Conduction of heat in inhomogeneous solids
In this letter we present a method for calculation of linear heat flow in inhomogeneous solids. The method is based on the evaluation of transfer matrices for each layer in a multilayered structure from the Laplace transformation of the partial differential equation of heat conduction. The multilayered structure is then described by a matrix obtained as a chain of products of individual layer transfer matrices and corresponding boundary thermal resistivity matrices. The analytic expression for the nth power of the multilayered transfer matrix is found, describing a periodic multilayered structure composed of n equal multilayered structures. The application of the presented method for calculation of photothermal signals is also shown. Dispersion relation for the thermal waves in inhomogeneous solids is obtained from the matrix elements of the transfer matrix. Finally, from the dispersion relation explicit expressions for the effective values of thermal diffusivity and conductivity of both the discontinuously and continuously inhomogeneous solids are evaluated.
Citation countsare sourced monthly fromand citation databases.
These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science generally from 1980 onwards.
Citations counts from theindexing service can be viewed at the linked Google Scholar™ search.
Full-text downloadsdisplays the total number of times this work’s files (e.g., a PDF) have been downloaded from QUT ePrints as well as the number of downloads in the previous 365 days. The count includes downloads for all files if a work has more than one.
|Item Type:||Journal Article|
|Divisions:||Past > QUT Faculties & Divisions > Faculty of Science and Technology|
|Copyright Owner:||Copyright 1998 American Institute of Physics|
|Copyright Statement:||Reproduced in accordance with the copyright policy of the publisher.|
|Deposited On:||18 Mar 2008|
|Last Modified:||09 Jun 2010 22:57|
Repository Staff Only: item control page