Abstract
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 HTC_{s} and friction factors in micro tubes agree well with the predicted conventional heat transfer correlations for laminar and turbulent flow, Poiseuille’ (f = 16/Re_{D}) theory, Blasius’ (f = 0.079Re_{D}^{−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.
This is a preview of subscription content, access via your institution.
Abbreviations
 A:

Area (m^{2})
 C:

Constant number (dimensionless)
 c_{p} :

Heat capacity (J/kg ∙ K)
 d:

Diameter (m)
 f:

Friction factor (dimensionless)
 G:

Mass velocity (kg/(m^{2}s))
 Gz:

Graetz number (dimensionless)
 H:

Hue (dimensionless)
 h:

Heat transfer coefficient (W/(m^{2} ∙ ℃))
 I:

Current (A)
 K_{c} :

Contract loss coefficient (dimensionless)
 K_{e} :

Expansion loss coefficient (dimensionless)
 k_{f} :

Thermal conductivity of fluid (W/(m ∙ ℃))
 k_{s} :

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

Length (m)
 M:

Axial conduction number (dimensionless)
 m:

Mass (kg)
 ṁ:

Mass flow rate (kg^{3}/s)
 Nu _{ D } :

Nusselt number (dimensionless)
 Pr :

Prandtl number (dimensionless)
 q:

Heat transfer rate (W)
 q” :

Heat flux (W/ m^{2})
 \(\dot{q}\) :

Heat generation (W/ m^{3})
 r:

Radius (m)
 Ra:

Average roughness (m)
 Re _{ D } :

Reynolds number (dimensionless)
 T:

Temperature (^{o}C)
 t:

Time (s)
 u:

Velocity (m/s)
 V:

Volt (V)
 x:

Length (m)
 ΔP:

Pressure drop (N/m^{2})
 μ:

Viscosity (N/(m^{2} ∙ s))
 σ:

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

Density (kg/m^{3})
 τ_{w} :

Wall shear stress (N/m^{2})
 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
References
Blasius H (1913) Das Aehnlichkeitsgesetz bei Reibungsvorgängen in Flüssigkeiten. Forschg Arb Ing Wes 131–137
Filonenko G (2011) On Friction Factor for a Smooth Tube, All Union Thermotechnical Institute, 1948, quoted. In: Bergman TL, Incropera FP, DeWitt DP, Lavine AS (eds) Fundamentals of heat and mass transfer. John Wiley & Sons
Kohl MJ, AbdelKhalik SI, Jeter SM, Sadowski DL (2005) An experimental investigation of microchannel flow with internal pressure measurements. Int J Heat Mass Transf 48(8):1518–1533
Hong C, Shigeishi T, Asako Y, Faghri M (2020) Experimental investigations of local friction factors of laminar and turbulent gas flows in smooth microtubes. Int J Heat Mass Transf 158:120035
Azizi N, Homayoon R, Hojjati MR (2019) Predicting the ColebrookWhite friction factor in the pipe flow by new explicit correlations. ASME J Fluids Eng 141:051201
Srinivasan K, Subbarao PMV, Kale SR (2017) Experimental and numerical studies on gas flow through silicon microchannels. ASME J Fluids Eng 139(8):081205
Roohi E, Darbandi M, Mirjalili V (2008) DSMC solution of supersonic to choked subsonic flow in micro to nano channels. Proceedings of the ASME 6th International Conference On Nanochannels, Microchannels And Minichannels, ICNMM2008–62282. Darmstadt, Germany
Kermani EL, Roohi E, PortéAgel F (2018) Evaluating the modulated gradient model in large eddy simulation of channel flow with OpenFOAM. J Turbul 19(7):600–620
Zahiri AP, Roohi E (2019) Anisotropic MinimumDissipation (AMD) SubgridScale Model Implemented in OpenFOAM: verification and assessment in singlephase and multiphase flows. Comput Fluids 180:190–205
Matsushita S, Hong C, Asako Y, Ueno I (2011) Experimental investigations of turbulent gas flow through a microtube. Proceedings of the 4th International Conference on Heat Transfer and Fluid Flow in Microscale, HTFFMIV069. Fukuoka, Japan
Murakami S, Asako Y (2011) Local pipe friction factor of compressible laminar or turbulent flow in microtubes. Proceedings of the ASME 9th International Conference on Nanochannels, Microchannels, and Minichannels, ICNMM2011–58036. Edmonton, Canada
Peng XF, Peterson GP, Wang BX (1994) Frictional flow characteristics of water flowing through rectangular microchannels. Exper Heat Transfer 7:249–264
Peng XF, Peterson GP, Wang BX (1994) Heat transfer characteristics of water flowing through microchannels. Exper Heat Transfer 7:265–283
Peng XF, Wang BX (1998) Forcedconvection and boiling characteristics in microchannels. In: Proceedings of the 11th IHTC 1. pp 371–390
Shah RK, Bhatti MS (1987) Laminar convective heat transfer in ducts, in: Kakac S, Shah RK, Aung W, (Eds.), Handbook of SinglePhase Convective Heat Transfer, Willy, New York
Dittus FW, Boelter LM (1930) Heat transfer in automobile radiators of the tubular type. Univ Calif Berkeley Publ Eng 2(13):443–461
Wilding P, Shoffner MA, Kircka LJ (1994) Manipulation and flow of biological fluids in straight channels micromachined in silicon. Clin Chem 40:43–47
Papautsky I, Gale BK, Mohanty S, Ameel TA, Frazier AB (1999) Effects of rectangular microchannel aspect ratio on laminar friction constant. SPIE 3877:147–158
Jiang XN, Zhou JY, Yao YL, Ye XY (1995) Microfluid flow in microchannel. Proc Transducers 95:317–320
Mala GM, Li D (1999) Flow characteristics of water in microtubes. Int J Heat Fluid Flow 20:142–148
Wu HY, Cheng P (2003) Friction factors in smooth trapezoidal silicon microchannels with different aspect ratios. Int J Heat Mass Transfer 46:2519–2525
Weilin Q, Mala GM, Dongqing L (2000) Pressuredriven water flows in trapezoidal silicon microchannels. Int J Heat Mass Transfer 43:353–364
Sharp KV, Adrian RJ (2004) Transition from laminar to turbulent flow in liquid filled microtubes. Exper Fluids 36:741–747
Pfahler J, Harley J, Bau H, Zemel J (1991) Liquid transport in micron and submicron channels. Sensors Actuat A21–A23:431–434
Pfahler J, Harley J, Bau H, Zemel J (1991) Gas and liquid flow in small channels. Micromech Sensors Actuat Syst 32:49–60
Harley JC, Huang Y, Bau HH, Zemel JN (1995) Gas flow in microchannels. J Fluid Mech 284:257–274
Chung PMY, Kawaji M, Kawahara A (2002) Characteristics of singlephase flow in microchannels. ASME Fluids Eng Div Publ FED 257(1B):1219–1227
Arkilic EB, Schmidt MA, Breuer KS (1997) Gaseous slip flow in long microchannels. J Microelectromech Syst 6:167–178
Vijayalakshmi K, Anoop KB, Patel HE, Harikrishna PV, Sundararajan T, Das SK (2009) Effects of compressibility and transition to turbulence on flow through microchannels. Int J Heat Mass Transf 52(9–10):2196–2204
Ho C, Tai Y (1998) Microelectromechanical systems (MEMS) and fluid flows. Annu Rev Fluid Mech 30:579–612
Shih JC, Ho C, Liu J, Tai Y (1996) Monatomic and polyatomic gas flow through uniform microchannels. Microelectromech Syst MEMS 59:197–203
Wu P, Little WA (1983) Measurement of friction factors for the flow of gases in very fine channels used for microminiature JouleThompson refrigerators. Cryogenics 23:273–277
Harley JC, Huang Y, Bau H, Zemel JN (1995) Gas flows in microchannels. J Fluid Mech 284:257–274
Choi SB, Barron RF, Warrington RO (1991) Fluid flow and heat transfer in microtubes, Micromech. Sensors, Actuators, Syst 32:123–134
Guo ZY, Wu XB (1997) Compressibility effects on the gas flow and heat transfer in a microtube. Int J Heat Mass Transfer 40:3251–3254
Choquette SF, Faghri M, Kenyon EJ, Sunden B (1996) Compressible fluid flow in micronsized channels. Natl Heat Transfer Conf 5:25–32
Urbanek W, Zemel JN, Bau H (1993) An investigation of the temperature dependence of Poiseuille numbers in microchannel flow. J Micromech Microeng: Struct Dev Syst 3:206–208
Papautsky I, Brazzle J, Ameel T, Frazier AB (1998) Laminar fluid behavior in microchannels using micropolar fluid theory. In: Sensors and Actuators, Physical Proceedings of the 1998 11th IEEE International Workshop on Micro Electro Mechanical Systems, MEMS, vol 73. Heidelberg, Germany, pp 101–108
Mala GM, Li D, Dale JD (1997) Heat transfer and fluid flow in microchannels. Int J Heat Mass Transfer 40:3079–3088
Harms TM, Kazmierczak M, Gerner FM, Holke A, Henderson HT, Pilchowski J, Baker K (1997) Experimental investigation of heat transfer and pressure drop through deep microchannels in a (1 1 0) silicon substrate. In: Proceedings of the ASME Heat Transfer Division, vol 1. pp 347–357
Pfund D, Shekarriz A, Popescu A, Welty JR (1998) Pressure drop measurements in a microchannel. In: Proceedings of the 1998 ASME International Mechanical Engineering Congress and Exposition: DSC MicroElectroMechanicalSystems, vol 66. pp 193– 198
Webb RL, Zhang M (1998) Heat transfer and friction in small diameter channels. Microscale Thermophys Eng 2:189–202
Peng XF, Peterson GP (1996) Convective heat transfer and flow friction for water flow in microchannel structures. Int J Heat Transfer Mass Transfer 39:2599–2608
Peng XF, Peterson GP, Wang BX (1994) Frictional flow characteristics of water flowing through rectangular microchannels. Exp Heat Transfer 7:249–265
Papautsky I, Gale BK, Mohanty S, Ameel TA, Frazier AB (1999) Effects of rectangular microchannel aspect ratio on laminar friction constant. In: Proceedings of SPIE – The International Society for Optical Engineering Proceedings of the 1999 Microfluidic Devices and Systems II, vol 3877. Santa Clara, pp 147–158
Ma HB, Peterson GP (1997) Laminar friction factor in microscale ducts of irregular crosssection. Microscale Thermophys Eng 1:253–265
Adams TM, Dowling MF, AbdelKhalik SI, Jeter SM (1999) Applicability of traditional turbulent singlephase forced convection to noncircular microchannels. Int J Heat Mass Transf 42:4411–4415
Hay JL, Hollingsworth DK (1996) A comparison of trichromic systems for use in the calibration of polymerdispersed thermochromic liquid crystals. Exp Thermal Fluid Sci 12:1–12
Maranzana G, Perry I, Maillet D (2004) Mini and Microchannels: influence of axial conduction in the walls. Int J Heat Mass Transf 47:3993–4004
Kays WM, London AL (1984) Compact heat exchangers. McGrawHill, New York, NY
Gnielinski V (1976) New equation for heat and mass transfer in turbulent pipe and channel flow. Int J Chem Eng 16:359–368
Incropera FP, DeWitt DP (2007) Fundamentals of heat and mass transfer. John Wiley & Sons, New York
Dittus FW, Boelter LMK (1930) Heat transfer in automobile radiators of the tubular type. University of California, Berkeley, Publications on Engineering 2(13):443–461
Petukhov BS, Kirillov VV (1958) The problem of heat exchanger in the turbulent flow of liquid in tubes (in Russia). Teploeenergetica 4(4):63–68. see also Petukhov, B. S., 1970 Advances in heat transfer 6 Academic press New York
Shah RK, Bhatti MS (1987) Laminar Convective Heat Transfer in Ducts. In: Kakac S, Shan RK, Aung W (eds) Handbook of SinglePhase Convective Heat Transfer. Willy, New York
Acknowledgements
None. No funding to declare.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interests regarding the publication of this paper.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
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). https://doi.org/10.1007/s00231022032636
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00231022032636