Micro tubes

Chapter 4 is devoted to single-phase heat transfer. Data on heat transfer in circular micro-tubes and in rectangular, trapezoidal and triangular ducts are presented. Attention is drawn to the effect of energy dissipation, axial conduction and wall roughness on the thermal characteristics of flow. Specific problems connected with electro-osmotic heat transfer in micro-channels, three-dimensional heat transfer in micro-channel heat sinks and optimization of micro-heat exchangers are also discussed. 

The liquid crystal thermographs method has been used for measuring microtube surface temperature with uncertainties of lower than 0.4 K by Lin and Yang (2007). The average outside diameter micro-tubes was 250 pm and 1,260 pm, respectively. The surface was coated with thermochromic liquid crystal (TLC). The diameters of encapsulated TLC were ranging from 5 to 15 pm. The TLC was painted on the tested tubes surface with thickness of approximately 30 pm. 

Celata GP, Cumo M, McPhail SJ, Tesfagabir L, Zummo G (2005) Experimental study on compressibility effects in micro-tubes, in Proceedings of the XXIII UIT Italian National Coference, 2005 53-60... 

Chaudhari AM, Woudenberg TM, Albin M, Goodson KE (1998) Transient liquid crystal thermometry of microfabricated PCR vessel arrays. J Microelectromech Sys 7 345-355 Cheng P, Wu WY (2006) Mesoscale and microscale phase heat transfer. In Greene G, Cho Y, Hartnett J, Bar-Cohen A (eds) Advances in heat transfer, vol 39. Elsevier, Amsterdam Choi SB, Barron RF, Warrington RQ (1991) Fluid flow and heat transfer in micro- tubes. ASME DSC 40 89-93... 

Lin Q, Jiang F, Wang X-Q, Han Z, Tai Y-C, Lew J, Ho C-M (2000) MEMS Thermal Shear-Stress Sensors Experiments, Theory and Modehng, Technical Digest, Solid State Sensors and Actuators Workshop, Hilton Head, SC, 4—8 June 2000, pp 304-307 Lin TY, Yang CY (2007) An experimental investigation of forced convection heat transfer performance in micro-tubes by the method of hquid crystal thermography. Int. J. Heat Mass Transfer 50 4736-4742... 

Morini Gl, Lorenzini M, Salvigini S (2006) Friction characteristics of compressible gas flows in micro-tubes. Exp. Thermal and Fluid Science 30 733-744 Mudawar 1 (2001) Assessment of high-heat-flux thermal management schemes. IEEE CPT Trans 24 122-141... 

Yu DL, Warrington RO, Barron RE, Ameel T (1995) An experimental and theoretical investigation of fluid flow and heat transfer in micro-tubes. ASME/JSME Thermal Eng Conf 1 523-530... 

Glass and silicon tubes with diameters of 79.9-166.3 iim, and 100.25-205.3 am, respectively, were employed by Li et al. (2003) to study the characteristics of friction factors for de-ionized water flow in micro-tubes in the Re range of 350 to 2,300. Figure 3.1 shows that for fully developed water flow in smooth glass and silicon micro-tubes, the Poiseuille number remained approximately 64, which is consistent with the results in macro-tubes. The Reynolds number corresponding to the transition from laminar to turbulent flow was Re = 1,700—2,000. 

Fig. 3.3 The normalized Poiseuille number as a function of pressure for carbon tetrachloride in 10 pm micro-tube. Reprinted from Cui et al. (2004) with permission...

The hypothesis on the earlier transition from laminar to turbulent flow in micro-tubes is based on analysis of the dependence of pressure gradient on Reynolds number. As shown by the experimental data by Mala and Li (1999), this dependence may be approximated by three power functions AP Re (Re < 600),... 

One of the possible ways to account for the effect of roughness on the pressure drop in a micro-tube is to apply a modified-viscosity model to calculate the velocity distribution. Qu et al. (2000) performed an experimental study of the pressure drop in trapezoidal silicon micro-channels with the relative roughness and hydraulic diameter ranging from 3.5 to 5.7% and 51 to 169 pm, respectively. These experiments showed significant difference between experimental and theoretical pressure gradient. 

Li et al. (2003) studied the flow in a stainless steel micro-tube with the diameter of 128.76-179.8 jm and relative roughness of about 3-4%. The Poiseuille number for tubes with diameter 128.76 and 171.8 jm exceeded the value of Po corresponding to conventional theory by 37 and 15%, respectively. The critical value of the Reynolds number was close to 2,000 for 136.5 and 179.8 pm micro-tubes and about 1,700 for micro-tube with diameter 128.76 pm. 

The effect of roughness on pressure drop in micro-tubes 620 and 1,067 pm in diameter, with relative roughness of 0.71, 0.58 and 0.321% was investigated by Kandlikar et al. (2003). For the 1,067 pm diameter tube, the effect of roughness on pressure drop was insignificant. For the 620 pm tube the pressure drop results showed dependence on the surface roughness. 

For the most part of the experiments one can conclude that transition from laminar to turbulent flow in smooth and rough circular micro-tubes occurs at Reynolds numbers about RCcr = 2,000, corresponding to those in macro-channels. Note that other results were also reported. According to Yang et al. (2003) RCcr derived from the dependence of pressure drop on Reynolds number varied from RCcr = 1,200 to RCcr = 3,800. The lower value was obtained for the flow in a tube 4.01 mm in diameter, whereas the higher one was obtained for flow in a tube of 0.502mm diameter. These results look highly questionable since they contradict the data related to the flow in tubes of diameter d> mm. Actually, the 4.01 mm tube may be considered... 

The transition from laminar to turbulent flow in micro-channels with diameters ranging from 50 to 247 pm was studied by Sharp and Adrian (2004). The transition to turbulent flow was studied for liquids of different polarities in glass micro-tubes having diameters between 50 and 247 pm. The onset of transition occurred at the Reynolds number of about 1,800-2,000, as indicated by greater-than-laminar pressure drop and micro-PIV measurements of mean velocity and rms velocity fluctuations at the centerline. 

In the laminar region the rms of streamwise velocity fluctuations was expected to be zero (Sharp et al. 2001). Figure 3.10 shows that the first evidence of transition, in the form of an abrupt increase in the rms, occurs at 1,800 < Re < 2,200, in full agreement with the flow resistance data. There was no evidence of transition below these values. Thus, the behavior of the flow in micro-tubes, at least down to a 50 pm diameter, shows no perceptible differences with the macro-scale flow. 

Hwang and Kim (2006) investigated the pressure drop in circular stainless steel smooth micro-tubes ks/d <0.1%) with inner diameters of 244 pm, 430 pm and 792 pm. The measurements showed that the onset of flow transition from laminar to turbulent motion occurs at the Reynolds number of slightly less than 2,000. It... 

Thus, the available data related to transition in circular micro-tubes testify to the fact that the critical Reynolds number, which corresponds to the onset of such transition, is about 2,000. The evaluation of critical Reynolds number in irregular micro-channels will entail great difficulty since this problem contains a number of characteristic length scales. This fact leads to some vagueness in definition of critical Reynolds number that is not a single criterion, which determines flow characteristics. 

An experimental study of the laminar-turbulent transition in water flow in long circular micro-tubes, with diameter and length in the range of 16.6-32.2 pm and 1-30 mm, respectively, was carried out by Rands et al. (2006). The measurements allowed to estimate the effect of heat released by energy dissipation on fluid viscosity under conditions of laminar and turbulent flow in long micro-tubes. 

The data on the drag for micro-tube diameters of 16.6, 19.7, 26.3 and 32.2 pm are presented in Fig. 3.11 in the form of the dependence of the Poiseuille number on Re. The latter was determined by an average of the mixed-mean temperature at the inlet and outlet of the micro-tube. The data of Pig. 3.11 show that the Poiseuille number practically shows no dependence on Re in the range 500 < Re < 2,000. The... 

The dependence of the measured rise in fluid mixed-cup temperature on Reynolds number is illustrated in Fig. 3.12. The difference between outlet and inlet temperatures increases monotonically with increasing Re at laminar and turbulent flows. Under conditions of the given experiments, the temperature rise due to energy dissipation is very significant AT = 15—35 K at L/ i = 900—1,470 and Re = 2,500. The data on rising temperature in long micro-tubes can be presented in the form of the dependence of dimensionless viscous heating parameter Re/[Ec(L/(i)] on Reynolds number (Fig. 3.13). 

The behavior of liquid flow in micro-tubes and channels depends not only on the absolute value of the viscosity but also on its dependence on temperature. The nonlinear character of this dependence is a source of an important phenomenon - hydrodynamic thermal explosion, which is a sharp change of flow parameters at small temperature disturbances due to viscous dissipation. This is accompanied by radical changes of flow characteristics. Bastanjian et al. (1965) showed that under certain conditions the steady-state flow cannot exist, and an oscillatory regime begins. 

Estimation of adiabatic increase in the liquid temperature in circular micro-tubes with diameter ranging from 15 to 150 pm, under the experimental conditions reported by Judy et al. (2002), are presented in Table 3.7. The calculations were carried out for water, isopropanol and methanol flows, respectively, at initial temperature Tin = 298 K and v = 8.7 x 10" m /s, 2.5 x 10 m /s, 1.63 x 10 m /s, and Cp = 4,178 J/kgK, 2,606J/kgK, 2,531 J/kgK, respectively. The lower and higher values of AT/Tm correspond to limiting values of micro-channel length and Reynolds numbers. Table 3.7 shows adiabatic heating of liquid in micro-tubes can reach ten degrees the increase in mean fluid temperature (Tin -F Tout)/2 is about 9 °C, 121 °C, 38 °C for the water d = 20 pm), isopropanol d = 20 pm) and methanol d = 30 pm) flows, respectively. 

Table 3.7 Estimation of adiabatic increase in the liquid temperature in a circular micro-tube. Experimental conditions correspond to those of Judy et al. (2002)...

Brutin D, Tadiist L (2003) Experimental friction factor of a liquid flow in micro-tubes. Phys Fluids 15 653-661... 

Celata GP, Cumo M, McPhail S, Zummo G (2006) Characterization of fluid dynamics behavior and channel wall effects in micro-tube. Int J Heat Fluid Flow 27 135-143... 

Cui HH, Silber-Li ZH, Zhu SN (2004) Flow characteristics of liquids in micro-tubes driven by high pressure. Phys Fluids 16 1803-1810... 

Hao PF, Zhang XW, Yao FHe (2007) Transitional and turbulent flow in circular micro-tube. Exp. Thermal and Fluid Science 32 423-431... 

Lelea D, Nishio S, Takano K (2004) The experimental research on micro-tube heat transfer and fluid flow of distilled water. Int J Heat Mass Transfer 47 2817-2830 Li ZX, Du DX, Guo ZY (2003) Experimental study on flow characteristics of liquid in circular micro-tubes. Microscale Thermophys Eng 7 253-265 Lindgren ER (1958) The transition process and other phenomena in viscous flow. Arkiv fur Physik 12 1-169... 

Mala GM, Li D (1999) Flow characteristics of water in micro-tubes. Int J Heat Fluid Flow 20 142-... 

The micro-channels utilized in engineering systems are frequently connected with inlet and outlet manifolds. In this case the thermal boundary condition at the inlet and outlet of the tube is not adiabatic. Heat transfer in a micro-tube under these conditions was studied by Hetsroni et al. (2004). They measured heat transfer to water flowing in a pipe of inner diameter 1.07 mm, outer diameter 1.5 mm, and 0.600 m in length, as shown in Fig. 4.2b. The pipe was divided into two sections. The development section of Lj = 0.245 m was used to obtain fully developed flow and thermal fields. The test section proper, of heating length Lh = 0.335 m, was used for collecting the experimental data. 

Celata GP, Cumo M, Marcom V, McPhail SJ, Zummo Z (2005) Micro-tube heat transfer scaling effects an experimental validation. In Proceedings of ECI International Conference on Heat Transfer and Fluid Flow in Microchannels, Caste/Vecchio PascoU, Italy, 25-30 September 2005... 

Choi SB, Barron R, Warrington RQ (1991) Fluid flow and heat transfer in micro-tubes. In Choi D et al. (eds) Micro-mechamcal sensors, actuators and systems. ASME DSC 32 121-128... 

Koo J, Kleinstreuer C (2004) Viscous dissipation effects in micro-tubes and micro-channels. Int J Heat Mass Transfer 47 3159-3169... 

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