Non-linear dynamical analyses of transient surface temperature ﬂuctuations during subcooled pool boiling on a horizontal disk Vijaykumar Sathyamurthi, Debjyoti Banerjee * Department of Mechanical Engineering, Texas A&M University, 3123, TAMU, College Station, TX 77843-3123, USA article info Article history: Received 20 December 2007 Received in revised form 1 May 2009 Available online 27 July 2009 Keywords: Boiling Thin ﬁlm thermocouples Correlation dimension Critical heat ﬂux Leidenfrost point Mutual information Chaos abstract The class of dynamics in pool boiling on a large-size heater is assessed under subcooled pool boiling con- ditions. Transient surface temperature measurements are obtained using surface micro-machined K-type thin ﬁlm thermocouples (TFT) in 10 °C subcooled pool boiling experiments on a 62.23 mm diameter silicon wafer using PF-5060 as the test liquid. Surface temperature data is obtained at each steady state condition to generate the boiling curve. The fraction of false-nearest neighbors, recurrence plots and space–time separation plots are obtained using the TISEAN package. The correlation dimension is then estimated from the re-constructed phase space data using a naïve algorithm. The correlation dimension varies from 11.2 to 11.5 near onset of nucleate boiling (ONB), to 7–10 in fully developed nucleate boil- ing (FDNB) 7–9 near critical heat ﬂux (CHF) condition, and from 6.6 to 7.7 in ﬁlm boiling. False-nearest neighbor estimates and recurrence plots show that nucleate boiling may be dominated by statistical pro- cesses near ONB and in partial nucleate boiling (PNB). In contrast, FDNB, CHF and ﬁlm boiling seem cha- otic and governed by deterministic processes. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction Pool boiling heat transfer is inﬂuenced by a number of transport processes with coupled parameters [1]. Understanding the dynam- ics of underlying transport mechanisms is vital to its applicability to new practical applications such as electronic chip cooling [2]. Extensive theoretical and experimental studies have been carried out to determine the factors inﬂuencing nucleation site activation and bubble dynamics [3]. Processes affecting the boiling processes include heater surface characteristics, the type of ﬂuid and the spa- tio-temporal variations of solid–liquid–vapor interfaces [4]. Earlier efforts [5] in this ﬁeld employed spatially and temporally averaged data in developing models to predict the heat ﬂuxes. The impor- tance of measuring surface temperatures with adequate spatial and temporal resolution in pool boiling systems has recently gained emphasis [6,7]. Micro-fabrication techniques can provide the necessary spatio-temporal resolution needed for a thorough understanding of the phase change process. Recently, Myers et al. [8] used a micro-heater and a high-speed camera to obtain spa- tio-temporally resolved temperature and heat ﬂux measurements in pool boiling of FC-72. Harris and Johnson in [9] reported the concept of thin ﬁlm thermo- couples in the 1930s. Marshall et al. [10] studied various combina- tions of thermocouple elements. Bullis [11], Assanis and Friedmann [12], Debey et al. [13], Tian et al. [14], and Laugier [15] used thin ﬁlm thermocouples (TFT) for various surface temperature measurements. TFT possess excellent high frequency response [16] due to its low thermal inertia. They can be fabricated at locations where a wire-bead thermocouple would interfere in the normal functioning of the object. Furthermore, the minimal thermal inertia and small feature size leads to a reduced distortion of the temperature and velocity ﬁelds in its vicinity. Ahn et al. [17] used thin ﬁlm thermocouples to measure the surface temperature ﬂuctuations in ﬁlm boiling in order to verify the presence of cold spots. Lüttich and others [6,7], recently used mi- cro-machined TFT to estimate the surface temperature and heat ﬂux ﬂuctuations in pool boiling. However, the TFT was covered with a sputtered layer of gold 0.001 mm in thickness leading once again to an indirect estimation of surface temperature and heat ﬂuxes. In the past decade alternative approaches to understanding pool boiling mechanisms has emerged. It has been suggested that a pool boiling system is dissipative and therefore chaotic [18– 21]. Dynamical systems that are chaotic have strange attractors. Strange attractors are those patterns that characterize the ﬁnal state of dissipative system [22]. The characterization of geometri- cal aspects of these strange attractors serves as a measure of the number of parameters required to describe the system. Strange attractors are found to possess fractal geometry and hence are characterized by fractal dimensions, which may or may not be a whole number (positive). High-dimensional experimental systems are known to possess low dimensional attractors [23]. Grassberger and Procaccia [24] suggested the use of a measure closely related 0017-9310/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2009.06.023 * Corresponding author. Tel.: +1 979 845 4500; fax: +1 979 845 3081. E-mail address: dbanerjee@tamu.edu (D. Banerjee). International Journal of Heat and Mass Transfer 52 (2009) 5608–5623 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt