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Young Women in Harmonic Analysis and PDE

December 2-4, 2016

Marija Prša (Faculty of Graphic Arts, Department of Mathematics, University of Zagreb, Croatia)

Heat conduction problem in a dilated pipe

We study the heat conduction through a pipe filled with incompressible viscous fluid. The goal of this work is to take into account the effects of the pipe's dilatation due to the heating. In view of that, we assume that the longitudinal dilatation of the pipe is described by a linear heat expansion law. We prove the existence and uniqueness theorems for the corresponding boundary-value problem. The main difficulty comes from the fact that the flow domain changes depending on the solution of the heat equation leading to a non-standard coupled governing problem. This is a joint work with Eduard Marušić-Paloka and Igor Pažanin from University of Zagreb.