Prof. Thomas Böhlke
Frederik Hille (M.Sc.)
Johannes Gisy (M.Sc.)

Methodological focus: theory and numerics
Specialisation in mechanics desired

M.Sc. Frederik Hille

Topic Description:
 

Classical models for describing temperature evolution often use the Fourier heat conduction law =- with the heat conduction coefficient, where the heat flow vector is assumed to be proportional to the temperature gradient. For isotropic rigid bodies without heat sources, the parabolic Laplace equation ˙ =Δ, which predicts an unphysical infinite propagation velocity for temperature perturbations, follows as the heat conduction equation. There are several approaches to extend the classical Fourier theory to obtain instead a hyperbolic heat conduction equation with a physical, finite propagation velocity (Müller, 1966; Šilhavý, 1997).
 

The effects of these approaches should first be theoretically analysed by the student in the context of thermodynamics - in particular when evaluating the classical Clausius-Duhem Inequality (CDU). In addition, newly introduced material parameters will be physically interpreted. Subsequently, a numerical implementation in Abaqus is planned in order to obtain and analyse comparable results between the classical and one or more extended approaches.