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Applied Mathematics and Mechanics

, Volume 33, Issue 6, pp 765–780 | Cite as

Thermophoresis and Brownian motion effects on boundary layer flow of nanofluid in presence of thermal stratification due to solar energy

  • N. Anbuchezhian
  • K. Srinivasan
  • K. Chandrasekaran
  • R. KandasamyEmail author
Article

Abstract

The problem of laminar fluid flow, which results from the stretching of a vertical surface with variable stream conditions in a nanofluid due to solar energy, is investigated numerically. The model used for the nanofluid incorporates the effects of the Brownian motion and thermophoresis in the presence of thermal stratification. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations, namely, the scaling group of transformations. An exact solution is obtained for the translation symmetrys, and the numerical solutions are obtained for the scaling symmetry. This solution depends on the Lewis number, the Brownian motion parameter, the thermal stratification parameter, and the thermophoretic parameter. The conclusion is drawn that the flow field, the temperature, and the nanoparticle volume fraction profiles are significantly influenced by these parameters. Nanofluids have been shown to increase the thermal conductivity and convective heat transfer performance of base liquids. Nanoparticles in the base fluids also offer the potential in improving the radiative properties of the liquids, leading to an increase in the efficiency of direct absorption solar collectors.

Key words

solar radiation Brownian motion nanofluid thermophoresis thermal stratification 

Nomenclature

C

nanoparticle volume fraction

Cf

skin-fraction coefficient

Cw

nanoparticle volume fraction at the wall

C

ambient nanoparticle volume fraction

cp

specific heat at constant pressure

DB

Brownian diffusion coefficient

DT

thermophoretic diffusion coefficient

f

dimensionless stream function

g

acceleration due to gravity

k

thermal conductive

Le

Lewis number

M

magnetic parameter

Nb

Brownian motion parameter

n

thermal stratification parameter

Nt

thermophoresis parameter

Nr

buoyancy ratio

Pr

Prandtl number

P

pressure

Ra

local Rayleigh number

S

suction/injection parameter

T

temperature of the fluid

Tw

temperature at the wall

T

ambient temperature

\(\bar v\)

velocity vector

u, υ

velocity components along the x- and y-axes

U(x)

uniform velocity of the free stream flow

V0

velocity of suction/injection

Greek symbols

α

thermal conductivity

β

coefficient of thermal expansion

θ

dimensionless temperature

ϕ

dimensionless nanoparticle volume fraction

η

similarity variable

μ

dynamic viscosity

ρf

density of the base fluid

ρp

nanoparticle mass density

(ρc)f

heat capacity of the base fluid

τ

heat capacity ratio

ν

kinematic viscosity

ψ

stream function

Chinese Library Classification

O357.1 

2010 Mathematics Subject Classification

75F15 73D50 

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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • N. Anbuchezhian
    • 1
  • K. Srinivasan
    • 2
  • K. Chandrasekaran
    • 3
  • R. Kandasamy
    • 4
    Email author
  1. 1.Department of Mechanical EngineeringSri Guru Institute of TechnologyCoimbatoreIndia
  2. 2.Department of Mechanical EngineeringAnna UniversityChennaiIndia
  3. 3.Department of Mechanical EngineeringR. M. K. Engineering CollegeChennaiIndia
  4. 4.Research Centre for Computational Mathematics, Faculty of Science, Technology and Human DevelopmentUniversiti Tun Hussein Onn MalaysiaJohorMalaysia

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