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An analytical solution to the extended Navier–Stokes equations using the Lambert W function
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| Zeitschriftentitel: | AIChE Journal |
|---|---|
| Personen und Körperschaften: | , |
| In: | AIChE Journal, 60, 2014, 4, S. 1413-1423 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Wiley
|
| Schlagwörter: |
| author_facet |
Jaishankar, Aditya McKinley, Gareth H. Jaishankar, Aditya McKinley, Gareth H. |
|---|---|
| author |
Jaishankar, Aditya McKinley, Gareth H. |
| spellingShingle |
Jaishankar, Aditya McKinley, Gareth H. AIChE Journal An analytical solution to the extended Navier–Stokes equations using the Lambert W function General Chemical Engineering Environmental Engineering Biotechnology |
| author_sort |
jaishankar, aditya |
| spelling |
Jaishankar, Aditya McKinley, Gareth H. 0001-1541 1547-5905 Wiley General Chemical Engineering Environmental Engineering Biotechnology http://dx.doi.org/10.1002/aic.14407 <jats:p>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 <jats:italic>W</jats:italic> 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. © 2014 American Institute of Chemical Engineers <jats:italic>AIChE J</jats:italic>, 60: 1413–1423, 2014</jats:p> An analytical solution to the extended Navier–Stokes equations using the Lambert <i>W</i> function AIChE Journal |
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| title |
An analytical solution to the extended Navier–Stokes equations using the Lambert W function |
| title_unstemmed |
An analytical solution to the extended Navier–Stokes equations using the Lambert W function |
| title_full |
An analytical solution to the extended Navier–Stokes equations using the Lambert W function |
| title_fullStr |
An analytical solution to the extended Navier–Stokes equations using the Lambert W function |
| title_full_unstemmed |
An analytical solution to the extended Navier–Stokes equations using the Lambert W function |
| title_short |
An analytical solution to the extended Navier–Stokes equations using the Lambert W function |
| title_sort |
an analytical solution to the extended navier–stokes equations using the lambert <i>w</i> function |
| topic |
General Chemical Engineering Environmental Engineering Biotechnology |
| url |
http://dx.doi.org/10.1002/aic.14407 |
| publishDate |
2014 |
| physical |
1413-1423 |
| description |
<jats:p>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 <jats:italic>W</jats:italic> 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. © 2014 American Institute of Chemical Engineers <jats:italic>AIChE J</jats:italic>, 60: 1413–1423, 2014</jats:p> |
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| author | Jaishankar, Aditya, McKinley, Gareth H. |
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| description | <jats:p>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 <jats:italic>W</jats:italic> 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. © 2014 American Institute of Chemical Engineers <jats:italic>AIChE J</jats:italic>, 60: 1413–1423, 2014</jats:p> |
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| spelling | Jaishankar, Aditya McKinley, Gareth H. 0001-1541 1547-5905 Wiley General Chemical Engineering Environmental Engineering Biotechnology http://dx.doi.org/10.1002/aic.14407 <jats:p>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 <jats:italic>W</jats:italic> 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. © 2014 American Institute of Chemical Engineers <jats:italic>AIChE J</jats:italic>, 60: 1413–1423, 2014</jats:p> An analytical solution to the extended Navier–Stokes equations using the Lambert <i>W</i> function AIChE Journal |
| spellingShingle | Jaishankar, Aditya, McKinley, Gareth H., AIChE Journal, An analytical solution to the extended Navier–Stokes equations using the Lambert W function, General Chemical Engineering, Environmental Engineering, Biotechnology |
| title | An analytical solution to the extended Navier–Stokes equations using the Lambert W function |
| title_full | An analytical solution to the extended Navier–Stokes equations using the Lambert W function |
| title_fullStr | An analytical solution to the extended Navier–Stokes equations using the Lambert W function |
| title_full_unstemmed | An analytical solution to the extended Navier–Stokes equations using the Lambert W function |
| title_short | An analytical solution to the extended Navier–Stokes equations using the Lambert W function |
| title_sort | an analytical solution to the extended navier–stokes equations using the lambert <i>w</i> function |
| title_unstemmed | An analytical solution to the extended Navier–Stokes equations using the Lambert W function |
| topic | General Chemical Engineering, Environmental Engineering, Biotechnology |
| url | http://dx.doi.org/10.1002/aic.14407 |