The next seminar “Modelling of materials – theory, model reduction and efficient numerical methods” will take place next Wednesday (April 14, 2021) from 9:00 till 10:00. The talk will be given by Josef Málek. Please see the details below.

Speaker: **Josef Málek**

Title: **A thermodynamic framework for heat-conducting flows of a mixture of two fluids**

Abstract: In the lecture, we focus on the development of a model for the heat conducting mixture of two compressible fluids described in the terms of the densities and the velocities for each fluid and the temperature field for the whole mixture. We use a general thermodynamic framework that determines the response of the material from the knowledge of two pieces of information, namely how the material stores the energy and how the energy of material is dissipated. This information is expressed in the form of the constitutive equations for two scalars: the Helmholtz free energy and the entropy production. Additionally, we follow the goal to determine the response of a complex mixture from a small set of material parameters (bulk and shear viscosity, heat conductivity, the drag coefficient) that can be associated with the mixture as the whole. The same thermodynamic approach is used to obtain the model when the whole mixture responses as an incompressible material. Various variants based on different definitions of the velocity of the mixture are considered. The models are developed within the theory of interacting continua. The lecture is based on a joint work with Ondrej Soucek.