Seminar on Qualitative Theory of Differential Equations - Patrik Mihala (21.3.2019)
Thursday 21.3.2019 at 14:00, Lecture room M/223
Patrik Mihala:
Solution of direct and inverse problems for transport of water and heat in porous media
Abstract:
We discuss a coupled problem of water flow, heat transport in the water and heat transport in the matrix with heat exchange between the infiltrated water and cylindrical shaped porous media matrix. We include the water expansion which influences the water saturation and viscosity which affects hydraulic permeability. The flow model is based on Richard's strongly non-linear parabolic differential equation based on empirical van Genuchten's model. Heat transport in water is strongly dependent on the water flow and connected to the heat transport in matrix. Numerical modelling includes the direct and inverse solution of the problem, determines model parameters of van Genuchten's model, hydraulic permeability coefficient of fully saturated medium, transverse and longitudinal dispersion coefficient, thermal transmission coefficient in pours, thermal conductivity of porous media matrix and external transmission coefficient. Only simple non-invasive measurements using real 3D sample are required for numerical experiment realisation.