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Vietnam Journal of Mathematics 40:1 (2012)
13-30
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Eigenvalue Approach to Two-Temperature
Magneto-Thermoelasticity
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Nantu Sarkar and Abhijit Lahiri
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Department of Mathematics, Jadavpur University,
Kolkata-700032, India
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Received October 28, 2010
Revised November 18, 2011
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Abstract. A generalized thermoelastic theory, in
the context of L-S theory, is used to investigate the two-temperature
magneto-thermoelastic one-dimensional problem for a perfect conducting
infinite medium whose surface is subjected to a thermal shock and is either
considered as (i) traction-free or (ii) laid on a rigid foundation. The
one-dimensional generalized magneto-thermoelastic coupled governing
equations are written into a vector-matrix differential equation by using
Laplace transform techniques and then solved by eigenvalue approach. The
inversion of the transforms solution is carried out numerically in the
space-time domain using Bellman method and illustrated graphically in two
different cases. The effects of applied magnetic field and the two-temperature
parameter on the field variables are studied.
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2000 Mathematics
Subject Classification. 74F15.
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Keywords. Generalized thermoelasticity,
magneto-thermoelasticity, two-temperature parameter, conducting medium,
Laplace transform, eigenvalue.
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Established
by Vietnam Academy of Science and Technology &
Vietnam Mathematical Society
Published by
Springer since January 2013
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