  We show that the Oldroyd B fluid model is the Eulerian form of a Lagrangian
model with an internal variable that satisfies the second law of thermodynamics
under some conditions on the initial value of the internal variable. We
similarly derive several new nonlinear versions of the Oldroyd B model as well
as Lagrangian formulations of the Zaremba-Jaumann and Oldroyd A fluid models.
We discuss whether or not these other models satisfy the second law.
