In this work we model uncertainty propagation in heat transfer via the multi-element generalized polynomial chaos (ME-gPC) method by focusing on the stochastic heat-transfer enhancement in a two-dimensional grooved channel. Based on the global energy balance, a similar technique as in [1] is employed to develop proper numerical schemes for the fully developed flow. The velocity and temperature field are expressed by the ME-gPC. Using a Galerkin projection, we reduce the stochastic PDE system to a high-dimensional deterministic one, which is solved by the spectral/hp element method. A time, spaced-averaged Nusselt number with error bars is obtained at different excitation frequencies. The probability density function (PDF) of the Nusselt number is also presented.
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ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems
July 17–22, 2005
San Francisco, California, USA
Conference Sponsors:
- Heat Transfer Division and Electronic and Photonic Packaging Division
ISBN:
0-7918-4734-9
PROCEEDINGS PAPER
Simulation of Heat Transfer With Uncertainty
Xiaoliang Wan,
Xiaoliang Wan
Brown University, Providence, RI
Search for other works by this author on:
George Em Karniadakis
George Em Karniadakis
Brown University, Providence, RI
Search for other works by this author on:
Xiaoliang Wan
Brown University, Providence, RI
George Em Karniadakis
Brown University, Providence, RI
Paper No:
HT2005-72530, pp. 947-954; 8 pages
Published Online:
March 9, 2009
Citation
Wan, X, & Karniadakis, GE. "Simulation of Heat Transfer With Uncertainty." Proceedings of the ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. Heat Transfer: Volume 4. San Francisco, California, USA. July 17–22, 2005. pp. 947-954. ASME. https://doi.org/10.1115/HT2005-72530
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