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Convective heat transfer in the vertical channel flow of a clear fluid adjacent to a nanofluid layer: a two-fluid model

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Abstract

A two-fluid vertical channel flow and convective heat transfer model in which one of the two fluids is a nanofluid demonstrates that the nanofluid can modify the fluid velocity at the interface of the two fluids, and can be used to reduce shear at both the surface of the clear fluid and the interface of the two fluids. Moreover, we find that the addition of a nanofluiod can favorably modify thermal properties of the fluid.

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Abbreviations

C p :

Specific heat at constant pressure

C :

Nano particle volume fraction

C w :

Nano particle volume fraction at the left channel

D B :

Brownian diffusion coefficient

D T :

Thermophoretic diffusion coefficient

h :

Ratio of the width of the two regions

h i :

Width of the region I and II

g :

Acceleration due to gravity

\( Gr \) :

Grashof number

K :

Ratio of thermal conductivities

m :

Ratio of viscosities

n :

Ratio of densities

N b :

Brownian motion parameter

N t :

Thermophoresis parameter

Pr:

Prandtl number

p :

Pressure

P :

Non-dimensional pressure gradient

Q i :

Heat generation/absorption coefficient of the region I and II

Re:

Reynolds number

T :

Temperature

\( T_{{w_{1} }} \) :

Temperature at the right wall

\( T_{{w_{2} }} \) :

Temperature at the left wall

u i :

Velocities in the x-component of the regions I and II

\( \tilde{u}_{1} \) :

Average velocity

x, y :

Space coordinates

α i :

Thermal diffusivity of the regions I and II

α :

Ratio of the thermal diffusivity

β i :

Coefficient of thermal expansion of the regions1 and 2

β :

Ratio of the coefficient of thermal expansion

μ i :

Viscosities of the regions I and II

ρ i :

Densities of the regions I and II

θ i :

Non-dimensional temperatures of the regions I and II

λ :

Mixed convection parameter

\( \phi \) :

Non-dimensional nanoparticle volume fraction

τ :

Heat capacity ratio

ν i :

Kinematic viscosities of regions I and II

δ i :

Non-dimensional internal heat generation/generation

*:

Dimensionless quantity

1 and 2:

Refer to quantities for regions I and II, respectively

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Acknowledgments

We appreciate the comments of the reviewers, which have led to definite improvement in the paper.

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Authors and Affiliations

  1. Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

    Robert A. Van Gorder & K. Vajravelu

  2. Department of Mathematics, Bangalore University, Bangalore, 560001, India

    K. V. Prasad

Authors
  1. Robert A. Van Gorder
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  2. K. V. Prasad
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  3. K. Vajravelu
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Correspondence to Robert A. Van Gorder.

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Van Gorder, R.A., Prasad, K.V. & Vajravelu, K. Convective heat transfer in the vertical channel flow of a clear fluid adjacent to a nanofluid layer: a two-fluid model. Heat Mass Transfer 48, 1247–1255 (2012). https://doi.org/10.1007/s00231-012-0973-2

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