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# APPL STATISTICAL THERMODYNAMIC CHEN 610

Colorado School of Mines

GPA 3.98

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This 5 page Class Notes was uploaded by Rosario Hills on Monday October 5, 2015. The Class Notes belongs to CHEN 610 at Colorado School of Mines taught by David Wu in Fall. Since its upload, it has received 13 views. For similar materials see /class/219622/chen-610-colorado-school-of-mines in Chemical Engineering at Colorado School of Mines.

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Date Created: 10/05/15

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 a 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 dT Qmmz k j FRoc Fla 5 dTxdx is for the conductive heat flux and FR F 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 0 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 3pm The other models consisted of random fibril distribution one with radii of 3pm and the other with radii of 10pm The Monte Carlo photon simulation was run for a total of 1000000 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 Wmz Thermal Conductance Wm2 K Penguin Feathers r 3pm 345 1725 Random r 3 pm 350 175 Random r 10 um 472 236 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 0 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 llHow 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 quotroundquot 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 lam 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 Works Reviewed Du et al An improved model of heat transfer through penguin feathers and down Journal of Theoretical Biology 248 2007 727735 Nisipaenu E and Jones P Monte Carlo simulationg of radiative heat transfer in coarse fibrous media Journal of HeatTransfer 125 4 748752 March 06 2008 Statistical Thermodynamics Theogy 0f Powders SF Edwards and RBS Oakeshott Journal Review Report Introduction The present paper presents a derivation of basic Statistical Mechanics principles to study powder systems The approach was followed given the nature of powders which are formed by a large number of particles ranging from 100 to 1016 ml and still can be completely de ned by a small number of parameters and constructed in a reproducible way by macroscopic means Development The authors start setting up the analogies between the descriptive variables of powders and Stat Mech in order to be able to use the Stat Mech ideas Given that powders are static systems where each of the particles is at rest and in contact with the other particles the energy due to thermal temperature is neglected there is no variation of the particles speed due to changes in T and it is the volume who plays the role of the energy Stat Mech Principles In the regular systems the easiest approach is the microcanonical ensemble constant N V and E where the system takes all possible con gurations with equal probability subject to the Hamiltonian function giving constant E In this case the distribution function as studied in the course is given by is 6 Ab 6E H However experimentally it is easier to use the canonical ensemble given that E is not easy to measure In this ensemble the distribution function is given by the expression below where F refers to the Helmholtz free energy FiH Analogy to powders As mentioned before to describe powders the volume occupied by it is the most useful variable Therefore the function W is introduced which similarly to the Hamiltonian gives the volume of the system based on the coordinates of the particles Besides W the function Q is introduced as well which picks out valid configurations of the particle system particles can t overlap and need to be in a stable state Given the assumption that for a given volume all the configurations are equally probable a table is constructed comparing regular systems with powders Statistical 39 39 Powders H W Kb 1 is is 6 95 H e 55W W 6E 6V T 8 X 3 6791 J eiHKbT 67r J39eeWJX FETS YVXS Alfredo Guariguata As we can see the new variable X is the analogue of the Temperature and measures the uf ness of the powder where X0 represents the most compact powder and Xoo the least On the other hand Y is similar to the free Energy but in this case the free volume or effective volume Overall we can see that the new system for powders has less independent variables Stat mech Powders EESV N vVsN FFTVN YYXN After de ning the analogies between stat mech and the powders theory the authors study the volume of a simple particle powder via two methods In the st one they study a 2 or 3 dimension system by looking at a 1D problem where particles of length a can be separated by a maximum distance b They de ne the volume for the system as well as the phase space available N W xn x7171 a and QH ab xn xH xn xn1 a And calculate the entropy of the system to obtain both the free energy and the volume as ab YN N1X1n1XebW e bW VNLbNAX N cothi 2 2 22X The second approach consists on using a smaller set of variables In this case they consider the compactivity of uniform grains and assume that their contribution to the overall volume will depend on the coordination number where vC is the volume of a particle coordinated with c neighbors and vcc is a correction factor for how different coordinated particles contribute to the volume Then the total volume will be given by 3997 W Zvcnc Z V5511 Or naming each gram 1 W 2v va 0 5539 1 1 Finally analyzing a simple example where there are only 2 types of coordination C0 and C1 the distribution function becomes V 1 YN N lncosh 7 VAX 7 6 AT 26 Eve e voAX 6 v1AXN v0vl VO Vl c10 VNTNv0 vltanh 7 From this formulas it can be calculated the maximum and minimum volume corresponding to X0 and X 00 As we can see both approaches are simpli ed models but let us characterize a powder system using Statistical Mechanics The paper argues that it is needed more detailed information of the local structure for a more realistic theory of powder but gives us the overall picture and connection to Stat Mech Alfredo Guariguata

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