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

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.

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

Mathematical Problems in Engineering ◽

10.1155/2010/579162 ◽

2010 ◽

Vol 2010 ◽

pp. 1-20 ◽

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

Journal of Nanofluids ◽

10.1166/jon.2020.1744 ◽

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.

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Axisymmetric Stagnation-Point Flow of Nanofluid Over a Stretching Surface

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.2013.m93 ◽

2014 ◽

Vol 6 (2) ◽

pp. 220-232 ◽

Cited By ~ 12

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

Journal of Heat Transfer ◽

10.1115/1.4027909 ◽

2014 ◽

Vol 136 (10) ◽

Cited By ~ 9

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.

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Stagnation-Point Flow Toward a Stretching/Shrinking Sheet in a Nanofluid Containing Both Nanoparticles and Gyrotactic Microorganisms

Journal of Heat Transfer ◽

10.1115/1.4026011 ◽

2014 ◽

Vol 136 (4) ◽

Cited By ~ 30

Author(s):

Khairy Zaimi ◽

Anuar Ishak ◽

Ioan Pop

Keyword(s):

Nusselt Number ◽

Friction Coefficient ◽

Stagnation Point ◽

Sherwood Number ◽

Local Nusselt Number ◽

Local Density ◽

Skin Friction Coefficient ◽

Shrinking Sheet ◽

Gyrotactic Microorganisms ◽

Local Sherwood Number

The stagnation-point flow and heat transfer toward a stretching/shrinking sheet in a nanofluid containing gyrotactic microorganisms with suction are investigated. Using a similarity transformation, the nonlinear system of partial differential equations is converted into nonlinear ordinary differential equations. These resulting equations are solved numerically using a shooting method. The skin friction coefficient, local Nusselt number, local Sherwood number, and the local density of the motile microorganisms as well as the velocity, temperature, nanoparticle volume fraction and the density of motile microorganisms profiles are analyzed subject to several parameters of interest, namely suction parameter, thermophoresis parameter, Brownian motion parameter, Lewis number, Schmidt number, bioconvection Péclet number, and the stretching/shrinking parameter. It is found that dual solutions exist for a certain range of the stretching/shrinking parameter for both shrinking and stretching cases. The results indicate that the skin friction coefficient, local Nusselt number, local Sherwood number, and the local density of the motile microorganisms increase with suction effect. It is also observed that suction widens the range of the stretching/shrinking parameter for which the solution exists.

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Theoretical Investigation of an Unsteady MHD Free Convection Heat and Mass Transfer Flow of a Non-Newtonian Fluid Flow Past a Permeable Moving Vertical Plate in the Presence of Thermal Diffusion and Heat Sink

International Journal of Engineering Research in Africa ◽

10.4028/www.scientific.net/jera.16.90 ◽

2015 ◽

Vol 16 ◽

pp. 90-109 ◽

Cited By ~ 7

Author(s):

V. Ravikumar ◽

M.C. Raju ◽

G.S.S. Raju

Keyword(s):

Boundary Layer ◽

Nusselt Number ◽

Fluid Flow ◽

Friction Coefficient ◽

Skin Friction ◽

Sherwood Number ◽

Skin Friction Coefficient ◽

Stream Velocity ◽

Local Skin ◽

Soret Number

The problem of unsteady, two-dimensional, laminar, boundary-layer flow of a viscous, incompressible, electrically conducting and heat-absorbing Rivlin-Ericksen flow fluid along a semi-infinite vertical permeable moving plate has been investigated. A uniform transverse magnetic field is applied in the direction of the flow. The presence of thermal and concentration buoyancy effects is considered. The plate is assumed to move with a constant velocity in the direction of fluid flow while the free stream velocity is assumed to follow the exponentially increasing small perturbation law. Time-dependent wall suction is assumed to occur at the permeable surface. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. Numerical evaluation of the analytical results is performed and some graphical results for the velocity, temperature and concentration distributions within the boundary layer are presented. Skin-friction coefficient, Nusselt number and Sherwood number are also discussed with the help of the graphs. Local skin-friction coefficient increases with an increase in the permeability parameter, and Soret number whereas reverse effects is seen in the case of dimensionless viscoelasticity parameter of the Rivlin-Ericksen fluid. Nusselt number decreases in the presence of heat absorption. The presence of Soret number Sherwood number increases.

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

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-01-2019-0057 ◽

2019 ◽

Vol 29 (9) ◽

pp. 3110-3127 ◽

Cited By ~ 37

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.

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

Volume 1A: Symposia, Part 2 ◽

10.1115/ajkfluids2015-25474 ◽

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.

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Nanofluid Viscoelastic Fluid Flow with Thermophoresis

Nanoscience and Nanotechnology Letters ◽

10.1166/nnl.2019.3061 ◽

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.

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