|M.Sc Student||Tuval Israel|
|Subject||A Hybrid Computational Method for Dynamic Thermal Analysis|
in Domains with Thin Layers
|Department||Department of Aerospace Engineering||Supervisors||Professor Dan Givoli|
|Professor Ehud Behar|
Thin layers appear in many applications in the field of aerospace engineering. Examples include external thin coatings of bare panels exposed to periodic solar radiation, the thin glue layer connecting the complex parts in aircraft or satellites, and the coating of fibers inside a reinforced material which are exposed to a sudden thermal shock. The layer has different mechanical and thermal properties from its surroundings and is usually smaller by an order of magnitude from its surrounding media. The two opposite approaches to handle the modeling and analysis of such thin layers are either to ignore the layer or to fully model it, using the Finite Element (FE) method for example. The former approach may suffer from severe inaccuracy, while the latter is time consuming for the human modeler and computationally expensive. Special asymptotic models, that constitute a compromise between these two approaches, have been proposed for linear heat transfer and linear elasticity. In these models the thin layer is replaced by an interface with zero thickness, and specific jump conditions are imposed on this interface in order to represent the special effect of the layer. One such asymptotic interface model is the first-order Bövik-Benveniste model. In a paper by Sussmann et al., this model was incorporated in a FE formulation for linear steady-state heat conduction problems, and was shown to yield an accurate and efficient computational scheme. Here, this work is extended to the time-dependent case. A hybrid asymptotic-FE scheme is proposed for linear transient heat conduction, with either implicit or explicit time stepping. The scheme is developed only for cylindrical geometry, but the extension to general geometry seems straight forward. Since the formulation can easily be symmetrized by one of several techniques, the lack of self-adjointness of the original formulation does not hinder an accurate and efficient solution. The performance of the scheme is demonstrated via numerical examples, and its computational benefits are discussed. While the above work is with regard to the internal layer case, another interesting case is that of an external “coating” layer with a general Robin (mixed) boundary condition, which models linear heat convection. In this case we develop an asymptotic mathematical model for the time dependent problem and in a similar fashion we incorporate it in the FE formulation. The performance of this scheme is also demonstrated via numerical examples.