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Ordered Rate Constitutive Theories for Non-Classical Thermoviscoelastic Fluids with Internal Rotation Rates

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Document pages: 33 pages

Abstract: The paper presents constitutive theories for non-classical thermoviscoelasticfluids with dissipation and memory using a thermodynamic framework basedon entirety of velocity gradient tensor. Thus, the conservation and the balancelaws used in this work incorporate symmetric as well as antisymmetric part ofthe velocity gradient tensor. The constitutive theories derived here hold in coandcontra-variant bases as well as in Jaumann rates and are derived usingconvected time derivatives of Green’s and Almansi strain tensors as well asthe Cauchy stress tensor and its convected time derivatives in appropriatebases. The constitutive theories are presented in the absence as well as in thepresence of the balance of moment of moments as balance law. It is shownthat the dissipation mechanism and the fading memory in such fluids are dueto stress rates as well as moment rates and their conjugates. The materialcoefficients are derived for the general forms of the constitutive theoriesbased on integrity. Simplified linear (or quasi-linear) forms of the constitutivetheories are also presented. Maxwell, Oldroyd-B and Giesekus constitutivemodels for non-classical thermoviscoelastic fluids are derived and are comparedwith those derived based on classical continuum mechanics. Both,compressible and incompressible thermoviscoelastic fluids are considered.

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