Ben Zeidman
March 3, 2007
CHEN 610
Journal Article Review: An Improved Model of Heat Transfer
Through Penguin Feathers and Down and
Monte Carlo Simulation of Radiative Heat Transfer in Coarse Fibrous Media
Introduction
Du, et al (2007) published in the Journal of Theoretic Biology a study on heat transfer entitled
An Improved Model of Heat Transfer through Penguin Feathers and Down. Penguin feathers are
lightweight and act as an extremely good insulator for heat transfer. Since the penguins feathers make
up so little of the bird’s mass, a group from the Hong Kong Polytechnic University set out to model why
penguins don’t freeze to death. The potential applications of their study include further work in
materials for clothing and building insulation. The primary algorithm they based their study on came
from an article by Nisipeanu and Jones published the Journal of Heat Transfer entitled Monte Carlo
Simulation of Radiative Heat Transfer in Coarse Fibrous Media. Together these articles offer an
insightful view into theoretical modeling of real life phenomena, particularly with geometry and Monte
Carlo simulation. Both of which are integral parts of my current research.
Model
The study made several assumptions. The Heat transfer was considered to be only due to
conduction and radiation; natural convection was ignored due to a small Rayleigh number. The
equation summarizing the heat flow is given blow:
𝑄𝑡𝑜𝑡𝑎𝑙 = −𝑘
𝑑𝑇(𝑥)
𝑑𝑥
+ 𝐹𝑅 (𝑥) − 𝐹𝑙 (𝑥)
(5)
dT(x)/dx is for the conductive heat flux and FR - Fl stands for radiative heat flow travelling from the right
and left respectively. The feather system was modeled using a Monte Carlo method proposed by
Nisipeanu and Jones. First, a Monte Carlo method is used to generate cylinders in three dimensions
with uniform radii but otherwise random locations in a control domain. Second, the Monte Carlo
routine generates a starting position and vector for a packet of thermal photons. The photon packets
that were able to make it across the control domain were tallied as heat loss. The only downfall
acknowledged by Du, et al, is that the model assumes a uniform feather distribution about the bird
when in reality there are varying distributions to account for feet, beaks, etc.
Experimental and Results
Using another reference in their paper, Du, et al, developed a model based on the Gentoo
Penguin. Two other models based on simple randomly distributed fibrils were also created. The
penguin model had a pattern developed to imitate feathers with a fibril radius of 3µm. The other
models consisted of random fibril distribution, one with radii of 3µm and the other with radii of 10µm
The Monte Carlo photon simulation was run for a total of 1,000,000 photons for each model. The
Monte Carlo results were used to calculate the heat flow and thermal conductance of the models. The
results were summarized in table 3 from the Du, et al, paper:
Model
Total Heat Flow (W/m2)
Thermal Conductance (W/m2 K)
Penguin Feathers (r = 3µm)
34.5
1.725
Random (r = 3 µm)
35.0
1.75
Random (r = 10 µm)
47.2
2.36
Table 3: Numerical results for heat loss and thermal conductance.
The final conclusions reached by the researchers in both papers are that penguin feathers make good
insulators. The ultimate goal of the Du, et al, study was to optimize the method first proposed in
Nisipeanu and Jones. They concluded that it is the fine structure of penguin fibrils that allow for the
insulation.
Conclusions
While the papers scientific goals may leave something to be desired, overall they provided an
insightful method of modeling physical phenomena. In my opinion the fundamental scientific question
being asked, “How do penguins keep from freezing?” seems a little comical and not fully addressed. It is
widely accepted that animals evolve to survive in their environments. Penguins live in cold climates.
Naturally they should develop a coat of feathers that shield them from their harsh environments. In my
opinion, modeling penguin feathers is a waste of resources. I failed to see how gaining insight into
thermal conductivity of penguin feathers advances the stated applications of clothing and building
insulation. Using feathers and down is already a common practice in society. The study validates the
fact that penguin feathers are good insulators but failed to provide any new insights as to why. The
question of how penguin feathers actually work was not addressed.
In my opinion, a study of the structure and composition of the feathers would provide a more
useful tool for the development of insulators and clothing. The models they used were randomly
generated columns that reflected and adsorbed photons. If the structure and composition of the
feathers was more fully explored, significant impact could be made in future development of insulation.
The papers did, however, provide an excellent example of modeling physical phenomena. Both
papers go into significant detail of the generation of their geometric model and the photon generating
process. In relation to my research, anything involving geometry related to “round” material is helpful.
The development of their fibril models gave me new ideas for my research field, models of granular
material. Second, a large portion of my research so far involves Monte Carlo simulation to develop the
models, also a tool I am employing. I particularly enjoyed that both papers developed their equations in
a logical and concise manner that was easy to follow.
While I felt that the papers failed to address any significant scientific issues, they provided an
excellent example of theoretical modeling.
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Works Reviewed
Du, et al. An improved model of heat transfer through penguin feathers and down. Journal of
Theoretical Biology 248 (2007), 727-735.
Nisipaenu, E. and Jones, P. Monte Carlo simulationg of radiative heat transfer in coarse fibrous media.
Journal of Heat Transfer 125 (4), 748-752.
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