On the differential equation for heat conduction
作者:
S. Simons,
期刊:
Transport Theory and Statistical Physics
(Taylor Available online 1972)
卷期:
Volume 2,
issue 2
页码: 117-128
ISSN:0041-1450
年代: 1972
DOI:10.1080/00411457208232532
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
A discussion based on the Boltzmann equation is given of the way in which the heat-conduction equation C(∂T/∂t) = KV2T must be modified when the temperature T changes appreciably within a mean free path. Assuming a temperature-independent relaxation time τ, a hierarchy of linear equations of increasing accuracy is obtained, of which the first member is the modification C[(∂T/∂t) + τ (∂2T/∂t2)] = = KV2T suggested earlier by many authors. Damped-wave solutions for T are shown to exist over a certain frequency range, and the corresponding dispersion relations are obtained. It is shown that if τ is temperature dependent, the above conduction equation takes the nonlinear form
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