We examine the local dynamics of nonisothermal viscous flows in the neighborhood of the constant equilibria using the thermomechanically consistent constrained theory for materials with prescribed temperature-dependent density developed by Cao et al.. We discover that the linearized growth rate of small length scale, infinitesimal disturbances near the equilibria is proportional to the reciprocal of their wave length, a classical phenomenon known as the Hadamard instability, indicating the local ill-posedness of the constrained theory. Therefore, the use of the theory to model transient flow phenomenon is not advised. [S0021-8936(00)01901-2]
Ill-Posedness in a Thermomechanically Consistent Constrained Theory for Materials With Prescribed Temperature-Dependent Density
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, July 7, 1998; final revision, June 25, 1999. Associate Technical Editor: D. A. Siginer. Discussion on the paper should be addressed to the Technical Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Wang, Q. (June 25, 1999). "Ill-Posedness in a Thermomechanically Consistent Constrained Theory for Materials With Prescribed Temperature-Dependent Density ." ASME. J. Appl. Mech. March 2000; 67(1): 29–32. https://doi.org/10.1115/1.321148
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