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Prediction of the Onset of Nucleate Boiling in Microchannel Flow

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Prediction of the Onset of Nucleate Boiling in Microchannel Flow International Journal of Heat and Mass Transfer 48 (2005) 5134–5149 www.elsevier.com/locate/ijhmt Prediction of the onset of nucleate boiling in microchannel flow Dong Liu, Poh-Seng Lee, Suresh V. Garimella * Cooling Technologies Research Center, School of Mechanical Engineering, Purdue University, West Lafayette, IA 47907-2088, USA Received 28 January 2005; received in revised form 30 July 2005 Available online 27 September 2005 Abstract The onset of nucleate boiling in the flow of water through a microchannel heat sink was investigated. The micro- channels considered were 275 lm wide by 636 lm deep. Onset of nucleate boiling was identified with a high-speed imag- ing system and the heat flux at incipience was measured under various flow conditions. An analytical model was developed to predict the incipient heat flux as well as the bubble size at the onset of boiling. The closed-form solution obtained sheds light on the impact of the important system parameters on the incipient heat flux. The model predictions yield good agreement with the experimental data. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Microchannels; Electronics cooling; Boiling; Incipience; High heat flux; Heat sink 1. Introduction of nucleate boiling (ONB) in microchannels. The first occurrence of vapor bubbles demarcates the transition Boiling and two-phase flow in microchannels has at- from a single-phase to a two-phase flow regime, with tracted increasing interest in recent years. Utilizing the the accompanying dramatic change in heat transfer latent heat of the coolant, two-phase microchannel heat and pressure drop. In addition, a prediction of the sinks can dissipate much higher heat fluxes while requir- ONB is necessary for understanding other flow boiling ing smaller rates of coolant flow than in the single-phase phenomena such as the onset of significant void (OSV) counterpart. Better temperature uniformity across the and departure from nucleate boiling (DNB) [5]. heat sink is also achievable. In spite of these attributes, A number of studies have been directed at under- the complex nature of convective flow boiling in micro- standing the ONB, with the majority considering channel heat sinks is still not well-understood, hindering conventional-sized channels. Table 1 summarizes ana- their application in industry practice [1–4]. One subject lytical and semi-analytical studies from the literature of particular importance is the prediction of the onset [6–14], including information on key assumptions, model development and incipient heat flux correlations proposed. Hsu [6] was the first to postulate a minimum superheat criterion for the ONB in pool boiling; he * Corresponding author. Tel.: +1 765 494 5621; fax: +1 765 proposed that the bubble nucleus would grow only if 494 0539. the minimum temperature surrounding the bubble (the E-mail address: [email protected] (S.V. Garimella). temperature at the tip of the bubble) is at least equal 0017-9310/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2005.07.021 D. Liu et al. / International Journal of Heat and Mass Transfer 48 (2005) 5134–5149 5135 Nomenclature 2 Ab area of microchannel heat sink, m Greek symbols cp specific heat, kJ/kg °C a microchannel aspect ratio C shape factor / portion of the total power absorbed by the Dh hydraulic diameter, lm water G mass flux, kg/s m2 g fin efficiency hfg latent heat, J/kg h contact angle, deg 3 Hc microchannel height, lm q density, kg/m I current, A r surface tension, N/m k thermal conductivity, W/m °C L channel length Subscripts n number of microchannels b bubble Nu Nusselt number c cavity p pressure, Pa f fluid q00 applied heat flux, W/cm2 fd fully developed flow 00 2 qw effective heat flux, W/cm in inlet r radius, lm out outlet Re Reynolds number (based on channel min minimum hydraulic diameter) max maximum T temperature, °C s saturate u0 fluid inlet velocity, m/s v vapor V voltage, V w wall wc microchannel width, lm ww microchannel fin thickness, lm yb bubble height, lm to the saturation temperature of the vapor inside the [14] employed nucleation kinetics to derive the wall bubble. Following the same rationale, Bergles and superheat at the ONB, and included a consideration of Rohsenow [8] extended HsuÕs model and proposed a the effects of contact angle, dissolved gas, and the exis- graphical solution to predict the incipient heat flux in tence of microcavities and corners in the microchannels flow boiling. Sato and Matsumara [7] derived an analy- on ONB. tical relationship for the incipient heat flux in terms of Most past studies of ONB have been based on the wall superheat. Davis and Anderson [9] provided an minimum superheat criterion of Hsu. However, HsuÕs analytical treatment of the approach of Bergles and model was developed for pool boiling and did not Rohsenow, and introduced the contact angle as a vari- incorporate features of convective flow boiling, espe- able in the prediction of ONB. More recently, Kandlikar cially the influence on heat flux of both the wall and fluid et al. [10] numerically computed the temperature at the temperatures. In the early models, therefore, convective location of the stagnation point around the bubble, heat transfer was either ambiguously incorporated [7–9] which was used as the minimum temperature in the or required graphical or numerical procedures to derive ONB criterion. Celata et al. [11] investigated the onset the ONB criterion [10,13,14]. An analytical model of subcooled boiling in the forced convective flow of which captures essential characteristics of forced convec- water and recommended ThomÕs correlation [15] for its tive flow is not available for predicting the ONB in good match with the experimental data. Basu et al. microchannels. [12] postulated the dependence of the available cavity The present study is aimed at experimentally identify- size on the contact angle and proposed a correlation ing the onset of nucleate boiling in forced convective for the incipient heat flux. flow in a microchannel heat sink. An analytical model Fewer studies have considered the ONB in micro- with a closed-form solution is developed to represent channels. Ghiaasiaan and Chedester [5] proposed a the thermodynamics of bubble nucleation as well as semi-empirical method to predict the ONB in turbulent the convective nature of flow boiling in microchan- flow in microtubes. Qu and Mudawar [13] measured the nels. The effects of fluid inlet subcooling, wall boundary incipient boiling heat flux in a microchannel heat sink conditions and microchannel geometry are incorporated and developed a mechanistic model to incorporate both in the model. Model predictions are validated against mechanical and thermal considerations. Li and Cheng the experimental results obtained. 5136 Table 1 Studies in the literature of ONB in subcooled flow boiling Reference Key assumptions Model development Proposed ONB correlation Past work for conventional-sized channels Hsu [6] • Limiting thermal layer exists below • Solve the transient-conduction problem D. Liu et al. / International Journal of Heat and Mass Transfer 48 (2005) 5134–5149 which molecular transport prevails • ONB occurs when the transient 2 • Bubble nucleus will grow when temperature meets the superheat 00 kf hfgqvðT w À T satÞ qONB ¼ ð1Þ superheat criterion is satisfied at criterion 12:8rT sat the distance of one bubble • Only cavities within a size diameter from the wall range can be active Sato and Matsumara • Spherical bubble nucleus • Critical bubble radius is determined [7] obtains thermal energy by solving the equation of the 2 indirectly from the thickness of superheated layer 00 kf hfgqvðT w À T satÞ qONB ¼ ð2Þ surrounding liquid 8rT sat Bergles and Rohsenow • Hemispherical bubble nucleus will • ONB occurs when the liquid [8] grow when the superheat criterion temperature is tangent to the 00 1:156 2:16=p0:0234 is satisfied at the distance of one superheat curve qONB ¼ 1082p ½1:8ðT w À T satÞ bubble radius from the wall • Graphical solution to predict 00 2 ðqONB is in W=m ; p is in bar and T in CÞð3Þ • Near-wall temperature of liquid is incipient heat flux for water over approximated by a linear a pressure range of 15–2000 psi relation (conduction) Davis and Anderson • Hemispherical bubble nucleus will • Tangent equations in [8] solved [9] grow when superheat criterion is analytically 2 satisfied at the distance of one 00 kf hfgqvðT w À T satÞ qONB ¼ ð4Þ bubble radius from the wall 8ð1 þ cos hÞrT sat Kandlikar et al. [10] • Liquid temperature at the bubble • Location of stagnation point top equals that of the stagnation was calculated numerically 2 point in the thermal boundary layer 00 kf hfgqvðT w À T satÞ qONB ¼ ð5Þ 9:2rT sat Celata et al. [11] • ONB occurs when experimental – data deviate from theoretical 00 2 prediction on a pressure vs. qONB ¼ 0:00195ðT w À T satÞ expð0:023pÞð6Þ heat flux plot Basu et al. [12] • Size of available cavity is • Correction factor for cavity proportional to that obtained size obtained from experiments 00 q ¼ hspðT w À T satÞþhspðT sat À T f Þ from superheat criterion • Superheat equation rewritten ONB with corrected cavity size 4rT 8rT k 1=2 T T sat ; D F sat f ð w À satÞ¼ c ¼ 00 Dchfgq hfgq q ð7Þ "#v v w ph 3 ph F ¼ 1 À exp À À 0:5 180 180 Recent work for microchannels Ghiaasiaan and • ONB occurs when thermocapillary • Semi-empirical method developed to Chedester [5] force balances aerodynamic force calculate the shape factor using 2 • Shape factor of contact angle is channel turbulence characteristics 00 kf hfgqvðT w À T satÞ qONB ¼ strongly dependent on the relative and experimental data of incipient CrT sat magnitude of the two forces heat flux 0:765 rf À rw C ¼ 22n ; n ¼ Ã ; ð8Þ • Davis and AndersonÕs correlation q u R D.
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