I would like a thermal conductivity model of low thermal conductivity nanofibers that combined of solid conduction and gas conduction and radiation. Can I obtain this model from the experimental result?
The theory of thermal conductivity is treated in some detail by J.M. Ziman in his celebrated book Electrons and Phonons: The Theory of Transport Phenomena in Solids (The Clarendon Press, Oxford, 1960). A much more concise treatment of the subject matter can be found in Chapter 25 of the book Solid State Physics, by Ashcroft and Mermin. In essence, the energies of the phonon modes of the (electrically insulating) system under consideration are to be calculated (consider for instance Eqs (25.31) and (25.38) in the latter book). If you consider the attached article, then you will notice that for this task the authors use the empirical Lennard-Jones potential to describe the interaction of the underlying atoms.
http://arxiv.org/ftp/arxiv/papers/1408/1408.0824.pdf
The theory of thermal conductivity is treated in some detail by J.M. Ziman in his celebrated book Electrons and Phonons: The Theory of Transport Phenomena in Solids (The Clarendon Press, Oxford, 1960). A much more concise treatment of the subject matter can be found in Chapter 25 of the book Solid State Physics, by Ashcroft and Mermin. In essence, the energies of the phonon modes of the (electrically insulating) system under consideration are to be calculated (consider for instance Eqs (25.31) and (25.38) in the latter book). If you consider the attached article, then you will notice that for this task the authors use the empirical Lennard-Jones potential to describe the interaction of the underlying atoms.
http://arxiv.org/ftp/arxiv/papers/1408/1408.0824.pdf
You may use the Heat Atlas edited by Prof. Schluender. There you find methods for calculating the three terms of heat Transfer: Radiation, convection and conduction. Anyway, if the gaseous Phase is the continuous one, the conductivity of the gas plays a major role in the overall conductivity, e.g. the conductivity in the article appended is close to this of air.
1. E.Ya. Litovsky, M. Shapiro. Gas Pressure and Temperature Dependences of Thermal Conductivity Porous Ceramic Materials. Part I. Refractories and Ceramics with porosity below 30%, J. American Ceram Soc. 75 [12], pp. 3425-3439, (1992).
2. Litovsky E., M. Shapiro, A. Shavit, “Gas pressure and temperature dependences of thermal conductivity porous ceramic materials. Part II. Refractories and ceramics with porosity above 30%”, J. American Ceram. Soc., 79/5, 1996 1366-1376.
3. Litovsky E., T. Gambaryan-Roisman, M. Shapiro, A. Shavit, “Effect of Grain Thermal Expansion Mismatch on Thermal Conductivity of Porous Ceramics”, J. American Ceram. Soc. , vol 82, No 4, pp 994-1000, 1999.
4. Litovsky E., Gambaryan-Roisman T., Shapiro M. and Shavit A, Heat Transfer Mechanisms Governing Thermal Conductivity of Porous Materials, Trends in Heat, Mass & Momentum Transfer, Research Trends, Invited, Vol. 3, pp 147-167, 1997.
5. Litovsky E., Gambaryan-Roisman T., Shapiro M., Shavit A., “Novel heat transfer mechanisms in porous ceramic materials”, High Temperatures-High Pressures, 1(33): 2001, pp. 27-34.
Is there a mathematical relationships between the diffusivity and specific heat and thermal conductivity and density of concrete? - ResearchGate. Available from: https://www.researchgate.net/post/Is_there_a_mathematical_relationships_between_the_diffusivity_and_specific_heat_and_thermal_conductivity_and_density_of_concrete [accessed Aug 28, 2015].
To fit a model into the experimental data this method might be usefull:
http://www.jatm.com.br/ojs/index.php/jatm/article/view/373/373
Article On Using Quasi-Newton Algorithms of the Broyden Class for Mo...
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