M.Sc Student | Tuval Israel |
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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.