Course Outline (graduate level):

Advances in Heterogeneous and Hierarchical Media Transport, Multiscale Descriptions and Applications

(Advances in Heterogeneous Media Transport - Hierarchical Multiscale Description)
Instructor: Travkin, V.S.

The objective of this course is to provide students with advanced elements of transport phenomena in heterogeneous media (volume averaging theory - VAT) and treatment of hierarchical multiscale phenomena. The subject of the course will be the description of different physical phenomena that are important to variety of physical disciplines with application to linear, nonlinear and turbulent regime momentum and heat transport in porous media, multiscale problems arising in materials science, in microscale and atomic scale transport phenomena, in electrodynamics, acoustics etc. in heterogeneous media.

Review and development of the governing equations for multi-field phenomenological and stochastic transport processes with focus on thermal physics and fluid mechanics will introduce students to the basics of the physics and mathematics of collective phenomena.

Additional topics to be covered are heat transport in heterogeneous media as semiconductors or piezoelectrics, and how to conduct meaningful experiments to measure effective transport coefficients in heterogeneous media. Several optimization and design applications in thermal physics and materials science will be described using the VAT based mathematical descriptions.

Current applications of VAT to unsolved problems in high temperature superconductivity, fundamentals of ferromagnetism in homogeneous and heterogeneous materials, phase transition and mobility of interface boundaries will be addressed and explained. The major engineering issues of estimation of effective characteristics and coefficients will be emphasized in the course with applications in thermal science. Specific topics include - effective conductivity coefficients, heat exchanger modeling methodologies and design, porous media fluid flow - permeability and flow regimes, experiments over composites and their data reduction.

Required Textbooks: none

Recommended Textbooks:

Travkin, V.S. and Catton, I., Chap. 1, "TRANSPORT PHENOMENA IN HETERO-GENEOUS MEDIA BASED ON VOLUME AVERAGING THEORY", in Advances in Heat Transf er, Vol. 34, pp.1-144, (2001).

Kaviany, M., Principles of Heat Transfer in Porous Media, 2nd. edition, Springer, (1995).

Slattery, J.C., Momentum, Energy and Mass Transfer in Continua, Krieger, Malabar, (1980).

Whitaker, S., Fluid Transport in Porous Media, Computational Mechanics Publications, Southampton, UK, (1997).

Gray, W.G., Leijnse, A., Kolar, R.L., and Blain, C.A., Mathematical Tools for Changing Spatial Scales in the Analysis of Physical Systems, CRC Press, Boca Raton, FL, (1993).


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