Abstract
A framework for linear viscous gradient fluids as extensions of the Navier–Stokes law is derived. More precisely, the list of the independent variables is enlarged up to an Nth-order velocity gradient and, accordingly, also the list of the dependent variables up to dual hyperstress tensors of the same rank. It is shown that due to general invariance requirements, such models must be hemitropic functions. A complete representation for a second-order linear fluid and its balance equation are derived from a dissipation potential. In doing so, we follow Trostel (in: Trostel (ed) Beitrage zu den Ingenieurwissenschaften, Universitats-Bibliothek der Technische Universitat Berlin, Berlin, 96–134, 1985) and coworkers.
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