M. Bulicek, M. Pokorny, N. Zamponi:

"Existence analysis for incompressible fluid model of electronically charged chemically reasting and heat conducting mixtures";

in: "ASC Report 04/2017", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2017, ISBN: 978-3-902627-10-0, 1 - 58.

We deal with a three dimensional model based on the use of barycentric velocity that describes unsteady ﬂows of a heat conducting electrically charged multicom-ponent chemically reacting non-Newtonian ﬂuid. We show that under certain assumptions on data and the constitutive relations for such a ﬂuid there exists a global in time and large data weak solution. The paper has two key novelties. The ﬁrst one is that we present a model that is thermodynamically and mechanically consistent and that is able to describe the cross eﬀects in a generality never considered before, i.e., we cover the so-called Soret eﬀect, Dufour eﬀect, Ohm law, Peltier eﬀect, Joul heating, Thompson eﬀect, Seebeck eﬀect and also the generalized Fick law. The second key novelty is that contrary to the previous works on the similar topic, we do not need to deal with the energy equality method and therefore we are able to cover a large range of power-law parameters in the Cauchy-stress. In particular, we cover even the Newtonian case (which is the most used model), for which the existence analysis was missing.

mixtures, non-Newtonian ﬂuid, heat conducting ﬂuid, electrically charged ﬂuid, cross eﬀects, existence of a weak solution

http://www.asc.tuwien.ac.at/preprint/2017/asc04x2017.pdf

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