained in detail with help of tables and graphs.

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

10.21203/rs.3.rs-701466/v1 ◽

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.

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