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

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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.

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Abbreviations

C :

nanoparticle volume fraction

C f :

skin-fraction coefficient

C w :

nanoparticle volume fraction at the wall

C ∞ :

ambient nanoparticle volume fraction

c p :

specific heat at constant pressure

D B :

Brownian diffusion coefficient

D T :

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

T w :

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

V 0 :

velocity of suction/injection

α :

thermal conductivity

β :

coefficient of thermal expansion

θ :

dimensionless temperature

ϕ :

dimensionless nanoparticle volume fraction

η :

similarity variable

μ :

dynamic viscosity

ρ f :

density of the base fluid

ρ p :

nanoparticle mass density

(ρc)f :

heat capacity of the base fluid

τ :

heat capacity ratio

ν :

kinematic viscosity

ψ :

stream function

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Authors and Affiliations

  1. Department of Mechanical Engineering, Sri Guru Institute of Technology, Coimbatore, 641110, India

    N. Anbuchezhian

  2. Department of Mechanical Engineering, Anna University, Chennai, 600025, India

    K. Srinivasan

  3. Department of Mechanical Engineering, R. M. K. Engineering College, Chennai, 601206, India

    K. Chandrasekaran

  4. Research Centre for Computational Mathematics, Faculty of Science, Technology and Human Development, Universiti Tun Hussein Onn Malaysia, Johor, 86400, Malaysia

    R. Kandasamy

Authors
  1. N. Anbuchezhian
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  2. K. Srinivasan
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  3. K. Chandrasekaran
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  4. R. Kandasamy
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Correspondence to R. Kandasamy.

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Anbuchezhian, N., Srinivasan, K., Chandrasekaran, K. et al. Thermophoresis and Brownian motion effects on boundary layer flow of nanofluid in presence of thermal stratification due to solar energy. Appl. Math. Mech.-Engl. Ed. 33, 765–780 (2012). https://doi.org/10.1007/s10483-012-1585-8

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  • DOI: https://doi.org/10.1007/s10483-012-1585-8

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