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We show that the Oldroyd B fluid model is the Eulerian form of a Lagrangianmodel with an internal variable that satisfies the second principle ofthermodynamics under some conditions on the initial value of the internalvariable. We similarly derive a compressible version of the Oldroyd B model andseveral nonlinear versions thereof. We also derive Lagrangian formulations ofthe Zaremba-Jaumann and Oldroyd A fluid models. We discuss whether or not thesenew models satisfy the second principle.

A Lagrangian formulation for the Oldroyd B fluid and the second principle of thermodynamics