scholarly journals Scaling Group Transformation for MHD Boundary Layer Slip Flow of a Nanofluid over a Convectively Heated Stretching Sheet with Heat Generation

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Md. Jashim Uddin ◽  
W. A. Khan ◽  
A. I. Md. Ismail
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Brownian Motion ◽  
Heat Generation ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Slip Flow ◽  
Nanoparticle Volume Fraction ◽  
Special Cases ◽  
Mhd Boundary Layer

Steady viscous incompressible MHD laminar boundary layer slip flow of an electrically conducting nanofluid over a convectively heated permeable moving linearly stretching sheet has been investigated numerically. The effects of Brownian motion, thermophoresis, magnetic field, and heat generation/absorption are included in the nanofluid model. The similarity transformations for the governing equations are developed. The effects of the pertinent parameters, Lewis number, magnetic field, Brownian motion, heat generation, thermophoretic, momentum slip and Biot number on the flow field, temperature, skin friction factor, heat transfer rate, and nanoparticle, volume fraction rate are displayed in both graphical and tabular forms. Comparisons of analytical (for special cases) and numerical solutions with the existing results in the literature are made and is found a close agreement, that supports the validity of the present analysis and the accuracy of our numerical computations. Results for the reduced Nusselt and Sherwood numbers are provided in tabular and graphical forms for various values of the flow controlling parameters which govern the momentum, energy, and the nanoparticle volume fraction transport in the MHD boundary layer.

scholarly journals Magnetohydrodynamic Boundary Layer Flow of Nanofluid over an Exponentially Stretching Permeable Sheet

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Krishnendu Bhattacharyya ◽  
G. C. Layek
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Brownian Motion ◽  
Volume Fraction ◽  
Lewis Number ◽  
Nanoparticle Volume Fraction ◽  
Layer Flow ◽  
Wall Mass

A mathematical model of the steady boundary layer flow of nanofluid due to an exponentially permeable stretching sheet with external magnetic field is presented. In the model, the effects of Brownian motion and thermophoresis on heat transfer and nanoparticle volume friction are considered. Using shooting technique with fourth-order Runge-Kutta method the transformed equations are solved. The study reveals that the governing parameters, namely, the magnetic parameter, the wall mass transfer parameter, the Prandtl number, the Lewis number, Brownian motion parameter, and thermophoresis parameter, have major effects on the flow field, the heat transfer, and the nanoparticle volume fraction. The magnetic field makes enhancement in temperature and nanoparticle volume fraction, whereas the wall mass transfer through the porous sheet causes reduction of both. For the Brownian motion, the temperature increases and the nanoparticle volume fraction decreases. Heat transfer rate becomes low with increase of Lewis number. For thermophoresis effect, the thermal boundary layer thickness becomes larger.

MHD Boundary Layer Slip Flow and Heat Transfer of Nanofluid Past a Vertical Stretching Sheet with Non-Uniform Heat Generation/Absorption

2014 ◽  
Vol 13 (03) ◽  
pp. 1450019 ◽  
Author(s):  
S. Das ◽  
R. N. Jana ◽  
O. D. Makinde
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Heat Generation ◽  
Stretching Sheet ◽  
Fluid Velocity ◽  
Slip Flow ◽  
Uniform Heat ◽  
Mhd Boundary Layer ◽  
Non Linear

An investigation of the magnetohydrodynamics (MHD) boundary layer slip flow over a vertical stretching sheet in nanofluid with non-uniform heat generation/absorbtion in the presence of a uniform transverse magnetic field has been carried out. The governing non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations using similarity transformations and then solved numerically using the Runge–Kutta fourth order method with shooting technique. Numerical results are obtained for the fluid velocity, temperature as well as the shear stress and the rate of heat transfer at the surface of the sheet. The results show that there are significant effects of various pertinent parameters on velocity and temperature profiles.

scholarly journals Influence of Variable Thermal Conductivity on MHD Boundary Layer Slip Flow of Ethylene-Glycol Based Cu Nanofluids over a Stretching Sheet with Convective Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
N. Bhaskar Reddy ◽  
T. Poornima ◽  
P. Sreenivasulu
Keyword(s):  
Thermal Conductivity ◽  
Boundary Layer ◽  
Boundary Condition ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Slip Flow ◽  
Velocity Slip ◽  
Convective Boundary Condition ◽  
Variable Thermal Conductivity ◽  
Convective Boundary

An analysis is carried out to investigate the influence of variable thermal conductivity and partial velocity slip on hydromagnetic two-dimensional boundary layer flow of a nanofluid with Cu nanoparticles over a stretching sheet with convective boundary condition. Using similarity transformation, the governing boundary layer equations along with the appropriate boundary conditions are transformed to a set of ordinary differential equations. Employing Runge-kutta fourth-order method along with shooting technique, the resultant system of equations is solved. The influence of various pertinent parameters such as nanofluid volume fraction parameter, the magnetic parameter, radiation parameter, thermal conductivity parameter, velocity slip parameter, Biot number, and suction or injection parameter on the velocity of the flow field and heat transfer characteristics is computed numerically and illustrated graphically. The present results are compared with the existing results for the case of regular fluid and found an excellent agreement.

THEMODIFFUSION EFFECTS ON MHD BOUNDARY LAYER SLIP FLOW OF NANOFLUID OVER A NONLINEAR STRETCHING SHEET THROUGH A POROUS MEDIUM

2017 ◽  
Vol 20 (11) ◽  
pp. 961-970
Author(s):  
V. Nagendramma ◽  
R.V.M.S.S. Kiran Kumar ◽  
P. Durga Prasad ◽  
A. Leelaratnam ◽  
S. Vijaya Kumar Varma
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Stretching Sheet ◽  
Slip Flow ◽  
Mhd Boundary Layer ◽  
Nonlinear Stretching

Transient two-dimensional natural convection flow of a nanofluid past an isothermal vertical plate using Buongiorno’s model

2017 ◽  
Vol 27 (1) ◽  
pp. 23-47 ◽  
Author(s):  
Marneni Narahari ◽  
Suresh Kumar Raju Soorapuraju ◽  
Rajashekhar Pendyala ◽  
Ioan Pop
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Brownian Motion ◽  
Natural Convection ◽  
Vertical Plate ◽  
Volume Fraction ◽  
Convection Flow ◽  
Nanoparticle Volume Fraction ◽  
Natural Convection Flow ◽  
Content Type

Purpose The purpose of this paper is to present a numerical investigation of the transient two-dimensional natural convective boundary-layer flow of a nanofluid past an isothermal vertical plate by incorporating the effects of Brownian motion and thermophoresis in the mathematical model. Design/methodology/approach The problem is formulated using the Oberbeck–Boussinesq and the standard boundary-layer approximations. The governing coupled non-linear partial differential equations for conservation of mass, momentum, thermal energy and nanoparticle volume fraction have been solved by using an efficient implicit finite-difference scheme of the Crank–Nicolson type, which is stable and convergent. Numerical computations are performed and the results for velocity, temperature and nanoparticle volume fraction are presented in graphs at different values of system parameters such as Brownian motion parameter, thermophoresis parameter, buoyancy ratio parameter, Prandtl number, Lewis number and dimensionless time. The results for local and average skin-friction and Nusselt number are also presented graphically and discussed thoroughly. Findings It is found that the velocity, temperature and nanoparticle volume fraction profiles enhance with respect to time and attain steady-state values as time progresses. The local Nusselt number is found to decrease with increasing thermophoresis parameter, while it increases slightly with increasing Brownian motion parameter. To validate the present numerical results, the steady-state local Nusselt number results for the limiting case of a regular fluid have been compared with the existing well-known results at different Prandtl numbers, and the results are found to be in an excellent agreement. Research limitations/implications The present analysis is limited to the transient laminar natural convection flow of a nanofluid past an isothermal semi-infinite vertical plate in the absence of viscous dissipation and thermal radiation. The unsteady natural convection flow of a nanofluid will be investigated for various physical conditions in a future work. Practical implications Unsteady flow devices offer potential performance improvements as compared with their steady-state counterparts, and the flow fields in the unsteady flow devices are typically transient in nature. The present study provides very useful information for heat transfer engineers to understand the heat transfer enhancement with the nanofluid flows. The present results have immediate relevance in cooling technologies. Originality/value The present research work is relatively original and illustrates the transient nature of the natural convective nanofluid boundary-layer flow in the presence of Brownian motion and thermophoresis.

Thermal radiation and chemical reaction effects on boundary layer slip flow and melting heat transfer of nanofluid induced by a nonlinear stretching sheet

2016 ◽  
Vol 5 (3) ◽  
Author(s):  
M.R. Krishnamurthy ◽  
B.J. Gireesha ◽  
B.C. Prasannakumara ◽  
Rama Subba Reddy Gorla
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Slip Flow ◽  
Melting Heat ◽  
Melting Heat Transfer ◽  
Nonlinear Stretching

AbstractA theoretically investigation has been performed to study the effects of thermal radiation and chemical reaction on MHD velocity slip boundary layer flow and melting heat transfer of nanofluid induced by a nonlinear stretching sheet. The Brownian motion and thermophoresis effects are incorporated in the present nanofluid model. A set of proper similarity variables is used to reduce the governing equations into a system of nonlinear ordinary differential equations. An efficient numerical method like Runge-Kutta-Fehlberg-45 order is used to solve the resultant equations for velocity, temperature and volume fraction of the nanoparticle. The effects of different flow parameters on flow fields are elucidated through graphs and tables. The present results have been compared with existing one for some limiting case and found excellent validation.

scholarly journals The effect of thermal radiation, heat generation and suction/injection on the mechanical properties of unsteady continuous moving cylinder in a nanofluid

2015 ◽  
Vol 19 (5) ◽  
pp. 1591-1601 ◽  
Author(s):  
El-Sayed El-Bashbeshy ◽  
Tarek Emam ◽  
Mohamed Abdel-Wahed
Keyword(s):  
Mechanical Properties ◽  
Boundary Layer ◽  
Thermal Radiation ◽  
Heat Generation ◽  
Volume Fraction ◽  
Nanoparticle Volume Fraction ◽  
Radiation Heat ◽  
Cooling Medium ◽  
Moving Cylinder ◽  
Radiation Heat Generation

The effect of thermal radiation, heat generation, suction/injection, nanoparticles type, and nanoparticle volume fraction on heat transfer characteristics and the mechanical properties of unsteady moving cylinder embedded into cooling medium consist of water with Cu; Ag or Al2O3 particles are studied. The governing time dependent boundary layer equations are transformed to ordinary differential equations containing unsteadiness parameter, thermal radiation parameter, heat source parameter, suction/injection parameter, curvature parameter, nanoparticle volume fraction and Prandlt number. These equations are solved numerically. The velocity and Temperature profiles within the boundary layer are plotted and discussed in details for various values of the different parameters. Also the effects of the cooling medium and the external thermal forces on the mechanical properties of the cylinder are investigated.

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