This paper presents an analytical investigation of the thermally developing and periodically fully-developed flow in a parallel-plate channel comprised of superhydrophobic walls. The superhydrophobic walls considered in this paper exhibit alternating micro-ribs and cavities positioned perpendicular to the flow direction and the transport scenario analyzed is that of constant wall heat flux through the rib surfaces with negligible thermal transport through the vapor cavity interface. Axial conduction is neglected in the analysis and the problem is one of Graetz flow with apparent slip-flow and periodicity of constant heating. Closed form solutions for the local Nusselt number and wall temperature are presented and are in the form of infinite series expansions. Previously it has been shown that significant reductions in the overall frictional pressure drop can be expected relative to the classical smooth channel laminar flow. The present results reveal that the overall thermal transport is markedly influenced by the relative cavity region (cavity fraction), the relative rib/cavity module width, and the flow Peclet number. The following conclusions can be made regarding thermal transport for a constant heat flux channel exhibiting the superhydrophobic surfaces considered: 1) Increases in the cavity fraction lead to decreases in the average Nusselt number; 2) Increasing the relative rib/cavity module length yields a decrease in the average Nusselt number; and 3) as the Peclet number increases the average Nusselt number increases. For all parameters explored, the limiting upper bound on the fully-developed average Nusselt number corresponds to the limiting case scenario of classical laminar flow through a smooth-walled channel with constant heat flux.
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ASME/JSME 2011 8th Thermal Engineering Joint Conference
March 13–17, 2011
Honolulu, Hawaii, USA
Conference Sponsors:
- Heat Transfer Division
ISBN:
978-0-7918-3892-1
PROCEEDINGS PAPER
Analysis of Laminar Slip-Flow Thermal Transport in Microchannels With Transverse Rib and Cavity Structured Superhydrophobic Walls at Constant Heat Flux
B. W. Webb,
B. W. Webb
Brigham Young University, Provo, UT
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V. Soloviev
V. Soloviev
Brigham Young University, Provo, UT
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D. Maynes
Brigham Young University, Provo, UT
B. W. Webb
Brigham Young University, Provo, UT
V. Soloviev
Brigham Young University, Provo, UT
Paper No:
AJTEC2011-44113, T10120; 10 pages
Published Online:
March 1, 2011
Citation
Maynes, D, Webb, BW, & Soloviev, V. "Analysis of Laminar Slip-Flow Thermal Transport in Microchannels With Transverse Rib and Cavity Structured Superhydrophobic Walls at Constant Heat Flux." Proceedings of the ASME/JSME 2011 8th Thermal Engineering Joint Conference. ASME/JSME 2011 8th Thermal Engineering Joint Conference. Honolulu, Hawaii, USA. March 13–17, 2011. T10120. ASME. https://doi.org/10.1115/AJTEC2011-44113
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