Non-isothermal non-Newtonian fluids: The stationary case
Maurizio Grasselli, Nicola Parolini, Andrea Poiatti, Marco Verani
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Source: Crossref
Published: May 25, 2023
DOI: 10.1142/s0218202523500410
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The stationary Navier–Stokes equations for a non-Newtonian incompressible fluid are coupled with the stationary heat equation and subject to Dirichlet-type boundary conditions. The viscosity is supposed to depend on the temperature and the stress depends on the strain through a suitable power law depending on [Formula: see text] (shear thinning case). For this problem we establish the existence of a weak solution as well as we prove some regularity results both for the Navier–Stokes and the Stokes cases. Then, the latter case with the Carreau power law is approximated through a FEM scheme and some error estimates are obtained. Such estimates are then validated through some two-dimensional numerical experiments.
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