On the solution of the heat equation in very thin tapes

This papers addresses two issues usually encountered when simulating thermal processes in forming processes involving tape-type geometries, as is the case of tape or tow placement, surface treatments, ... The first issue concerns the necessity of solving the transient model a huge number of times because the thermal loads are moving very fast on the surface of the part and the thermal model is usually nonlinear. The second issue concerns the degenerate geometry that we consider in which Preprint submitted to Elsevier 10 October 2011 the thickness is usually much lower than the in-plane characteristic length. The solution of such 3D models involving fine meshes in all the directions becomes rapidly intractable despite the huge recent progresses in computer sciences. In this paper we propose to consider a reduced and fully space-time separated representation of the unknown field. This choice allows circumventing both issues allowing the solution of extremely fine models very fast, sometimes in real time.