Nonclassical continuum theories for fluent media incorporating rotation rates and their thermodynamic consistency

Abstract

AbstractIn this paper, we present three micropolar nonclassical continuum theories (NCCT) for fluent medium in which a material point always has velocities as degrees of freedom, additionally, we consider (i) in the first NCCT, we consider classical or internal rotations rates (known) due to skew‐symmetric part of velocity gradient tensor; (ii) in the second NCCT, we consider rotation rates and Cosserat or microrotation rates (unknown degrees of freedom); (iii) in the third NCCT, we consider Cosserat or microrotation rates only, hence are neglected. Conservation and balance laws (CBL) and the constitutive theories are derived for all three NCCT. We examine consistent choice of kinematic variables, modification of the CBL of classical continuum theories (CCT) due to new physics and determine if the new physics of rotation rates requires additional balance law. All three NCCT derived here are examined for thermodynamic and/or mathematical consistency and are compared with published works. Model problem studies are also presented.