Generalized hydrodynamics and heat waves
Abstract
By using the evolution equations of generalized hydrodynamics we investigate heatpulse propagation in a LennardJones liquid contained in the annulus between two concentric cylinders at different temperatures. It is found that the heat pulse propagates as a wave of a finite speed when a composite fluid dynamic number N(R) that depends on the thermal conductivity and wall temperature ratio is above a critical value, but in the subcritical region the heat pulse propagates diffusively as if predicted by a parabolic differential equation with an infinite speed of propagation. Therefore the question of the hyperbolicity of the system of differential (evolution) equations used is mainly determined by the parameter N(R). This implies that the hyperbolicity of evolution equations, i.e., the finiteness of pulsepropagation speed, cannot be the main reason for extending the thermodynamics of irreversible processes as believed by some authors in the literature.
 Publication:

Canadian Journal of Physics
 Pub Date:
 January 1992
 DOI:
 10.1139/p92006
 Bibcode:
 1992CaJPh..70...62K
 Keywords:

 Heat Flux;
 Heat Transmission;
 Hydrodynamic Equations;
 Knudsen Flow;
 Liquids;
 Concentric Cylinders;
 Hyperbolic Systems;
 LennardJones Potential;
 Momentum Transfer;
 Prandtl Number;
 Fluid Mechanics and Heat Transfer