Thermodynamic compatibility and mechanical analogue of the generalized Jeffreys and generalized Oldroyd-B fluids with fractional derivatives

The study of generalized Jeffreys and generalized Oldroyd-B fluids with fractional derivatives has made rapid progress as an example of applications of fractional calculus in rheology.However,their thermodynamic compatibility and mechanical analogue have not yet been properly considered.In the present study,by discussing both these issues,we find that the two orders of fractional derivatives in the constitutive equation of the generalized Jeffreys fluid must be the same in order to ensure that the equation is physically correct.Based on this generalized Jeffreys fluid,a thermodynamically compatible generalized Oldryd-B fluid is also proposed by the convected coordinates approach.