(360a) Study of Local Boiling Heat Transfer for Micro Nano Surface Structures Using a 3D Transient Heat Conduction Model

Corresponding author. E-mail address: hengyi@mail.sysu.edu.cn (Yi Heng)

Inverse heat conduction problems (IHCP) play an important role in both
theory and applications. It has a wide range of applications in different
fields, such as aerospace engineering, chemical engineering and nuclear
engineering [1-2]. In particular, towards the understanding of a complex
nonlinear dynamic process - pool boiling, which is commonly used in chemical
engineering, efficient 3D IHCP solution techniques in the study of boiling heat
transfer mechanism have received more and more attention. Together with the
experimental efforts, the reconstruction of surface heat flux distribution and
information about two-phase vapor-liquid structures above the surface are indispensable for full understanding of boiling
heat transfer in all stages. To this end, many researchers make every effort to
modify surfaces to enhance boiling heat transfer [3]. Wang et al. [4]enhanced
heat transfer performance by improving the wettability of surfaces. Enhancing
boiling heat transfer by using micropores with reentrant cavities and various
microchannel geometries was demonstrated by Deng et al. [5] and Walunj et al. [6],
respectively.

In
order to precisely study the mechanism of enhanced boiling in micro-nano
structures, we consider complex geometric domains (inspired by the micro-nano surface
structures produced in our recent work [7]) to accurately modeling the 3D
transient heat conduction process in pool boiling experiments. We have already
analyzed the forward heat conduction problems for flat-plate surface structures
focusing on the study of the influence of heater thickness on the inverse
solution quality against perturbed temperature measurements [8]. In this work, we
want to extend and use the aforementioned analysis method to investigate how honey-comblike
porous structures (cf. Figure 1) enhance boiling heat transfer.

Figure 1 Produced honey-comblike micro
porous copper surfaces (adopted from [7])

The 3D
transient nonlinear forward heat conduction model defined on the computational
domain constrained by the complex micro-nano surface structures is illustrated
as follows:

where Ω represents the heater
geometry. The observation time is [0, t_f] and n denotes the
outer normal on the boundaries. q_i, q_b and q_r
denote the heat fluxes through the heated boundary, the
boiling surface , and
the rest of the boundaries . , c_p
and  denote
the temperature-dependent density, heat capacity and heat conductivity of the
material, respectively.  represents
the temperature variable and  corresponds
to the initial temperature.

Figure 2 Heater geometries based on the
flat-plate surface structure (c, f, i) and two artificial honey-comblike porous
structures (hexagonal prisms (a, d, g) and cones (b, e, h)

For the
numerical simulations, we consider 9 heaters with the size of 1000um*1000um*130um
(see Figure 2). The length of hexagonal micropores are 80um (Figure 2 (a), (d))
and 40um (Figure 2 (g)). The radius of cone micropores are 80um (Figure 2 (b),
(e)), 40um (Figure 2 (h)) and the depth of pores are all set to be 75 um. All
these geometric settings are based on our recent experiments [7]. Furthermore,
according to the micro-layer theory proposed
by Stephan [9], most of the heat during boiling is transferred in the micro region
of the three-phase contact line (TPCL) by evaporation. Therefore we consider a
ring-shaped boiling heat-flux pattern that has been investigated in our
previous work [8] for the simulation tests. In Figure 2, the areas of TPCL are
marked in blue. The ring width is 16 um, consisting of one part of 8um on the
surface and the other part of 8um on the side of hexagonal and cone micropores.
The simulated input heat flux q_i at  is
set to 0.1 MW/m² and the simulation time is [t₀, t_f]
= [0, 0.05] s. The heat flux out from TPCL complies with

Since the surrounding of heater is
covered by aerogel blanket we assume q_r=0. The maximum heat flux out
from TPCL is set to 10MW/m² following the results from our previous
work Heng et al. [10]. In this study, we conduct
9 simulations considering different pore structures, pore density and local
heat-flux patterns. The initial temperature for all
simulations is set to be 143. While in the cases of Figure 2(a), (b), (c) and (f) we
assume TPCLs randomly occur on the boiling surface that lead to a few
small-sized ring-shaped local boiling heat fluxes. A single, large ring-shaped
boiling heat-flux pattern is investigated in the cases of Figure 2(d), (e), (g),
(h) and (i).

COMSOL Multiphysics
is used for the simulations. The finite elements used for all case studies are chosen
between 1.6 million and 9 million. The simulation time step is 0.001s. Simulation
results of temperature distributions on the heated wall are shown in Figure 3,
Table 1 and Table 2, respectively. The order of the results in Figure 3 follows
that of the case studies shown in Figure 2. While Figure 3 (a), (b), (c) show the
influence of different structures on temperature distributions, Figure 3 (d), (e),
(g), (h) show the simulated temperature distributions as the pore density
increases.

Figure 3 Representative examples of
simulated temperature distributions at t = 0.025s

Furthermore,
Table 1 and Table 2 summarize the temperature variations on the heated wall in
all cases. Due to the increased TPCL areas, at the same level of boiling heat
fluxes, the honey-comblike surface structures (Table 1 (a), (b)) lead to higher
temperature variations on the heated wall than those on the flat-plate
surfaces. As shown in Table 2, we observe that the increasing of pore density
for both hexagonal and cone surface structures (Table 2 (g), (h)) lead to even
higher temperature variations than those using low-density ones (Table 2 (d),
(e)), respectively, which are all higher than those using the flat-plate
surface structure (Table 2 (i)). It is concluded that micro-nano surface
structures can in general lead to high temperature variations and enhance the
local boiling heat transfer. Besides, as discussed in our previous work [8],
higher temperature variations in the temperature measurements can also help
improve the solution accuracy of IHCP in the presence of same level of
measurement error. Hence, the use of micro-nano surface structures shows its
advantages.

Table 1
Temperature variations on the heated wall for the
simulations of a few randomly distributed small-sized ring-shaped
boiling heat fluxes

Table 2 Temperature variations on the heated wall for the
simulations of a single, large ring-shaped boiling heat flux

In
summary, we studied the local boiling heat transfer for micro-nano surface
structures using a 3D transient heat conduction model. The effects of selecting
different surface structures and pore densities on the temperature distribution
results were investigated. Numerical results show the modified micro-nano
surface structures can help enhance local boiling heat transfer, which validated
our experimental studies [7]. One of our future research will be the study of more
complex surface structures containing crystal branches arising from real
experiments. Furthermore, we aim to extend our CG-based Iterative
regularization method [8] to solve 3D transient IHCP that can deal with complex
surface structures. In this way, suitable optimal experimental design
techniques are expected to be developed to optimize the surface preparation procedures
and boiling experiments to further enhance boiling heat transfer.

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