scholarly journals Numerical method approach for magnetohydrodynamic radiative ferrofluid flows over a solid sphere surface

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 379-385
Author(s):  
Yasin Mat ◽  
Muhammad Mohamed ◽  
Zulkhibri Ismail ◽  
Basuki Widodo ◽  
Mohd Salleh
Keyword(s):  
Boundary Layer ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Solid Sphere ◽  
Skin Friction Coefficient ◽  
Fluid Temperature ◽  
Sphere Surface ◽  
Boundary Layer Equations ◽  
Keller Box Method ◽  
Layer Flow

In this paper, the theoretical study on the laminar boundary-layer flow of ferrofluid with influences of magnetic field and thermal radiation is investigated. The viscosity of ferrofluid flow over a solid sphere surface is examined theoretically for magnetite volume fraction by using boundary-layer equations. The governing equations are derived by applied the non-similarity transformation then solved numerically by utilizing the Keller-box method. It is found that the increments in ferro-particles (Fe3O4) volume fraction declines the fluid velocity but elevates the fluid temperature at a sphere surface. Consequently, the results showed viscosity is enhanced with the increase of the ferroparticles volume fraction and acts as a pivotal role in the distribution of velocity, temperature, reduced skin friction coefficient, and reduced Nusselt number of ferrofluid.

NATURAL CONVECTION BOUNDARY LAYER FLOW ALONG A SPHERE EMBEDDED IN A POROUS MEDIUM FILLED WITH A NANOFLUID

2014 ◽  
Vol 44 (2) ◽  
pp. 149-157
Author(s):  
A. M. RASHAD
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Boundary Layer Flow ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Convection Boundary Layer ◽  
Physical Parameters ◽  
Extended Model ◽  
Local Skin ◽  
Layer Flow

 A boundary-layer analysis is presented for the natural convec tion boundary layer flow about a sphere embedded in a porous medium filled with a nanofluid using Brinkman-ForchheimerDarcy extended model. The model used for the nanofluid incorporates the ef fects of Brownian motion and thermophoresis. The governing partial differential equa tions are transformed into a set of nonsimilar equations and solved numerically by an efficient implicit, iterative, finite-difference method. Comparisons with previously published work are performed and excellent agreement is obtained. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity, temperature, and nanoparticles volume fraction profiles as well as the local skin-friction coefficient, local Nusselt and Sherwood numbers is illustrated graphically to show interesting features of the solutions.

Boundary-layer flow of a micropolar fluid on a continuous moving or fixed surface

2006 ◽  
Vol 84 (5) ◽  
pp. 399-410 ◽  
Author(s):  
Anuar Ishak ◽  
Roslinda Nazar ◽  
Ioan Pop
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Boundary Layer Flow ◽  
Micropolar Fluid ◽  
Plane Surface ◽  
Velocity Ratio ◽  
Skin Friction Coefficient ◽  
Keller Box Method ◽  
Moving Plane ◽  
Layer Flow

The present paper deals with the analysis of boundary-layer flow of a micropolar fluid on a fixed or continuous moving plane surface. Both parallel and reverse moving surfaces to the free stream are considered. The resulting system of nonlinear ordinary differential equations is solved numerically using the Keller-box method. Numerical results are obtained for skin friction coefficient, local Nusselt number, velocity, angular velocity, and temperature profiles. The results indicate that the effect of the material parameter on skin friction and heat transfer depends on the velocity ratio of the plate and the fluid.PACS No.: 47.15.Cb

Mixed Convection Boundary Layer Flow of Viscoelastic Fluids Past a Sphere

2013 ◽  
Vol 336 ◽  
pp. 57-63 ◽  
Author(s):  
Anisah Dasman ◽  
Abdul Rahman Mohd Kasim ◽  
Nurul Farahain Mohammad ◽  
Aurangzaib Mangi ◽  
Sharidan Shafie
Keyword(s):  
Boundary Layer ◽  
Mixed Convection ◽  
Viscoelastic Fluid ◽  
Classical Problem ◽  
Convection Boundary Layer ◽  
Boundary Layer Equations ◽  
Keller Box Method ◽  
Convection Boundary ◽  
Layer Flow ◽  
Newtonian Viscous Fluid

The mixed convection boundary layer of a viscoelastic fluid past a sphere with constant temperature is discussed. The boundary layer equations are an order higher than those for the Newtonian (viscous) fluid and the adherence boundary conditions are insufficient to determine the solution of these equations completely. The governing non-similar partial differential equations are first transformed into dimensionless forms and then solved numerically using the Keller-box method by augmenting an extra boundary condition at infinity. Numerical results are presented for different values of the viscoelastic and mixed convection parameters K and , respectively. It is found that for cases of cooling sphere and heating sphere, the boundary layer separates from the sphere. To the best of our knowledge, this important classical problem has not been studied before for the case of a viscoelastic fluid. Thus, the results are original and new for this type of fluids.

scholarly journals Melting Heat Transfer and MHD Boundary Layer Flow of Eyring-Powell Nanofluid Over a Nonlinear Stretching Sheet with Slip

2019 ◽  
Vol 24 (1) ◽  
pp. 161-178 ◽  
Author(s):  
N. Vijaya Bhaskar Reddy ◽  
N. Kishan ◽  
C. Srinivas Reddy
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Local Skin ◽  
Layer Flow ◽  
Nonlinear Stretching ◽  
The Impact

Abstract The steady laminar incompressible viscous magneto hydrodynamic boundary layer flow of an Eyring- Powell fluid over a nonlinear stretching flat surface in a nanofluid with slip condition and heat transfer through melting effect has been investigated numerically. The resulting nonlinear governing partial differential equations with associated boundary conditions of the problem have been formulated and transformed into a non-similar form. The resultant equations are then solved numerically using the Runge-Kutta fourth order method along with the shooting technique. The physical significance of different parameters on the velocity, temperature and nanoparticle volume fraction profiles is discussed through graphical illustrations. The impact of physical parameters on the local skin friction coefficient and rate of heat transfer is shown in tabulated form.

scholarly journals MHD Mixed Convective Boundary Layer Flow of a Nanofluid through a Porous Medium due to an Exponentially Stretching Sheet

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
M. Ferdows ◽  
Md. Shakhaoath Khan ◽  
Md. Mahmud Alam ◽  
Shuyu Sun
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Boundary Layer Equations ◽  
Exponentially Stretching Sheet ◽  
Layer Flow ◽  
Exponentially Stretching

Magnetohydrodynamic (MHD) boundary layer flow of a nanofluid over an exponentially stretching sheet was studied. The governing boundary layer equations are reduced into ordinary differential equations by a similarity transformation. The transformed equations are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six-order iteration schemes. The effects of the governing parameters on the flow field and heat transfer characteristics were obtained and discussed. The numerical solutions for the wall skin friction coefficient, the heat and mass transfer coefficient, and the velocity, temperature, and concentration profiles are computed, analyzed, and discussed graphically. Comparison with previously published work is performed and excellent agreement is observed.

scholarly journals Separation time analysis of transient magnetohydrodynamic mixed convection flow of nanofluid at lower stagnation point past a sphere

2017 ◽  
Vol 13 (3) ◽  
Author(s):  
Mohamad Alif Ismail ◽  
Nurul Farahain Mohammad ◽  
Sharidan Shafie
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Magnetic Particles ◽  
Volume Fraction ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Boundary Layer Equations ◽  
Keller Box Method

In this paper, the unsteady magnetohydrodynamics (MHD) mixed convection flow of nanofluid at lower stagnation point past a sphere is studied. Nanoparticles Cu and TiO2 with water as a base fluid are considered. The separation times of the flow as the boundary layer start to separate at the surface of the sphere are given attention. The governing boundary layer equations in the form of partial differential equations are transformed into nonlinear coupled ordinary differential equations and solved numerically using an implicit finite-difference scheme known as Keller-box method. Results of the separation times of boundary layer flow for viscous and nanofluid influenced by magnetic parameter and volume fraction are shown in tabular form and analysed. This study concluded that the separation times can be delayed by added more magnetic particles and small amount the volume fraction.

Boundary Layer Flow About and Inside a Liquid Sphere

1997 ◽  
Vol 119 (1) ◽  
pp. 42-49 ◽  
Author(s):  
Maged A. I. El-Shaarawi ◽  
Abdulghani Al-Farayedhi ◽  
Mohamed A. Antar
Keyword(s):  
Boundary Layer ◽  
Solid Sphere ◽  
External Flow ◽  
Droplet Surface ◽  
Laminar Flows ◽  
Surface Velocity ◽  
Immiscible Fluid ◽  
Interface Shear ◽  
Boundary Layer Equations ◽  
Layer Flow

A finite-difference scheme has been developed to solve the boundary-layer equations governing laminar flows around and inside a spherical fluid droplet moving steadily in another immiscible fluid. Using this scheme, results not available in the literature have been obtained for circulating droplets at intermediate and high interior-to-exterior viscosity ratios (μ*) and large values of the external flow Reynolds number (Re). Detailed results over the range 1.01 ≤ μ* ≤ ∞ (solid sphere) and 100 ≤ Re ≤ 10000 are presented for the velocity profiles outside and inside the droplet, the interface shear stress, the external flow separation angle, the droplet surface velocity and the drag coefficient.

An Analytical Solution for Boundary Layer Flows Over a Moving-Flat Porous Plate With Viscous Dissipation

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
C. J. Toki
Keyword(s):  
Boundary Layer ◽  
Viscous Dissipation ◽  
Porous Plate ◽  
Fluid Temperature ◽  
Boundary Layer Flows ◽  
Boundary Layer Equations ◽  
Dissipation Parameter ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Layer Flow

The problem of boundary layer flow of an incompressible fluid over a moving porous flat plate is investigated, by taking into account the heat due to viscous dissipation. The governing boundary layer equations of this flow field were solved analytically using the Laplace transform technique. These new exact analytical solutions for velocity and temperature were obtained with arbitrary Prandtl number and dissipation parameter (or Eckert number Ec). The corresponding solutions for nonporous plate are discussed. Applying numerical values into the analytical expressions of the temperature and heat transfer coefficient, we also discussed the effects of the dissipation parameter in the cases of water, gas, and ammonia flow. We can finally deduce that the fluid temperature of the present problem will increase in the case of viscous dissipation with positive Ec, but this temperature will decrease with negative Ec.

scholarly journals Heat and Mass Transfer in the Boundary Layer of Unsteady Viscous Nanofluid along a Vertical Stretching Sheet

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
Eshetu Haile ◽  
B. Shankar
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Stretching Sheet ◽  
Skin Friction Coefficient ◽  
Similarity Transformations ◽  
Keller Box Method ◽  
Layer Flow

Heat and mass transfer in the boundary-layer flow of unsteady viscous nanofluid along a vertical stretching sheet in the presence of magnetic field, thermal radiation, heat generation, and chemical reaction are presented in this paper. The sheet is situated in the xz-plane and y is normal to the surface directing towards the positive y-axis. The sheet is continuously stretching in the positive x-axis and the external magnetic field is applied to the system parallel to the positive y-axis. With the help of similarity transformations, the partial differential equations are transformed into a couple of nonlinear ordinary differential equations. The new problem is then solved numerically by a finite-difference scheme known as the Keller-box method. Effects of the necessary parameters in the flow field are explicitly studied and briefly explained graphically and in tabular form. For the selected values of the pertinent parameters appearing in the governing equations, numerical results of velocity, temperature, concentration, skin friction coefficient, Nusselt number, and Sherwood number are obtained. The results are compared to the works of others (from previously published journals) and they are found in excellent agreement.

scholarly journals Boundary-Layer Flow and Heat Transfer of Nanofluids over a Permeable Moving Surface in the Presence of a Coflowing Fluid

2014 ◽  
Vol 6 ◽  
pp. 521236 ◽  
Author(s):  
Amin Noor ◽  
Roslinda Nazar ◽  
Khamisah Jafar ◽  
Ioan Pop
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Free Stream ◽  
Volume Fraction ◽  
Lewis Number ◽  
Skin Friction Coefficient ◽  
Numerical Results ◽  
Nanoparticle Volume Fraction ◽  
Flow And Heat Transfer ◽  
Layer Flow

The steady boundary-layer flow of a nanofluid past a permeable moving flat plate in the presence of a coflowing fluid is theoretically investigated. The plate is assumed to move in the same or opposite direction of the free stream. The governing partial differential equations are first transformed into ordinary differential (similarity) equations before they are solved numerically using a finite-difference scheme along with a shooting method. Numerical results are obtained for the skin-friction coefficient, the local Nusselt number, and the local Sherwood number as well as the velocity, temperature, and nanoparticle volume fraction profiles for some values of the governing parameters, namely, the plate velocity parameter, the Prandtl number, the Lewis number, the Brownian motion parameter, the thermophoresis parameter, and the nanoparticle volume fraction parameter. The numerical results indicate that dual solutions exist when the plate and the free stream move in the opposite directions.

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