An exact analytical solution to the extended Navier-Stokes equations using the Lambert W function
Microchannel gas flows are of importance in a wide range of microelectro mechanical devices. In these flows, the mean free path of the gas can be comparable to the characteristic length of the microchannel, leading to strong diffusion-enhanced transport of momentum. Numerical solutions to the extend...
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| Format: | Article |
| Language: | en_US |
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Wiley Blackwell
2015
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| Online Access: | http://hdl.handle.net/1721.1/97683 https://orcid.org/0000-0001-8323-2779 |
| _version_ | 1826196261876793344 |
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| author | Jaishankar, Aditya McKinley, Gareth H |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Jaishankar, Aditya McKinley, Gareth H |
| author_sort | Jaishankar, Aditya |
| collection | MIT |
| description | Microchannel gas flows are of importance in a wide range of microelectro mechanical devices. In these flows, the mean free path of the gas can be comparable to the characteristic length of the microchannel, leading to strong diffusion-enhanced transport of momentum. Numerical solutions to the extended Navier–Stokes equations (ENSE) have successfully modeled such microchannel flows. Analytical solutions to the ENSE for the pressure and velocity fields using the Lambert W function are derived. We find that diffusive contributions to the total transport are only dominant for low average pressures and low pressure drops across the microchannel. For large inlet pressures, we show that the expressions involving the Lambert W function predict steep gradients in the pressure and velocity localized near the channel exit. We extract a characteristic length for this boundary layer. Our analytical results are validated by numerical and experimental results available in the literature. |
| first_indexed | 2024-09-23T10:24:07Z |
| format | Article |
| id | mit-1721.1/97683 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:24:07Z |
| publishDate | 2015 |
| publisher | Wiley Blackwell |
| record_format | dspace |
| spelling | mit-1721.1/976832022-09-30T20:50:17Z An exact analytical solution to the extended Navier-Stokes equations using the Lambert W function An analytical solution to the extended Navier-Stokes equations using the Lambert W function Jaishankar, Aditya McKinley, Gareth H Massachusetts Institute of Technology. Department of Mechanical Engineering Massachusetts Institute of Technology. Hatsopoulos Microfluids Laboratory Jaishankar, Aditya McKinley, Gareth H. Microchannel gas flows are of importance in a wide range of microelectro mechanical devices. In these flows, the mean free path of the gas can be comparable to the characteristic length of the microchannel, leading to strong diffusion-enhanced transport of momentum. Numerical solutions to the extended Navier–Stokes equations (ENSE) have successfully modeled such microchannel flows. Analytical solutions to the ENSE for the pressure and velocity fields using the Lambert W function are derived. We find that diffusive contributions to the total transport are only dominant for low average pressures and low pressure drops across the microchannel. For large inlet pressures, we show that the expressions involving the Lambert W function predict steep gradients in the pressure and velocity localized near the channel exit. We extract a characteristic length for this boundary layer. Our analytical results are validated by numerical and experimental results available in the literature. 2015-07-06T17:59:50Z 2015-07-06T17:59:50Z 2014-03 Article http://purl.org/eprint/type/JournalArticle 00011541 1547-5905 http://hdl.handle.net/1721.1/97683 Jaishankar, Aditya, and Gareth H. McKinley. “An Analytical Solution to the Extended Navier-Stokes Equations Using the Lambert W Function.” AIChE Journal 60, no. 4 (March 5, 2014): 1413–1423. https://orcid.org/0000-0001-8323-2779 en_US http://dx.doi.org/10.1002/aic.14407 AIChE Journal Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Wiley Blackwell MIT web domain |
| spellingShingle | Jaishankar, Aditya McKinley, Gareth H An exact analytical solution to the extended Navier-Stokes equations using the Lambert W function |
| title | An exact analytical solution to the extended Navier-Stokes equations using the Lambert W function |
| title_full | An exact analytical solution to the extended Navier-Stokes equations using the Lambert W function |
| title_fullStr | An exact analytical solution to the extended Navier-Stokes equations using the Lambert W function |
| title_full_unstemmed | An exact analytical solution to the extended Navier-Stokes equations using the Lambert W function |
| title_short | An exact analytical solution to the extended Navier-Stokes equations using the Lambert W function |
| title_sort | exact analytical solution to the extended navier stokes equations using the lambert w function |
| url | http://hdl.handle.net/1721.1/97683 https://orcid.org/0000-0001-8323-2779 |
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