JP Journal of Heat and Mass Transfer
Volume 8, Issue 1, Pages 25 - 67
(August 2013)
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RESOLUTION ALGORITHM BY REANALYSIS COUPLED WITH THE FINITE ELEMENT METHOD FOR UNSTEADY HEAT TRANSFER PROBLEMS
Raouf Khelalfa, Pierre-Olivier Logerais, Youssef Sfaxi and Jean-Félix Durastanti
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Abstract: The optimization of technical data (geometrical, physical) when designing a mechanical or a thermal system is generally a cost-computing stage because it requires numerous testing adjustments and therefore long time calculations when using conventional methods. The problem arises in unsteady heat transfer for the resolution in loop of the heat equation by finite elements. In this paper, a reanalysis algorithm is proposed in order to overcome this time constraint. The presented approach allows to formulate from a decoupling of the phenomenology and the boundary conditions, a general solution to the problem which can then be particularized by taking into account, for example, various boundary conditions. Unlike the known methods, we obtain in this case a system of reduced dimension easier to solve. The approach is applied to the case of the cooling of a furnace. The results obtained by this new procedure are validated by their good agreement with those of a classical resolution. The comparison of these two processes in terms of computation time shows that the reanalysis significantly reduces the duration of the operations especially for sparse meshes, high repetitive resolutions and elevated number of time steps. Therefore, this reanalysis algorithm represents a low cost simulation tool with regard to a standard numerical approach. |
Keywords and phrases: reanalysis, finite elements, unsteady heat conduction, boundary conditions, computing time, iterations. |
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