scholarly journals The Magneto-Natural Convection Flow of a Micropolar Hybrid Nanofluid Over a Vertical Plate Saturated in a Porous Medium

Fluids ◽  
2021 ◽  
Vol 6 (6) ◽  
pp. 202
Author(s):  
A. Mahdy ◽  
E. R. El-Zahar ◽  
A. M. Rashad ◽  
W. Saad ◽  
H. S. Al-Juaydi
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Non Linear ◽  
The Magnetic Field ◽  
Linear Odes

In this study, we investigate the convective flow of a micropolar hybrid nanofluid through a vertical radiating permeable plate in a saturated porous medium. The impact of the presence or absence of the internal heat generation (IHG) in the medium is examined as well as the impacts of the magnetic field and thermal radiation. We apply similarity transformations to the non-dimensionalized equations and render them as a system of non-linear ODEs (Ordinary Differential Equations) subject to appropriate boundary conditions. This system of non-linear ODEs is solved by an adaptive mesh transformation Chebyshev differential quadrature method. The influence of the governing parameters on the temperature, microrotation and velocity is examined. The skin friction coefficient and the Nusselt number are tabulated. We determine that the skin friction coefficient and heat transport rate increase with the increment in the magnetic field. Moreover, the increment in the micropolarity and nanoparticle volume fraction enhances the skin friction coefficient and the Nusselt number. We also conclude that the IHG term improved the flow of the hybrid nanofluid. Finally, our results indicate that employing a hybrid nanofluid increases the heat transfer compared with that in pure water and a nanofluid.

Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface

2019 ◽  
Vol 29 (9) ◽  
pp. 3110-3127 ◽  
Author(s):  
Iskandar Waini ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

PurposeThis paper aims to investigate the steady flow and heat transfer of a Cu-Al2O3/water hybrid nanofluid over a nonlinear permeable stretching/shrinking surface with radiation effects. The surface velocity condition is assumed to be of the power-law form with an exponent of 1/3. The governing equations of the problem are converted into a system of similarity equations by using a similarity transformation.Design/methodology/approachThe problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The results of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented through graphs and tables for several values of the parameters. The effects of these parameters on the flow and heat transfer characteristics are examined and discussed.FindingsResults found that dual solutions exist for a certain range of the stretching/shrinking and suction parameters. The increment of the skin friction coefficient and reduction of the local Nusselt number on the shrinking sheet is observed with the increasing of copper (Cu) nanoparticle volume fractions for the upper branch. The skin friction coefficient and the local Nusselt number increase when suction parameter is increased for the upper branch. Meanwhile, the temperature increases in the presence of the radiation parameter for both branches.Originality/valueThe problem of Cu-Al2O3/water hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface with radiation effects is the important originality of the present study where the dual solutions for the flow reversals are obtained.

On Two-Dimensional Laminar Hydromagnetic Fluid-Particle Flow Over a Surface in the Presence of a Gravity Field

2000 ◽  
Vol 123 (1) ◽  
pp. 43-49 ◽  
Author(s):  
Ali J. Chamkha
Keyword(s):  
Magnetic Field ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Analytical Solutions ◽  
Fluid Phase ◽  
Skin Friction Coefficient ◽  
Two Dimensional ◽  
Particle Phase ◽  
Phase Stresses ◽  
The Magnetic Field

A continuum two-phase fluid-particle model accounting for particle-phase stresses and a body force due to the presence of a magnetic field is developed and applied to the problem of two-dimensional laminar hydromagnetic flow of a particulate suspension over a horizontal surface in the presence of a gravity field. Analytical solutions for the velocity distributions and the skin-friction coefficients of both phases are reported. Two cases of wall hydrodynamic (velocity) conditions corresponding to stationary and oscillatory velocity distributions are considered. Numerical evaluations of the analytical solutions are performed and the results are reported graphically to elucidate special features of the solutions. The effects of the particle-phase stresses and the magnetic field are illustrated through representative results for the horizontal velocity profiles, fluid-phase displacement thickness, and the complete skin-friction coefficient for various combinations of the physical parameters. It is found that the presence of the magnetic field increases the fluid-phase skin-friction coefficient for various particulate volume fraction levels while the presence of the particle-phase viscous stresses reduces it for various particle-to-fluid density ratios.

Passive control of nanoparticle of micropolar fluid past a stretching sheet with nanoparticles, convective boundary condition and second-order slip

2016 ◽  
Vol 231 (4) ◽  
pp. 704-719 ◽  
Author(s):  
Wubshet Ibrahim
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Micropolar Fluid ◽  
Passive Control ◽  
Stretching Sheet ◽  
Skin Friction Coefficient ◽  
Second Order ◽  
Non Linear

This article deals with a second-order slip flow and magnetic field on boundary layer flow of micropolar fluid past a stretching sheet. Situation of nil normal flux of nanoparticles at the wall for the stretching flow is taken into account. By employing appropriate similarity transformation and non-dimensional variables, the governing non-linear boundary-value problems were reduced into coupled higher order non-linear ordinary differential equation. Then, numerical solution for velocity, angular velocity (microrotation), temperature, and concentration has been established. The equations were numerically solved using the function bvp4c from the matlab software for different values of governing parameters. Numerical results have been obtained and discussed for non-dimensional velocity, temperature, microrotation, the skin friction coefficient, and local Nusselt number using some fixed values of the governing parameters. The results indicate that the skin friction coefficient Cf increases as the values of slip parameter γ increase. However, the local Nusselt number − [Formula: see text] increases as thermophoresis parameter Nt, microrotation parameter β, and convective parameter Bi increase. The wall couple stress coefficient decreases as the values of governing parameters such as magnetic parameter M, material parameter β, and for both slip parameters γ and δ increase. A comparison with earlier investigations available in the literature has been done and an excellent agreement is achieved.

Heat Transfer Enhancement of Magneto-Micropolar Nanofluid Over a Wedge

2020 ◽  
Vol 9 (3) ◽  
pp. 168-176
Author(s):  
E. R. EL-Zahar ◽  
M. A. Mansour ◽  
A. M. Rashad ◽  
Z. M. A. Abdelrahman ◽  
A. M. A. EL-Hakiem
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Magnetic Force ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Alumina Nanoparticles ◽  
Similarity Transformations ◽  
Micropolar Nanofluid ◽  
Linear Odes

Current investigation characterizes the flow and heat transmission of magneto-micropolar nanofluid through a non-isothermal wedge. The base-fluid as water and micropolar nanofluid as Copper or Alumina-nanoparticles are considered. Applying the similarity transformations along with non-dimensional quantities the formulated equations of the investigation are transmuted into a system of non-linear ODEs with a collection of convenient boundary conditions. The fourth-order finite difference method (FFDM) is then applied to determine the solution of a collection of resultant equations. The outcomes obtained by FFDM have also compared with cited works. Illustrations describing influences of prominent parameters which provide physical interpretations of temperature, micro rotation and velocity fields are examined in detail with the help of graphical representations. Both the skin friction coefficient and Nusselt number are computed and exhibited through tabular forms. This investigation determined that the skin-friction coefficient and heat transport rate improved along with augmentation in the magnetic force. micropolar parameter and the nanoparticle volume fraction augmented the Both skin friction coefficient and Nusselt number.

Mixed convective non-linear radiative flow with TiO2-Cu-water hybrid nanomaterials and induced magnetic field

2019 ◽  
Vol 29 (8) ◽  
pp. 2754-2774 ◽  
Author(s):  
Sohail Ahmad Khan ◽  
Muhammad Ijaz Khan ◽  
Tasawar Hayat ◽  
Muhammad Faisal Javed ◽  
Ahmed Alsaedi
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Skin Friction ◽  
Volume Fraction ◽  
Hybrid Nanofluid ◽  
Induced Magnetic Field ◽  
Content Type ◽  
Non Linear ◽  
Physical Variables ◽  
The Impact

Purpose The purpose of this paper is to address the impact of induced magnetic field in mixed convective stagnation flow of TiO2-Cu-water hybrid nanofluid towards a stretchable sheet. Non-linear thermal radiation and heat source/sink are accounted. Flow of hybrid nanofluid is discussed. Non-linear partial differential expressions are converted to ordinary ones through appropriate transformations. Design/methodology/approach The obtained systems are solved for convergence solutions via homotopy analysis method. Graphical results are discussed for different physical variables on the velocity, induced magnetic field and temperature fields for both Cu water nanofluid and TiO2-Cu-water hybrid nanofluid. Finally, the effect of different physical variables on skin friction coefficient (Cfx) and Nusselt number Nux in the presence of water nanofluid and TiO2-Cu-water hybrid nanofluid are discussed. Findings Velocities and induced magnetic field are increasing functions of mixed convection parameter and nanoparticle volume fraction. Temperature rises for higher radiation parameter. Skin friction is greater in case of Cu-water nanoliquid, while Nusselt number is less for Cu-water nanofluid when they are compared with hybrid nanoliquid TiO2-Cu-water. Originality/value No such work is not yet present in the literature.

scholarly journals MHD Williamson Nanofluid Flow over a Stretching Sheet through a Porous Medium under Effects of Joule Heating, Nonlinear Thermal Radiation, Heat Generation/Absorption, and Chemical Reaction

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
J. Bouslimi ◽  
M. Omri ◽  
R. A. Mohamed ◽  
K. H. Mahmoud ◽  
S. M. Abo-Dahab ◽  
...  
Keyword(s):  
Porous Medium ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Heat Generation ◽  
Joule Heating ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Physical Parameters

In this article, the effect of electromagnetic force with the effect of thermal radiation on the Williamson nanofluid on a stretching surface through a porous medium was studied considering the effect of both heat generation/absorption and Joule heating. On the other hand, the effect of Brownian motion and thermophoresis coefficients was considered. The system of nonlinear partial differential equations governing the study of fluid flow has transformed into a system of ordinary differential equations using similarity transformations and nondimensional variables which were subsequently solved numerically by using the Rung-Kutta fourth-order method with shooting technique. Moreover, the effect of the resulting physical parameters on the distributions of velocity, temperature, and concentration of nanoparticles has been studied by using graphical forms with an interest in providing physical meanings to each parameter. Finally, special diagrams were made to explain the study of the effect of some physical parameters on the skin friction coefficient and the local Nusselt number; these results led to reinforcement in the values of the skin friction coefficient for the increased values of the magnetic field and the Darcy number while the effect on the local Nusselt number by thermal radiation as well as the heat generation/absorption coefficients became negative.

Nanofluid flow past an impulsively started vertical plate with variable surface temperature

2016 ◽  
Vol 26 (1) ◽  
pp. 328-347 ◽  
Author(s):  
Rajesh Vemula ◽  
A J Chamkha ◽  
Mallesh M. P.
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Vertical Plate ◽  
Aluminium Oxide ◽  
Skin Friction Coefficient ◽  
Viscous Drag ◽  
Content Type ◽  
Variable Surface ◽  
Variable Surface Temperature

Purpose – The purpose of this paper is to focus on the numerical modelling of transient natural convection flow of an incompressible viscous nanofluid past an impulsively started semi-infinite vertical plate with variable surface temperature. Design/methodology/approach – The problem is governed by the coupled non-linear partial differential equations with appropriate boundary conditions. A robust, well-tested, Crank-Nicolson type of implicit finite-difference method, which is unconditionally stable and convergent, is used to solve the governing non-linear set of partial differential equations. Findings – The local and average values of the skin-friction coefficient (viscous drag) and the average Nusselt number (the rate of heat transfer) decreased, while the local Nusselt number increased for all nanofluids, namely, aluminium oxide-water, copper-water, titanium oxide-water and silver-water with an increase in the temperature exponent m. Selecting aluminium oxide as the dispersing nanoparticles leads to the maximum average Nusselt number (the rate of heat transfer), while choosing silver as the dispersing nanoparticles leads to the minimum local Nusselt number compared to the other nanofluids for all values of the temperature exponent m. Also, choosing silver as the dispersing nanoparticles leads to the minimum skin-friction coefficient (viscous drag), while selecting aluminium oxide as the dispersing nanoparticles leads to the maximum skin-friction coefficient (viscous drag) for all values of the temperature exponent m. Research limitations/implications – The Brinkman model for dynamic viscosity and Maxwell-Garnett model for thermal conductivity are employed. The governing boundary layer equations are written according to The Tiwari-Das nanofluid model. A range of nanofluids containing nanoparticles of aluminium oxide, copper, titanium oxide and silver with nanoparticle volume fraction range less than or equal to 0.04 are considered. Practical implications – The present simulations are relevant to nanomaterials thermal flow processing in the chemical engineering and metallurgy industries. This study also provides an important benchmark for further simulations of nanofluid dynamic transport phenomena of relevance to materials processing, with alternative computational algorithms (e.g. finite element methods). Originality/value – This paper is relatively original and illustrates the influence of variable surface temperature on transient natural convection flow of a viscous incompressible nanofluid and heat transfer from an impulsively started semi-infinite vertical plate.

Analysis of Blasius Flow of Hybrid Nanofluids over a Convectively Heated Surface

2017 ◽  
Vol 377 ◽  
pp. 29-41 ◽  
Author(s):  
Abdulyaqin Taslimah Olatundun ◽  
Oluwole Daniel Makinde
Keyword(s):  
Nusselt Number ◽  
Skin Friction ◽  
Heated Surface ◽  
Fluid Velocity ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Blasius Flow ◽  
Shaped Nanoparticles ◽  
Hybrid Nanofluids ◽  
Model Equations

This article explores the problem of Blasius flow of water based hybrid nanofluid containing Al2O3 and Cu as nanoparticles over a convectively heated surface. Five different geometries of nanoparticles shape viz spherical, bricks, cylindrical, platelets and blades are considered in our analysis. The nonlinear model equations are obtained and tackled numerically using shooting method coupled with Runge-Kutta Fehlberg numerical scheme. The effects of nanoparticle shapes and other relevant thermophysical parameters on fluid velocity, temperature, skin friction and Nusselt number are discussed with the help of computational illustrations. The result for skin friction coefficient is compared with already existing results in the literature and excellent agreement was obtained. It is found that the heat transfer rate of hybrid nanofluid (Cu-Al2O3/Water) is higher than that of nanofluid (Al2O3/Water) and the Nusselt number increment for blade shaped nanoparticles is the highest as compared to that of platelet, cylindrical, brick and spherical shaped nanoparticles.

scholarly journals Effects of Slip and Heat Generation/Absorption on MHD Mixed Convection Flow of a Micropolar Fluid over a Heated Stretching Surface

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Mostafa Mahmoud ◽  
Shimaa Waheed
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Mixed Convection ◽  
Skin Friction ◽  
Heat Generation ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Local Skin ◽  
Local Skin Friction

A theoretical analysis is performed to study the flow and heat transfer characteristics of magnetohydrodynamic mixed convection flow of a micropolar fluid past a stretching surface with slip velocity at the surface and heat generation (absorption). The transformed equations solved numerically using the Chebyshev spectral method. Numerical results for the velocity, the angular velocity, and the temperature for various values of different parameters are illustrated graphically. Also, the effects of various parameters on the local skin-friction coefficient and the local Nusselt number are given in tabular form and discussed. The results show that the mixed convection parameter has the effect of enhancing both the velocity and the local Nusselt number and suppressing both the local skin-friction coefficient and the temperature. It is found that local skin-friction coefficient increases while the local Nusselt number decreases as the magnetic parameter increases. The results show also that increasing the heat generation parameter leads to a rise in both the velocity and the temperature and a fall in the local skin-friction coefficient and the local Nusselt number. Furthermore, it is shown that the local skin-friction coefficient and the local Nusselt number decrease when the slip parameter increases.

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