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Thermal Wave Propagation in Helium II


Schlueter, Roger Selig (1969) Thermal Wave Propagation in Helium II. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/3T5S-CN85.


Landau's equations for the two-fluid model of liquid helium II are us ed as the basis for an investigation of the properties of thermal wave propagation. A number of assumptions are made which reduce the four original equations to a system of two non-linear partial differential equations valid to first order in the relative velocity of the two components. These equations are analogous to Riemann's equations which describe pressure waves in a classical fluid.

This system of equations, when reduced to just one space dimension is shown to be hyperbolic and a set of characteristics and invariants is found. A particularly simple, one-dimensional problem is then formulated and an explicit solution is given. This solution is then studied in detail to show the distortion of a temperature pulse as it propagates and also to show effects such as non-linear breaking.

Subsequently, the restrictive assumptions are eliminated individually and the equations are then valid to second order in the relative velocity; the effects of including thermal expansion and using the relative velocity as a thermodynamic variable are given. Also, some effects due to the interaction of first and second sound are investigated. In all cases, the results are compared with other results based on equations differing from the Landau equations and with results found by using perturbation techniques.

Finally, equations based on the same Landau equations are derived and discussed which describe steady state shock (discontinuous) solutions.

Suggestions for further theoretical and experimental work are made.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Engineering
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Engineering and Applied Science
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Hsieh, Din-Yu
Thesis Committee:
  • Unknown, Unknown
Defense Date:13 December 1968
Funding AgencyGrant Number
Alfred P. Sloan FoundationUNSPECIFIED
Record Number:CaltechTHESIS:03312017-093136052
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10121
Deposited By: Benjamin Perez
Deposited On:31 Mar 2017 16:58
Last Modified:09 Nov 2022 19:20

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