The University of Montana
Department of Mathematical Sciences

Technical report #12/2012

Heat Waves in a Supercritical Fluid

W. R. Derrick
Department of Mathematical Sciences
University of Montana, Missoula, MT 59802
derrick@mso.umt.edu

L. V. Kalachev
Department of Mathematical Sciences
University of Montana, Missoula, MT 59802
kalachev@mso.umt.edu

J. A. Cima
Department of Mathematics
University of North Carolina, Chapel Hill, NC 27599
cima@email.unc.edu

Abstract

Experiments reveal that thermal energy transfers as an acoustic wave near the critical point of a classical fluid under microgravity. In this paper we use asymptotic methods and Fourier analysis to provide a complete mathematical proof of this piston effect. Our two-step method provides a “fast-time” solution describing the piston effect in detail, and a “slow-time” solution leading to solutions that agree in nature with those obtained by numerical methods applied to the original model system on “slow-time” scale.

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