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Characterization of heat transfer and frictional pressure drops for water flows through micro tubes


The heat transfer and pressure drops characterization of water through round micro tubes is investigated experimentally. Nine tube diameters in the range of 50 µm, 80 µm, 100 µm, 250 µm, 300 µm, 400 µm, 800 µm, 900 µm, and 950 µm and over a wide range of Reynolds numbers are tested to characterize the friction factor, the pressure drops, heat transfer coefficient, fully developed heat transfer, thermal developing heat transfer, the effect of viscous heating, and evaluating the surface temperature on the wall of the micro tubes. It is observed that the fully developed HTCs and friction factors in micro tubes agree well with the predicted conventional heat transfer correlations for laminar and turbulent flow, Poiseuille’ (f = 16/ReD) theory, Blasius’ (f = 0.079ReD−0.25) equation [1], and Filonenko [2]. It is also observed that the transition takes place at (Re = 2288 ~ 2989), which corresponds to that in the conventional sizes of tubes. It is also observed that the thermal entrance length in the laminar region for the test micro tubes is longer than that of the conventional sizes of tubes predicted by the empirical correlations. Moreover, since the specific heat of water is very high and the velocity is very low, there is no significant effect of the viscous heating.

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Area (m2)


Constant number (dimensionless)

cp :

Heat capacity (J/kg ∙ K)


Diameter (m)


Friction factor (dimensionless)


Mass velocity (kg/(m2s))


Graetz number (dimensionless)


Hue (dimensionless)


Heat transfer coefficient (W/(m2 ∙ ℃))


Current (A)

Kc :

Contract loss coefficient (dimensionless)

Ke :

Expansion loss coefficient (dimensionless)

kf :

Thermal conductivity of fluid (W/(m ∙ ℃))

ks :

Thermal conductivity of tube ((W/m ∙ ℃))


Length (m)


Axial conduction number (dimensionless)


Mass (kg)


Mass flow rate (kg3/s)

Nu D :

Nusselt number (dimensionless)

Pr :

Prandtl number (dimensionless)


Heat transfer rate (W)

q :

Heat flux (W/ m2)

\(\dot{q}\) :

Heat generation (W/ m3)


Radius (m)


Average roughness (m)

Re D :

Reynolds number (dimensionless)


Temperature (oC)


Time (s)


Velocity (m/s)


Volt (V)


Length (m)


Pressure drop (N/m2)


Viscosity (N/(m2 ∙ s))


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


Density (kg/m3)

τw :

Wall shear stress (N/m2)








Fully developed








Long tube length






Short tube length






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Mudhafar, M.A.H., Lin, Y. Characterization of heat transfer and frictional pressure drops for water flows through micro tubes. Heat Mass Transfer 59, 283–297 (2023).

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