COLLOQUIUM
Modeling the Microstructure of the
Temperature Field and the
Effective Properties of Heat
Conduction through Polydisperse
Spherical Suspensions
Dr. Abhinandan Chowdhury
Department of Mathematics
Western Illinois University
Abstract
A practically important issue is to find the expressions for the
effective transport coefficients of suspensions which comprise
particles (the filler) randomly dispersed throughout a continuous
phase of different material properties. For the case of heat
conduction in polydisperse spherical suspension, we have used the
method of Random Point functions based on truncated VolterraWiener Expansion (VWE). It is shown that the effect of the filler is
related to the one-sphere and two-sphere solutions in a field with
a constant gradient at infinity. For finding the two-sphere solution,
bi-spherical coordinates are used. A transformation of the
dependent variable is used that leads to separation of variables
allowing the use of Legendre's series with exponential
convergence. Obtained results outline the quantitative importance
of the second order terms in the VWE. The first-order VWE method
is again applied for identifying the response of the effective heat
flux to temporal changes of the averaged temperature gradient.
The boundary value problem for the time dependent first-order
kernel is solved by the Laplace transform method. The result
shows that the constructive relationship between the average flux
and the averaged temperature gradient involves a convolution
integral representing the memory due to the heterogeneity of the
system.
Department of
Mathematics
Thursday,
December 4, 2010
4:00 p.m.
204 Morgan Hall
Refreshments will be
served at 3:45 p.m.