Abstract
We study the system of equations describing a stationary thermoconvective flow of a non-Newtonian fluid. We assume that the stress tensor S has the form
\(\displaystyle \mathbf{S}=-P\mathbf{I}+\left( \mu (\theta )+\tau (\theta ){|\mathbf{D(u)}|}^{p(\theta )-2}\right) {\mathbf{D(u)}}, \)
where u is the vector velocity, P is the pressure, θ is the temperature and μ ,p and τ are the given coefficients depending on the temperature. D and I are respectively the rate of strain tensor and the unit tensor. We prove the existence of a weak solution under general assumptions and the uniqueness under smallness conditions.
Keywords: Non-Newtonian fluids, Nonlinear thermal diffusion equations, Heat and mass transfer
Mathematics Subject Classification (2000): 76A05, 76D07, 76E30, 35G15
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Antontsev, S.N., Rodrigues, J.F. On stationary thermo-rheological viscous flows. Ann. Univ. Ferrara 52, 19–36 (2006). https://doi.org/10.1007/s11565-006-0002-9
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DOI: https://doi.org/10.1007/s11565-006-0002-9