Pub. Date:
Elsevier Science
Damped Wave Transport and Relaxation

Damped Wave Transport and Relaxation

by Kal Renganathan Sharma


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Product Details

ISBN-13: 9780444519436
Publisher: Elsevier Science
Publication date: 10/01/2005
Pages: 462
Product dimensions: 1.00(w) x 7.00(h) x 10.00(d)

Table of Contents

1. The Damped Wave Conduction and Relaxation Equation.
2. Transient Heat Conduction and Relaxation.
3. Transient Mass Diffusion and Relaxation.

4. Transient Momentum Transfer and Relaxation.

5. Applications.

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Damped Wave Transport and Relaxation 5 out of 5 based on 0 ratings. 1 reviews.
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The papers by Cattaneo and Vernotte that introduced the damped wave conduction and relaxation equation has been cited only 106 and 133 times. Compared with the text by Bird, Stewart and Lightfoot on Transport phenomena which has been cited 4208 times this is small. As pointed out in Sharma, a number of objections to this equation has clouded its wider use. He points out that the use of physically reasonable final steady state time condition as a fourth condition leads to well bounded series solution using the damped wave conduction and relaxation equation. A possible analogy with the viscoelastic spring and dashpot model or the combination of Hooke and Newton leads to a fourth mode of heat transfer - wave conduction. Through worked examples and problems the author shows the time lag, critical length of zero penetration, subcritical damped oscillation well. 15 new dimensionless groups have been introduced. The blow-up found in the Fourier parabolic solution for a semi-infinite slab and finite slab is replaced with a bounded solution when the hyperbolic equation is used. From the free electron theory, the damped wave transport and relaxation equations can be derived. Some of the objections to the use of the equation that stems from second law of thermodynamics can be seen to be unrealistic. For a Clausius inequality violation by use of hyperbolic equation the primary force that causes the drift velocity and acceleration have to be in opposite directions. Acceleration is in the same direction as the force that caused its movement and hence the entropy of the system always increases. Simultaneous reaction and diffusion and relaxation problems have been treated well. Analytical solutions from the method of separation of variables, relativisitc transformation of coordinates, method of complex temperatures, method of Laplace transforms are given. Appendices with Bessel equations, Laplace inversions and the generalized Navier-Stokes equations make the endeavor self-contained. Whereever appproximations are made they are clearly stated and justified. This 2800 equation effort is a treat to transient applications. The cylcling limit and shape limit in nuclear industry will find uses.