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The measurement of friction factors and heat transfer Nusselt numbers for the flow of air and CO2 through micro tubes

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Abstract

The heat transfer and pressure drops characterization of air and CO2 through smooth and rough micro tubes are investigated experimentally. Nine smooth stainless steel micro tubes with inner diameters of 50, 80, 100, 250, 300, 400, 800, 900, and 950 μm, and six rough micro tubes with inner surface roughness are tested in the present study to characterize the friction factors, the pressure drops, the heat transfer Nusselt numbers, and evaluating the surface temperature on the wall of the micro tubes. It was observed that heat transfer Nusselt numbers on smooth micro tubes fitted well with the conventional correlations of the Gnielinski’ (Gnielinski in Int J Chem Eng 16:359–368, 1976) correlation, the Dittus-Boelter’ (Dittus and Boelter in Univ Cali Berkeley Publ Eng 2(13):443–461, 1930) correlation, and the Petukhov’ (Petukhov and Kirillov in Teploeenergetica 4(4):63–68, 1958) correlation. Moreover, the test results of the friction factors were in a very good agreement of the Gnielinski’ (Gnielinski in Int J Chem Eng 16:359–368, 1976) correlation, and Blasius’ (Blasius in Forschg. Arb. Ing. -Wes, pp 131–137, 1913) equation in both laminar and turbulent regions, except for the micro tubes in the range of 50~100 μm. However, for the rough micro tubes, the test results scattered above the standard predictions of the Filonenko’ (Filonenko in All Union Thermotechnical Institute, 1948) correlation. The test results showed that the heat transfer enhancement of the fabricated smooth surface micro tubes is better than that of the structural rough surface micro tubes. It was also observed that the transition regime occurred at Re of approximately 1,500~2,000 due to the increase in surface roughness.

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Abbreviations

A:

Area (m2)

C:

Constant number (dimensionless)

cp :

Heat capacity (J/(kg · K))

d:

Diameter (m)

di:

Smooth Inside Diameter (m)

dcf :

Rough Inside Diameter (m)

f:

Friction factor (dimensionless)

G:

Mass velocity (kg/(m2 · s))

Gz:

Graetz number (dimensionless)

H:

Hue (dimensionless)

h:

Heat transfer coefficient (W/(m2 · °C))

I:

Current (A)

Kc :

Contract loss coefficient (dimensionless)

Ke :

Expansion loss coefficient (dimensionless)

kf :

Thermal conductivity of fluid (W/(m · °C))

ks :

Thermal conductivity of tube ((W/m · °C))

L:

Length (m)

Lh :

Thermal Length (m)

Lm :

Measured Length (m)

M:

Axial conduction number (dimensionless)

m:

Mass (kg)

\(\dot{\mathrm{m}}\) :

Mass flow rate (kg3/s)

Nud :

Nusselt number (dimensionless)

Pr:

Prandtl number (dimensionless)

q:

Heat transfer rate (W)

q”:

Heat flux (W/m2)

\(\dot{\mathrm{q}}\) :

Heat generation (W/m3)

r:

Radius (m)

Ra:

Average roughness (m)

Red :

Reynolds number (dimensionless)

T:

Temperature (°C)

t:

Time (s)

u:

Velocity (m/s)

V:

Volt (V)

x:

Length (m)

ΔP:

Pressure drop (N/m2)

μ:

Viscosity (Pas. s)

σ:

Ratio of the test section cross sectional area to the frontal area of the inlet and exit plenums (dimensionless)

ρ:

Density (kg/m3)

τw :

Wall shear stress (N/m2)

d:

Diameter

e:

Exit

f:

Friction

fd:

Fully developed

h:

Heating

i:

Inner

in:

Inlet

L:

Long tube length

mea:

Measured

o:

External

S:

Short tube length

w:

Water

wa:

Wall

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  1. Department of Mechanical Engineering, National Central University, 320 Jhong-Li, Taoyuan City, Taiwan

    Mudhafar A. H. Mudhafar

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Mudhafar, M.A.H. The measurement of friction factors and heat transfer Nusselt numbers for the flow of air and CO2 through micro tubes. Heat Mass Transfer 59, 989–1004 (2023). https://doi.org/10.1007/s00231-022-03315-x

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