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Flow and heat transfer of a weak concentration micropolar-nanofluid over steady/unsteady-moving surface

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Abstract

A mathematical simulation to the cooling process of a flat moving surface using a weak concentration micropolar-nanofluid as a cooling medium has been investigated. The modelling based on the conservation equations of the unsteady case for the momentum and thermal boundary layer taking into consider the effect of suction process and thermal radiation. Using similarity transformation technique, the conservation equations have been transformed to ordinary differential equations that are solved numerically for general case and analytically for the steady case. Surface shear stress, couple shear stress, and the rate of heat transfer are deduced, and the impact of these physical characteristics on the final quality and the mechanical properties of the surface to be cooled discussed.

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Abbreviations

a,b,c :

Constants parameter (t−1)

T :

Temperature (K)

\({q_{\text{r}}}\) :

Radiative heat flux \(\left( {\frac{{\text{W}}}{{{{\text{m}}^2}}}} \right)\)

k :

Thermal conductivity (W/mk)

\({C_{\text{p}}}\) :

Specific heat (J/kg K)

\({C_{\text{f}}}\) :

Skin friction coefficient

j :

Micro-inertia per unit mass

\(\gamma\) :

Spin gradient viscosity

\({k^\prime }\) :

Vortex viscosity

\(\phi\) :

Nanoparticles volume fraction

\(\omega\) :

Angular velocity (rad/s)

\(\rho\) :

Fluid density (kg/m3)

\(\mu\) :

Dynamic viscosity (Ns/m2)

\(\nu\) :

Kinematic viscosity (m2/s)

\(\sigma\) :

Stefen–Boltzman constant (1.3806488 × 10−23 m2 kg/s2 K)

\({\alpha ^*}\) :

Mean absorption coefficient

\(K = \frac{{{k^\prime }}}{\mu }\) :

Material parameter

\(Pr = \frac{{{\nu _{\text{f}}}{{(\rho {C_{\text{p}}})}_{\text{f}}}}}{{{k_{\text{f}}}}}\) :

Prandtl number

\({\text{Rd}} = \frac{{4\sigma T_\infty ^3}}{{{k_{\text{f}}}{\alpha ^ * }}}\) :

Radiation parameter

\(A = \frac{c}{a}\) :

Unsteadiness parameter

fw :

Suction parameter

f:

Fluid phase

nf:

Nanofluid

s:

Solid particles

w:

Condition of the wall

\(\infty\) :

Ambient condition

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Authors and Affiliations

  1. Basic Sciences Department, Faculty of Engineering at Benha, Benha University, Cairo, Egypt

    Mohamed S. Abdel-wahed

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  1. Mohamed S. Abdel-wahed
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Correspondence to Mohamed S. Abdel-wahed.

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Abdel-wahed, M.S. Flow and heat transfer of a weak concentration micropolar-nanofluid over steady/unsteady-moving surface. Appl. Phys. A 123, 195 (2017). https://doi.org/10.1007/s00339-017-0815-7

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