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Numerical investigation on heat transfer of liquid flow at low Reynolds number in micro-cylinder-groups

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Abstract

Heat transfer of de-ionized water over in-line and staggered micro-cylinder-groups have been numerically investigated with Reynolds number varying in the range from 25 to 150. A 3-D incompressible numerical model is employed to investigate the vortex distributions and the influences of the vortices on heat transfer characteristics at low Re numbers in micro-cylinder-groups with different geometrical parameters, including micro-cylinder diameters (100, 250 and 500 μm), ratios of pitch to micro-cylinder diameter (1.5, 2 and 2.5) and ratios of micro-cylinder height to diameter (0.5, 1, 1.5 and 2). The vortex distributions, the temperature fields, and the relationships among them are investigated by solving the numerical model with the finite volume method. It is found that the vortex number become more with the increase of pitch ratio and the change of flow rate distribution affects the heat transfer characteristics apparently. Meanwhile, the local heat transfer coefficients nearby the locations of vortices greatly increase due to the boundary layer separation, which further enhance the heat transfer in micro-cylinder-groups. The new correlations which to Nusselt number of de-ionized water over micro-cylinders with Re number varying from 25 to 150 have been proposed considering the differential pressure resistance and the buoyancy effect basing on numerical calculations in this paper.

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Abbreviations

a :

Constant

b :

Constant

D :

Micro-cylinder diameter (m)

f :

Friction factor

H :

Micro-cylinder height (m)

L :

Micro-cylinder-group length (m)

N :

Micro-cylinder column number

p :

Pressure (Pa)

Δp :

Pressure difference between inlet and outlet (Pa)

q :

Heat flux (W/m2)

S :

Micro-cylinder pitch ratio (m)

S w :

Distance between the first row and the wall (m)

T/ \(\bar{T} \) :

Temperature/average temperature

u :

Velocity along x-direction (m/s)

v :

Velocity along y-direction (m/s)

w :

Velocity along z-direction (m/s)

x :

x-coordinate

y :

y-coordinate

z :

z-coordinate

ρ :

Density of the working fluid (kg/m3)

μ :

Viscosity of the working fluid

f :

Working fluid

in :

Inlet

out :

Outlet

symmetry :

Symmetry plane

wall_a :

Adiabatic walls

wall_cylinder :

Surfaces of micro-cylinders

wall_h :

Heating walls

max :

Maximum

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Acknowledgments

The authors acknowledge the support of National Science Foundation of China under Grant No. 50976062 and Shandong Provincial Natural Science Foundation of China under Grant No. ZR2011EEQ015.

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Authors and Affiliations

  1. Energy Research Institute, Shandong Academy of Sciences, Jinan, 250014, China

    Ning Guan, Zhi-Gang Liu & Cheng-Wu Zhang

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  1. Ning Guan
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  2. Zhi-Gang Liu
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  3. Cheng-Wu Zhang
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Correspondence to Zhi-Gang Liu.

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Guan, N., Liu, ZG. & Zhang, CW. Numerical investigation on heat transfer of liquid flow at low Reynolds number in micro-cylinder-groups. Heat Mass Transfer 48, 1141–1153 (2012). https://doi.org/10.1007/s00231-011-0956-8

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  • DOI: https://doi.org/10.1007/s00231-011-0956-8

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