Transient quasi-static thermal stresses in a bar subject to transverse 2D-Gaussian heating and to lateral cooling

Many of the CERN secondary-particle production targets are plate shaped, and intercept a centred 'slow' extracted (order of ms) primary beam, which heats the material. This heat distribution can be modelled as Gaussian profiles in both the horizontal and vertical transverse planes. Modern techniques such as finite element methods provide fast and reliable analyses of the transient thermal and mechanical response of such a 'slow' process (no dynamic effects). However, it is of interest to compare these results wih those obtained by simplified anlytical calculations which, moreover, allow an easier optimisation of the various geometrical and physical parameters.