Analytical solution of pressure driven gas flow and heat transfer in micro-Couette using the Burnett equations
In the current work, an incompressible thermal flow in a micro-Couette in the presence of a pressure gradient is investigated utilizing the analytical solution of the Burnett equations with first-order and second-order slip boundary conditions, for the first time. The lower plate of this micro-Couet...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Semnan University
2018-10-01
|
| Series: | Journal of Heat and Mass Transfer Research |
| Subjects: | |
| Online Access: | https://jhmtr.semnan.ac.ir/article_2702_56d450929f2143ab16e918bf2972a49a.pdf |
| _version_ | 1827316357418450944 |
|---|---|
| author | AhmadReza Rahmati F. Najati |
| author_facet | AhmadReza Rahmati F. Najati |
| author_sort | AhmadReza Rahmati |
| collection | DOAJ |
| description | In the current work, an incompressible thermal flow in a micro-Couette in the presence of a pressure gradient is investigated utilizing the analytical solution of the Burnett equations with first-order and second-order slip boundary conditions, for the first time. The lower plate of this micro-Couette is stationary while the upper plate moves with a constant velocity. Both non-dimensional axial velocity and temperature profiles were obtained using two types of the slip boundary conditions and compared in transition flow regime (0.1≤ Kn ≤10). The results show that the effect of the rarefaction is considerable on both velocity and temperature profiles in this regime. Because of the presence of pressure gradient in direction of the flow, both the non-dimensional velocity and temperature profiles are obtained parabolically and become flatter as the Knudsen number increases. Besides, both Poiseuille number and Nusselt number were obtained using analytical solution. The obtained results show that the Poiseuille number and Nusselt number decrease with increasing the Knudsen number. It should be noted that at the absence of an axial pressure gradient, velocity profile is obtained linearly and show a good agreement with the other works in literature. |
| first_indexed | 2024-04-24T23:13:11Z |
| format | Article |
| id | doaj.art-f02dfd983b1b43f6b1c83e7698a6a85a |
| institution | Directory Open Access Journal |
| issn | 2345-508X 2383-3068 |
| language | English |
| last_indexed | 2024-04-24T23:13:11Z |
| publishDate | 2018-10-01 |
| publisher | Semnan University |
| record_format | Article |
| series | Journal of Heat and Mass Transfer Research |
| spelling | doaj.art-f02dfd983b1b43f6b1c83e7698a6a85a2024-03-17T08:03:21ZengSemnan UniversityJournal of Heat and Mass Transfer Research2345-508X2383-30682018-10-0152879410.22075/jhmtr.2017.1775.11312702Analytical solution of pressure driven gas flow and heat transfer in micro-Couette using the Burnett equationsAhmadReza Rahmati0F. Najati1university of Kashanuniversity of KashanIn the current work, an incompressible thermal flow in a micro-Couette in the presence of a pressure gradient is investigated utilizing the analytical solution of the Burnett equations with first-order and second-order slip boundary conditions, for the first time. The lower plate of this micro-Couette is stationary while the upper plate moves with a constant velocity. Both non-dimensional axial velocity and temperature profiles were obtained using two types of the slip boundary conditions and compared in transition flow regime (0.1≤ Kn ≤10). The results show that the effect of the rarefaction is considerable on both velocity and temperature profiles in this regime. Because of the presence of pressure gradient in direction of the flow, both the non-dimensional velocity and temperature profiles are obtained parabolically and become flatter as the Knudsen number increases. Besides, both Poiseuille number and Nusselt number were obtained using analytical solution. The obtained results show that the Poiseuille number and Nusselt number decrease with increasing the Knudsen number. It should be noted that at the absence of an axial pressure gradient, velocity profile is obtained linearly and show a good agreement with the other works in literature.https://jhmtr.semnan.ac.ir/article_2702_56d450929f2143ab16e918bf2972a49a.pdfburnett equationsknudsen number (kn)micro couettepressure gradientthermal flowtransition regime |
| spellingShingle | AhmadReza Rahmati F. Najati Analytical solution of pressure driven gas flow and heat transfer in micro-Couette using the Burnett equations Journal of Heat and Mass Transfer Research burnett equations knudsen number (kn) micro couette pressure gradient thermal flow transition regime |
| title | Analytical solution of pressure driven gas flow and heat transfer in micro-Couette using the Burnett equations |
| title_full | Analytical solution of pressure driven gas flow and heat transfer in micro-Couette using the Burnett equations |
| title_fullStr | Analytical solution of pressure driven gas flow and heat transfer in micro-Couette using the Burnett equations |
| title_full_unstemmed | Analytical solution of pressure driven gas flow and heat transfer in micro-Couette using the Burnett equations |
| title_short | Analytical solution of pressure driven gas flow and heat transfer in micro-Couette using the Burnett equations |
| title_sort | analytical solution of pressure driven gas flow and heat transfer in micro couette using the burnett equations |
| topic | burnett equations knudsen number (kn) micro couette pressure gradient thermal flow transition regime |
| url | https://jhmtr.semnan.ac.ir/article_2702_56d450929f2143ab16e918bf2972a49a.pdf |
| work_keys_str_mv | AT ahmadrezarahmati analyticalsolutionofpressuredrivengasflowandheattransferinmicrocouetteusingtheburnettequations AT fnajati analyticalsolutionofpressuredrivengasflowandheattransferinmicrocouetteusingtheburnettequations |