scholarly journals Series Solutions of Boundary Layer Flow of a Micropolar Fluid Near the Stagnation Point Towards a Shrinking Sheet

2009 ◽  
Vol 64 (9-10) ◽  
pp. 575-582 ◽  
Author(s):  
Sohail Nadeem ◽  
Saeid Abbasbandy ◽  
Majid Hussain
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Micropolar Fluid ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Local Skin ◽  
Similarity Transformations ◽  
Homotopy Analysis ◽  
Local Skin Friction ◽  
Layer Flow

An analysis has been carried out to obtain the series solution of boundary layer flow of a micropolar fluid towards a shrinking sheet. The governing equations of micropolar fluid are simplified using suitable similarity transformations and then solved by homotopy analysis method (HAM). The convergence of the HAM solutions has been obtained by using homotopy-pade approximation. The effects of various parameters such as porosity parameter R, the ratio λ and the microinertia K on the velocity and microinertia profiles as well as local skin friction coefficient are presented graphically and in tabulated form.

scholarly journals Inclusion of Viscous Dissipation on the Boundary Layer Flow of Cu-TiO2 Hybrid Nanofluid over Stretching/Shrinking Sheet

2021 ◽  
Vol 88 (2) ◽  
pp. 64-79
Author(s):  
Yap Bing Kho ◽  
Rahimah Jusoh ◽  
Mohd Zuki Salleh ◽  
Muhammad Khairul Anuar Mohamed ◽  
Zulkhibri Ismail ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Boundary Layer Flow ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Layer Flow

The effects of viscous dissipation on the boundary layer flow of hybrid nanofluids have been investigated. This study presents the mathematical modelling of steady two dimensional boundary layer flow of Cu-TiO2 hybrid nanofluid. In this research, the surface of the model is stretched and shrunk at the specific values of stretching/shrinking parameter. The governing partial differential equations of the hybrid nanofluid are reduced to the ordinary differential equations with the employment of the appropriate similarity transformations. Then, Matlab software is used to generate the numerical and graphical results by implementing the bvp4c function. Subsequently, dual solutions are acquired through the exact guessing values. It is observed that the second solution adhere to less stableness than first solution after performing the stability analysis test. The existence of viscous dissipation in this model is dramatically brought down the rate of heat transfer. Besides, the effects of the suction and nanoparticles concentration also have been highlighted. An increment in the suction parameter enhances the magnitude of the reduced skin friction coefficient while the augmentation of concentration of copper and titanium oxide nanoparticles show different modes.

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

Boundary-layer flow of a micropolar fluid on a continuous flatplate moving in a parallel stream with uniform surface heat flux

2007 ◽  
Vol 85 (8) ◽  
pp. 869-878 ◽  
Author(s):  
A Ishak ◽  
R Nazar ◽  
I Pop
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Boundary Layer Flow ◽  
Surface Heat Flux ◽  
Micropolar Fluid ◽  
Free Stream ◽  
Velocity Ratio ◽  
Skin Friction Coefficient ◽  
Surface Heat ◽  
Layer Flow

The laminar boundary-layer flow of a micropolar fluid on a fixed or continuously moving flat plate with uniform surface heat flux is investigated. The plate is assumed to move in the same oropposite direction to the free stream. The resulting system of nonlinear ordinary differential equations is solved numerically using the Keller-box method. Numerical results are obtained for the skin-friction coefficient and the local Nusselt number as well as the velocity, microrotation, and temperature profiles for some values of the governing parameters, namely, the velocity ratio parameter, material parameter, and Prandtl number. The results indicate that dual solutions exist when the plate and the free stream move in the opposite directions.PACS No.: 47.15.Cb

scholarly journals Heat Transfer in Hydromagnetic Flow over an Unsteady Stretching Permeable Sheet

2019 ◽  
Vol 4 (4) ◽  
pp. 1018-1030
Author(s):  
Susheela Chaudhary ◽  
Santosh Chaudhary ◽  
Sawai Singh
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Research Work ◽  
Magnetic Field Effect ◽  
Skin Friction Coefficient ◽  
Local Skin ◽  
Layer Flow ◽  
Fourth Order Method

Unsteady laminar boundary layer flow of viscous incompressible electrically conducting fluid along a continuous stretched permeable surface with the magnetic field effect is investigated. The defining characteristics of unsteady laminar boundary layer flow are governed a more than one independent variables, stretching velocity and surface temperature of the field. Governing equations are obtained for influencing parameters and transformed into ordinary differential equations by taking convenient similarity variables. Runge-Kutta fourth order method in corporation by the shooting technique is introduced to carry out numerical computations of the investigation. Velocity and temperature profiles are computed and represented graphically for the influences of suction/injection parameter, unsteadiness parameter, magnetic parameter and Prandtl number, while numerical solutions of local skin friction coefficient and local Nusselt number are discussed through tables. For non-magnetic condition, results are found in concordance with earlier research work.

scholarly journals A boundary layer flow analysis of a magnetohydrodynamic fluid over a shrinking sheet

2019 ◽  
Vol 11 (3) ◽  
pp. 168781401983506 ◽  
Author(s):  
Cheng-Hsing Hsu ◽  
Te-Hui Tsai ◽  
Ching-Chuan Chang ◽  
Wen-Han Huang
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Flow Analysis ◽  
Shear Thickening ◽  
Transformation Method ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Layer Flow

A steady-state boundary layer flow analysis of a non-Newtonian magnetic fluid over a shrinking sheet was studied. The boundary layer thickness and the velocity distribution in the layer were studied under the conditions of a uniform magnetic field normal to the shrinking sheet and/or a vertical uniform mass suction across the sheet. The similarity transformation method was used to transform the governing partial differential equations to ordinary differential equations. The shooting method with Newton’s algorithm and Runge–Kutta integration method were used to obtain the solutions of the equations. The results showed that the variation of the flow velocity profiles in the boundary layer was significant, the thickness of the boundary layer was thinner, and the skin friction coefficient was bigger for either shear thinning or shear thickening magnetic fluids under the conditions of a stronger magnetic field or a larger mass suction effect.

Mixed Convection in Viscoelastic Boundary Layer Flow and Heat Transfer Over a Stretching Sheet

2014 ◽  
Vol 6 (3) ◽  
pp. 359-375 ◽  
Author(s):  
Antonio Mastroberardino
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Boundary Layer Flow ◽  
Skin Friction Coefficient ◽  
Convection Boundary Layer ◽  
Electrically Conducting ◽  
Homotopy Analysis ◽  
Layer Flow

AbstractAn investigation is carried out on mixed convection boundary layer flow of an incompressible and electrically conducting viscoelastic fluid over a linearly stretching surface in which the heat transfer includes the effects of viscous dissipation, elastic deformation, thermal radiation, and non-uniform heat source/sink for two general types of non-isothermal boundary conditions. The governing partial differential equations for the fluid flow and temperature are reduced to a nonlinear system of ordinary differential equations which are solved analytically using the homotopy analysis method (HAM). Graphical and numerical demonstrations of the convergence of the HAM solutions are provided, and the effects of various parameters on the skin friction coefficient and wall heat transfer are tabulated. In addition it is demonstrated that previously reported solutions of the thermal energy equation given in [1] do not converge at the boundary, and therefore, the boundary derivatives reported are not correct.

Axisymmetric Stagnation-Point Flow of Nanofluid Over a Stretching Surface

2014 ◽  
Vol 6 (2) ◽  
pp. 220-232 ◽  
Author(s):  
M. Nawaz ◽  
T. Hayat
Keyword(s):  
Nusselt Number ◽  
Sherwood Number ◽  
Base Fluid ◽  
Convective Heat Transfer Coefficient ◽  
Skin Friction Coefficient ◽  
Local Skin ◽  
Homotopy Analysis ◽  
Local Skin Friction ◽  
Layer Flow ◽  
Local Sherwood Number

AbstractThis paper investigates the laminar boundary layer flow of nanofluid induced by a radially stretching sheet. Nanofluid model exhibiting Brownian motion and thermophoresis is used. Series solutions for a reduced system of nonlinear ordinary differential equations are obtained by homotopy analysis method (HAM). Comparative study between the HAM solutions and previously published numerical results shows an excellent agreement. Velocity, temperature and mass fraction are displayed for various values of parameters. The local skin friction coefficient, the local Nusselt number and the local Sherwood number are computed. It is observed that the presence of nanoparticles enhances the thermal conductivity of base fluid. It is found that the convective heat transfer coefficient (Nusselt number) is decreased with an increase in concentration of nanoparticles whereas Sherwood number increases when concentration of nanoparticles in the base fluid is increased.

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