Natural Convective Boundary Layer Flow of Nanofluids Above an Isothermal Horizontal Plate

2014 ◽  
Vol 136 (10) ◽  
Author(s):  
Kaustav Pradhan ◽  
Subho Samanta ◽  
Abhijit Guha
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Nanoparticle Volume Fraction ◽  
Convective Boundary ◽  
Local Skin ◽  
Local Skin Friction ◽  
Layer Flow

The natural convective boundary layer flow of a nanofluid over an isothermal horizontal plate is studied analytically. The model used for the nanofluid accounts for the effects of Brownian motion and thermophoresis. The analysis shows that the velocity, temperature, and nanoparticle volume fraction profiles in the respective boundary layers depend not only on the Prandtl number (Pr) and Lewis number (Le) but also on three additional dimensionless parameters: the Brownian motion parameter Nb, the buoyancy ratio parameter Nr and the thermophoresis parameter Nt. The velocity, temperature, and nanoparticle volume fraction profiles for the nanofluid are found to have a weak dependence on the values of Nb, Nr, and Nt. The effect of the above-mentioned parameters on the local skin-friction coefficient and Nusselt number has been studied extensively. It has been observed that as Nr increases, the local skin-friction coefficient decreases whereas local Nusselt number remains almost constant. As Nb or Nt increases, the local skin-friction coefficient increases whereas the local Nusselt number decreases.

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.

Non-similar characteristics of mixed convective slip flow over a wedge with temperature-dependent thermo-physical properties

2019 ◽  
Vol 33 (36) ◽  
pp. 1950455
Author(s):  
Nepal Chandra Roy ◽  
Sudharonjon Roy ◽  
Naved Azum ◽  
Anish Khan ◽  
Abdullah M. Asiri ◽  
...  
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Sherwood Number ◽  
Local Nusselt Number ◽  
Slip Flow ◽  
Skin Friction Coefficient ◽  
Local Skin ◽  
Local Skin Friction ◽  
Local Sherwood Number

We examined heat and mass transfer characteristics of mixed convective slip flow over a wedge taking into account the effect of variable transport properties. Unlike other studies, we have utilized non-similar transformation to get the non-similar features of the mixed convective slip flow. For comparison, stream function formulation is used to reduce the governing equation into a convenient form for short- and long-time regimes. We have determined the series solutions by adopting the perturbation techniques. The agreement between the numerical and series solutions is found to be excellent. Numerical solutions reveal that the slip parameters augment the momentum, thermal and concentration boundary layers. The local skin friction coefficient, the local Nusselt number and the local Sherwood number are found to decrease for higher value of slip parameters. For the increasing value of the variable viscosity parameter, the velocity is stronger, but the temperature and concentration lessen. Contrary to this, this parameter diminishes the local skin friction coefficient, local Nusselt number and local Sherwood number. Due to the increase of mass diffusivity parameter, the velocity and concentration significantly increase whereas the temperature remains almost unaffected. Moreover, the mass diffusivity variation parameter leads to an increase in the local skin friction coefficient and local Nusselt number, but it reduces the local Sherwood number.

Homotopy analysis method for unsteady mixed convective stagnation-point flow of a nanofluid using Tiwari-Das nanofluid model

2016 ◽  
Vol 26 (1) ◽  
pp. 40-62 ◽  
Author(s):  
Saeed Dinarvand ◽  
Reza Hosseini ◽  
Ioan Pop
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Mixed Convection ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Magnetic Parameter ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Nanoparticle Volume Fraction ◽  
Content Type

Purpose – The current study is mainly motivated by the need to the development of the transient MHD mixed convection stagnation-point flow and heat transfer of an electrically conducting nanofluid over a vertical permeable stretching/shrinking sheet by means of Tiwari-Das nanofluid model. The purpose of this paper is to investigate the effects of the parameters governing the flow i.e. the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter and the velocity ratio parameter on dimensionless velocity and temperature distributions, skin friction coefficient and local Nusselt number. Design/methodology/approach – The mathematical model has been formulated based on Tiwari-Das nanofluid model. Three different types of water-based nanofluid with copper, aluminum oxide (alumina) and titanium dioxide (titania) as nanoparticles are considered in this investigation. Using appropriate similarity variables, the governing equations are transformed into nonlinear ordinary differential equations in the dimensionless stream function, which is solved analytically by the well-know homotopy analysis method. The present simulations agree closely with the previous studies in the especial cases. Findings – The results show that by increasing the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter or reducing the velocity ratio parameter, the skin friction coefficient enhances. Furthermore, the local Nusselt number enhances with different rates by increasing the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter and the velocity ratio parameter. Besides, the skin friction coefficient and the local Nusselt number are highest for copper-water nanofluid compared to the alumina-water and titania-water nanofluids. Originality/value – Tiwari-Das nanofluid model has not been applied for the flow with these characteristics as mentioned in the paper. A comprehensive survey on boundary layer behavior has been presented. There are few studies regarding as analysis on thermal and hydrodynamics boundary layer. All plots presented in the paper are new and did not report in any other study. The effects of the parameters governing the flow on skin friction coefficient and local Nusselt number have been illustrated in the paper while there are some conflicts with previous published article that have been interpreted in details in the paper.

Measurement of the Wall Shear Stress With Sublayer Thin Plate of Thermochromic Liquid Crystal

2015 ◽  
Author(s):  
Takashi Kodama ◽  
Shinsuke Mochizuki
Keyword(s):  
Shear Stress ◽  
Liquid Crystal ◽  
Friction Coefficient ◽  
Wall Shear Stress ◽  
Skin Friction ◽  
Channel Flow ◽  
Skin Friction Coefficient ◽  
Local Skin ◽  
Local Skin Friction ◽  
Wall Shear

New optical method for measurement of the local wall shear stress has been developed by using thermo-chromic liquid crystal temperature measurement based on hue [1], [2] of the camera view. The flow field is the fully developed turbulent channel flow. Thin film made of thermo-chromic liquid crystal is placed on the wall. A rectangular shaped obstacle is glued on the film. The obstacle is within a region of buffer layer with height from the wall. Temperature of the film and the obstacle are slightly raised by a heater below the wall. The air flow makes non-uniform temperature distribution and non-uniform color distribution appears on the surface of the film. Relations between hue and local skin friction coefficient were examined in a turbulent air channel flow. It is indicated that a certain hue of a point is varying linearly against the corresponding local skin friction coefficient.

Nanofluid Viscoelastic Fluid Flow with Thermophoresis

2019 ◽  
Vol 11 (12) ◽  
pp. 1739-1749
Author(s):  
Gamal M. Abdel-Rahman ◽  
Faiza M. N. El-Fayez
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Numerical Solutions ◽  
Fluid Model ◽  
Skin Friction Coefficient ◽  
Jeffrey Fluid ◽  
Deposition Flux ◽  
Local Skin ◽  
Linear Ordinary Differential Equations

We in this study investigated Brownian motion and thermophoresis effects embedded in a porous medium flow with heat transfer generation and chemical reaction on a stretching sheet and Jeffrey fluid model for viscoelastic nanofluid under the effects of magnetic field and thermal radiation. The nanofluid was assumed incompressible and the flow was laminar, with base fluid containing the following types of nanoparticles: Copper (Cu), Aluminum (Al2O3) and Titanium Oxide (TiO2). The governing continuity, momentum, and energy equations for the nanofluid were reduced using similarity transformation and converted into a system of non-Linear ordinary differential equations which were solved numerically. Numerical solutions were also obtained for the velocity, temperature and nanoparticle concentration fields, as well as for skin friction coefficient and Nusselt number. Finally, numerical values for the physical quantities, such as local skin-friction coefficient, local Nusselt number, local Sherwood number and wall deposition flux are herein presented in tabular form.

Viscous Dissipation and Joule Heating Effects on MHD Bioconvection Flow of a Nanofluid Containing Gyrotactic Microorganisms Over a Vertical Isothermal Cone

2020 ◽  
Vol 9 (3) ◽  
pp. 242-255
Author(s):  
Hossam A. Nabwey ◽  
S. M. M. El-Kabeir ◽  
A. M. Rashad ◽  
M. M. M. Abdou
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Sherwood Number ◽  
Local Density ◽  
Skin Friction Coefficient ◽  
Local Skin ◽  
Gyrotactic Microorganisms ◽  
Local Skin Friction ◽  
Local Sherwood Number

The main objective of the present study is to explore the flow of a nanofluid containing gyrotactic microorganisms over a vertical isothermal cone surface in the presence of viscous dissipation and Joule heating. The combined effects of a transverse magnetic field and Navier slip in the flow are considered. Using appropriate transforms the set of partial differential equations governing the flow are converted to a set of ordinary differential equations. Influence of the parameters governing the flow is shown for velocity, temperature, concentration and motilemicroorganisms as well as local skin Friction coefficient, local Nusselt number, local Sherwood number and local density of the motile microorganisms number. An increasing in the value of Eckert number rises the velocity of the fluid and reduce the temperature, concentration and density of motile microorganisms profiles, while buoyancy ratio Nr and magnetic field parameters increase local skin friction coefficient, local Nusselt number, local Sherwood number and local density of the motile microorganisms number decrease as a result of the presence of Lorentz force which resist the motion of the flow. On the other hand, the motile microorganisms boundary layer thickness decreases with an increasing on the bioconvection Lewis number.

Nanofluid Viscoelastic Fluid Flow with Thermophoresis

2019 ◽  
Vol 11 (12) ◽  
pp. 1739-1749
Author(s):  
Gamal M. Abdel-Rahman ◽  
Faiza M. N. El-Fayez
Keyword(s):  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Numerical Solutions ◽  
Fluid Model ◽  
Skin Friction Coefficient ◽  
Jeffrey Fluid ◽  
Deposition Flux ◽  
Local Skin ◽  
Linear Ordinary Differential Equations

We in this study investigated Brownian motion and thermophoresis effects embedded in a porous medium flow with heat transfer generation and chemical reaction on a stretching sheet and Jeffrey fluid model for viscoelastic nanofluid under the effects of magnetic field and thermal radiation. The nanofluid was assumed incompressible and the flow was laminar, with base fluid containing the following types of nanoparticles: Copper (Cu), Aluminum (Al2O3) and Titanium Oxide (TiO2). The governing continuity, momentum, and energy equations for the nanofluid were reduced using similarity transformation and converted into a system of non-Linear ordinary differential equations which were solved numerically. Numerical solutions were also obtained for the velocity, temperature and nanoparticle concentration fields, as well as for skin friction coefficient and Nusselt number. Finally, numerical values for the physical quantities, such as local skin-friction coefficient, local Nusselt number, local Sherwood number and wall deposition flux are herein presented in tabular form.

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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