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Forced Convection Heat Transfer of Nanofluids in a Porous Channel

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Abstract

This article is concerned with the effects of flow and migration of nanoparticles on heat transfer in a straight channel occupied with a porous medium. Investigation of force convective heat transfer of nanofluids in a porous channel has not been considered completely in the literature and this challenge is generally considered to be an open research topic that may require more study. The fully developed flow and steady Darcy–Brinkman–Forchheimer equation is employed in porous channel. The thermal equilibrium model is assumed between nanofluid and solid phases. It is assumed that the nanoparticles are distributed non-uniformly inside the channel. As a result the volume fraction distribution equation is also coupled with governing equations. The effects of parameters such as Lewis number, Schmidt number, Brownian diffusion, and thermophoresis on the heat transfer are completely studied. The results show that the local Nusselt number is decreased when the Lewis number is increased. It is observed that as the Schmidt number is increased, the wall temperature gradient is decreased and as a consequence the local Nusselt number is decreased. The effects of Lewis number, Schmidt number, and modified diffusivity ratio on the volume fraction distribution are also studied and discussed.

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Abbreviations

x, y :

Cartesian coordinate (m)

u :

Axial velocity (ms−1)

K :

Permeability (m2)

Da :

Darcy number

P :

Pressure (Nm−2)

T :

Temperature (K)

D T :

Thermophoretic diffusion coefficient (m2 s−1)

D B :

Brownian diffusion coefficient (m2 s−1)

H :

Half length of channel

t :

Time (s)

Re :

Reynolds number

Pr :

Prandtl number

N BT :

Brownian motion parameter

k :

Thermal conductivity (Wm−1 K−1)

Le :

Lewis number

Sc :

Schmidt number

μ :

Viscosity (kg m−1 s−1)

\({\varepsilon}\) :

Porosity

ρ :

Density (kgm−3)

\({{\varphi}}\) :

Volume fraction

σ :

Thermal capacity ratio

Δ:

Inertia parameter

α :

Effective thermal diffusivity (m2 s−1)

τ :

Modified diffusivity ratio

f:

Fluid

m:

Porous media

p:

Particle

c:

Reference

*:

Dimensionless variables

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Authors and Affiliations

  1. Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    M. J. Maghrebi

  2. Department of Mechanical Engineering, Shahrood University of Technology, P.O. Box: 3619995161, Shahrood, Iran

    M. Nazari & T. Armaghani

Authors
  1. M. J. Maghrebi
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  2. M. Nazari
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  3. T. Armaghani
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Correspondence to M. Nazari.

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Maghrebi, M.J., Nazari, M. & Armaghani, T. Forced Convection Heat Transfer of Nanofluids in a Porous Channel. Transp Porous Med 93, 401–413 (2012). https://doi.org/10.1007/s11242-012-9959-2

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  • DOI: https://doi.org/10.1007/s11242-012-9959-2

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