Enhanced pool boiling heat transfer on mini- and micro- structured surfaces

The surfaces used for investigating nucleate pool boiling for four working fluids had mini- and micro-fins of variable configurations, cross-sections and pitches, restrained by perforated foil or mesh cloth with various pore/opening diameters. Unique enhanced structures on these surfaces formed a system of interconnected horizontal and vertical tunnels. Four structured surfaces were proposed, each being a system of subsurface tunnels connected to 10 and 5 mm fins or 1 and 0.5 mm mini-fins. Measurement results for boiling water, ethanol, Fluorinert FC-72 and R-123 from more than 60 samples constituted the database used to verify the proposed theoretical models. These models were based on the results from the visualization studies, including internal visualization allowing observation of bubble nucleation, growth and displacement inside the tunnels, and on the analysis of existing boiling models for mini- and micro-structures.


Introduction
Traditional cooling methods based on natural or forced convection used in thermal management of electronic devices and systems are not capable of achieving the required performance in terms of effective heat removal. Harnessing boiling processes occurring on enhanced surfaces with an adequately formed system of subsurface tunnels is a very effective cooling option. The change of phase that accompanies a boiling process provides high heat fluxes at small temperature differences between the heating surface and the saturated fluid, thus increasing the heat transfer coefficient and reducing the size of heat exchanger.
The author of this paper and his collaborators at the Kielce University of Technology have been carrying out in-depth research devoted to determining pool boiling heat transfer coefficients for various working fluids from surface structures with mini-and micro-fins and/or subsurface tunnels and constructing theoretical models [1][2][3][4][5][6][7]. At the same time, the research team headed by Dr. M. Piasecka is studying flow boiling heat transfer for FC-72 in rectangular minichannels with enhanced heating surfaces [8,9,10].
This article summarizes the results of the analysis of pool boiling from four types of mini-and microstructured surfaces. Three main fins, 5 or 10 mm high (h f ) and 5 mm thick (į f ), with inter-fin space of 5 mm (s), were modified to create tunnels on the vertical surfaces and in the horizontal inter-fin spaces. Perforated copper foil was sintered to the machined surfaces thereby forming a structure of combined U-shaped tunnels. The following variable parameters were used (figure 1): • pore diameters: 0.3 -0.4 -0.5 mm (d p ), • pore pitch: 0.6 -0.8 -1.0 mm (p p =2d p ), • tunnel pitch: 2.0 -2.25 -2.5 mm (p tun ).

Narrow tunnel structure (NTS) surfaces
The main fins, milled through, formed mini-fins with width corresponding to the thickness of the base fins. In addition, an array of interconnected narrow tunnels was obtained, closed with sintered perforated foil (figure 2). Constant parameters of the main fin geometry were identical to those on TS surfaces. Constant tunnel pitch of 2 mm (p tun ) was adopted. Variable parameters of the specimens were as follows:

Mini-fins with porous layer (MF+M/MF+F)
These are structural surfaces formed by sintering the copper wire mesh or perforated foil to the mini-fin tips. The copper specimens, square in shape with a side of 26.5 mm, have 112 mini-fins and form a system of tunnels ( figure 3).

Experimental set-up
The experimental set-up designed for determining boiling curves and heat transfer coefficients was composed of the four modules and systems (figure 4).

Working fluids
The following boiling fluids were used: • fluorinert FC-72 -perfluorohexane or tetradecafluorohexane (C 6 F 14 ).      Figure 5 shows the relationships between heat transfer coefficient and heat flux obtained for 10 mm high main fins. The highest heat transfer coefficients, about 47.5 kW/m 2 K, were noted for the 10 mm fins with tunnels spaced at the highest pitch (2.5 mm) and pores with the largest diameter (0.5 mm).

NTS surfaces -boiling of ethanol
As for ethanol, NTS surfaces are especially advantageous when the main fins are 5 mm high ( figure 6). An increase in heat transfer coefficients for smooth fins (Į/Į sf ) and the NTS-5-0.6-0.3 surface is 3.3 -2.3 in the range of q = 100 -300 kW/m 2 .
The analysis of ethanol boiling curves for NTS surfaces demonstrates the advantages of coatings with pores 0.3 mm in diameter coupled with the narrowest tunnels (0.6 mm). Two-sided supply in the vertical tunnels compensates evaporation of the ethanol, even when the pores are 0.3 mm in diameter. When 1.5 mm wide tunnels are used, perforated foil with 0.5 mm holes provides the tunnel with suitable supply of fluid, precluding it from evaporating. explained by the dry-out of the inter-micro-fin spaces, a condition that precludes boiling crisis.

Examples of boiling visualization
Identification of the phenomena that occur inside the confined space is the necessary condition to meet in order to describe theoretically the boiling process in tunnels, from the initiation to developed nucleate boiling to boiling crisis. To able to analyse nucleate boiling in the complex system of subsurface tunnels, the following data need to be found: the sites of vapour bubble nucleation, growth and departure, the sites of the influx of the fluid into the tunnels, and the sites of determining diameters of the departing bubbles together with their departure frequency.
The visual recording of boiling processes on the surfaces under investigation has been described by the author in several publications [2,4,6]. Examples below illustrate external visualization for the NTS surfaces with 10 mm high main fins.  At minor superheats (figure 8), there is a considerable difference in the number of active vertical tunnel outlets in each main fin. The appearing bubbles had spherical shapes; average bubble departure frequency at 1.8 K superheat can be estimated to have reached 16 Hz. The pores in the horizontal tunnels remained inactive.
With increasing superheat ( figure 9), a larger number of vertical tunnel outlets become active and some of the departing bubbles are irregular in shape. The frequency of bubble departure increases to about 30 Hz. Marked differences in their diameters are observed.

Pool boiling models
Based on the own visualization studies and the existing boiling analytical models, the author proposed the models for boiling from four named above structured surfaces. These models have been thoroughly discussed in [2,4,6].

Model for TS surface [2]
In the semi-analytical model developed by the author, briefly described below, one of the mechanisms accounted for was the fluid evaporation in the corners of the tunnels, associated with the bubble nucleation cycle. This mechanism was considered together with nonisothermity of the main fin, i.e., assumed onedimensional temperature distribution along the vertical tunnel walls. Another mechanism taken into account was that of the nucleation, movement and departure of vapour bubbles, different in vertical and horizontal tunnels. This model enables determining diameters of the departing bubbles, their frequency, density of nucleation sites and the overall heat flux for the system of interconnected subsurface tunnels confined with the perforated foil.

Simplifying assumptions
The boiling mechanism in subsurface tunnels (TSfigures 10, 11) is defined by the following major simplifying assumptions: • the holes in the foil act as elements supplying the surface tunnel structure; • evaporation occurs from the menisci in the four corners of the tunnels; • suction and evaporation occur independently for vertical and horizontal tunnels; • the sites where the bubbles are released, that is, where vapour generated from the menisci in the tunnel corners outflows include: tunnels outlets in vertical tunnels and holes in the foil (pores) in the horizontal tunnels; • bubble formation cycle in vertical and horizontal tunnels comprises a waiting period (Δt 0-1 ), a growth period (Δt 1-2 ) and a period of filling with fluid (Δt 2-3 ) -figure 11.

Heat flux calculation algorithm for the TS surface
These input data were used: • Parameters: geometric, of the boiling fluid and the material of the structure: h tun , w tun , p tun , h f , δ f, , w f , d p , p p , ρ v sat , ρ l, σ, λ v, λ l , i lv , T sat , λ Cu .
• Experimental constants: exponent n in dependence α  In the case of flat, homogeneous surfaces with horizontal tunnels, the model is simplified to the calculation of heat flux only according to the procedure for the surfaces with horizontal tunnels -exponent n necessary in the case of the TS complex structures, do not have to be calculated. The calculations were verified against the literature-based measurement data for tunnel structures for the boiling of R-123 and R-11 (figure 13). Chien-Webb [11], R-123 model TS -Chien-Webb surface [11] Nakayama et al. [12], R-11, C model TS -Nakayama et al. surface [12] Nakayama et al. [13], R-11, T model TS -Nakayama et al. surface [13] C 1-2 = 0.03 Figure 13. Verification of the model for experimental data from publications [11,12,13].

NTS surface model
This model, which is a modification of the one presented in [3], treats the area of the vertical tunnel and the area of adjacent horizontal tunnels jointly. One assumption remained -the holes in the foil are made only to supply the tunnels with fluid. Compared with the TS surface model, here the periods of waiting and growth are calculated in a different manner. To provide for the geometry of the structure, the author modified the Mikic and Rohsenow [14] relationship and introduced his own definition of the area of influence. Additional simplifying assumptions include: • pores in the horizontal tunnels remain inactive -the bubbles form only at the outlets of vertical tunnel, • the overall heat flux, calculated jointly for the horizontal and vertical tunnel, comprises the evaporation heat flux inside the interconnected tunnels and the external heat flux associated with bubble departure. Figure 14 shows the segment of the pitch of the main fins (p f ) and tunnels (p tun ) in relation to which the simplified model was formulated.  In relation to the main fin surface, the spatial domain of influence was defined as a surface covering the front of the fin and its lateral planes ( figure 16). The dependence for the modified area of influence of the departing bubble has the following form Convective (external) heat flux for defined area of influence is the following where ΔT tip is the superheat at the tip of the mini-fin, corresponding to the superheat at the vertical tunnel outlet. The overall heat flux for the surface with narrow tunnels is expressed by

Simplified model for surfaces MF+M/MF+F [6]
The calculation procedure is similar to that discussed in the previous simplified model (NTS). The diameter of the departing bubble was calculated according to (1). The way for the calculation of the waiting period was changed, assuming after Van Stralen et al. [16] that in pure liquids, the waiting period is related to the growth period by To determine the growth period (Δt 1-2 ), d p was substituted for w tun in relationship (3). The value of C 1-2 in this equation was selected through numerical simulation in terms of minimizing errors in the calculation of the frequency of bubble departure and heat flux. Figure 18 presents the comparison of experimental data for Fluorinert with the values of q calculated from the presented model.

Conclusions
• Compared with smooth surfaces, the mini and micro structured surfaces allow a substantial heat flux enhancement and up to seven times higher heat transfer coefficients.
• The presented models provide a prediction of heat flux within ±35% -±40 % error margin for the boiling of water, ethanol and FC-72. Calculations require a selection of two (model for TS) or one experimental constant (NTS and MF+M/MF+F models) in the relationship for the growth period (C 1-2 ).
• These surfaces can be applied to the cooling of elements and systems which generate huge heat fluxes. They can be also used as evaporators of heat pipes or thermosyphons delivering heat to a Stirling engine heater.