In this article, we answer the question of how to optimally design a rarefied gas distribution network from a source point to a given number of equidistant users such that the diameters of the pipes used to carry the fluid fall in the microscale. A slip boundary condition is used to take into account the effects introduced by the smallness of the pipes. By specifying the overall pressure drop across the network, we maximize the total mass flow rate through the dendritic structure under global volume constraint using an evolutionary algorithm. Four complexity levels are considered, , 1, 2, and 3, where is the number of levels of bifurcation present in the structure. The results show that the version of Murray’s law originally proposed in order to determine the optimal diameters of the pipes is not valid when rarefaction is present, since the power-law exponent varies significantly with the number of outlet users . Additionally, the results show that the bifurcation angles decrease in the presence of rarefaction as increases. The article ends by exploring the robustness of nonoptimized complex gas distribution networks.
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1 June 2007
Research Article|
June 04 2007
Constructal microchannel networks of rarefied gas with minimal flow resistance
Louis Gosselin;
Louis Gosselin
a)
Département de Génie Mécanique,
Université Laval, Québec
, Québec, G1K 7P4, Canada
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Alexandre K. da Silva
Alexandre K. da Silva
Department of Mechanical Engineering,
University of Hawaii at Mānoa
, Honolulu, Hawaii 96822
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a)
Author to whom correspondence should be addressed; electronic mail: [email protected]
J. Appl. Phys. 101, 114902 (2007)
Article history
Received:
November 28 2006
Accepted:
February 27 2007
Citation
Louis Gosselin, Alexandre K. da Silva; Constructal microchannel networks of rarefied gas with minimal flow resistance. J. Appl. Phys. 1 June 2007; 101 (11): 114902. https://doi.org/10.1063/1.2721783
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