Int J Thermophys (2010) 31:637–647
DOI 10.1007/s10765-010-0730-z
Propagation of Thermoelastic Waves in Micropolar
Mixture of Porous Media
Baljeet Singh
Received: 24 February 2009 / Accepted: 18 March 2010 / Published online: 2 April 2010
© Springer Science+Business Media, LLC 2010
Abstract The theory of coupled thermoelasticity for a micropolar mixture of porous
media (Eringen AC, J Appl Phys 94:909, 2003) is generalized in the context of Lord
and Shulman and Green and Lindsay theories of generalized thermoelasticity. The
governing equations of generalized thermoelasticity of a micropolar mixture of porous
media are solved to show the existence of three coupled longitudinal displacement
waves, two coupled longitudinal microrotational waves, and six coupled transverse
waves, which attenuate and are dispersive in nature.
Keywords Attenuation · Dispersion · Micropolar mixture ·
Thermal relaxation times · Wave propagation
1 Introduction
Biot [1] formulated the theory of coupled thermoelasticity to eliminate the para-
dox inherent in the classical uncoupled theory that elastic changes have no effect
on the temperature. The heat equations for both coupled and uncoupled theories of the
diffusion type, predicting infinite speeds of propagation for heat waves, are contrary to
physical observations. Hetnarski and Ignaczack [2] examined five generalizations to
the coupled theory and obtained a number of important analytical results. The first gen-
eralized theory of thermoelasticity is due to Lord and Shulman [3] who introduced the
theory of generalized thermoelasticity with one relaxation time by postulating a new
law of heat conduction to replace the classical Fourier law. This new law contains the
heat flux vector as well as its time derivative. It contains also a new constant that acts as
a relaxation time. The heat equation of this theory is of the wave-type, ensuring finite
B. Singh (B )
Department of Mathematics, Post Graduate Government College, Sector 11, Chandigarh 160 011, India
e-mail: dr_baljeet@hotmail.com
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