The modeling of thermal expansion: Instability of constrained theories and constitutive limits

Qi Wang
Department of Mathematics
Indiana University-Purdue University

Abstract: The stability of the rest state of a Newtonian fluid subjected to small perturbations is examined. For unconstrained materials the rest state is found to be stable but when the density of the fluid is constrained to be a function of temperature along the rest state becomes unstable. We suggest a possible remedy for this situation, considering density to be a function of the specific entropy. We consider these constrained situations as limits of the unconstrained case and show the connection between the two types of constraints.