The Effect of Random Roughness on the Electromagnetic Flow in a Micropipe
The features of stationary random processes and the small parameter expansion approach are used in this work to examine the impact of random roughness on the electromagnetic flow in cylindrical micropipes. Utilizing the perturbation method, the analytical solution until second order velocity is achi...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-11-01
|
| Series: | Micromachines |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2072-666X/14/11/2054 |
| _version_ | 1797458400792018944 |
|---|---|
| author | Zhili Wang Yanjun Sun Yongjun Jian |
| author_facet | Zhili Wang Yanjun Sun Yongjun Jian |
| author_sort | Zhili Wang |
| collection | DOAJ |
| description | The features of stationary random processes and the small parameter expansion approach are used in this work to examine the impact of random roughness on the electromagnetic flow in cylindrical micropipes. Utilizing the perturbation method, the analytical solution until second order velocity is achieved. The analytical expression of the roughness function <i>ζ</i>, which is defined as the deviation of the flow rate ratio with roughness to the case having no roughness in a smooth micropipe, is obtained by integrating the spectral density. The roughness function can be taken as the functions of the Hartmann number <i>Ha</i> and the dimensionless wave number <i>λ</i>. Two special corrugated walls of micropipes, i.e., sinusoidal and triangular corrugations, are analyzed in this work. The results reveal that the magnitude of the roughness function rises as the wave number increases for the same Ha. The magnitude of the roughness function decreases as the <i>Ha</i> increases for a prescribed wave number. In the case of sinusoidal corrugation, as the wave number <i>λ</i> increases, the Hartmann number <i>Ha</i> decreases, and the value of <i>ζ</i> increases. We consider the <i>λ</i> ranging from 0 to 15 and the <i>Ha</i> ranging from 0 to 5, with <i>ζ</i> ranging from −2.5 to 27.5. When the <i>λ</i> reaches 15, and the <i>Ha</i> is 0, <i>ζ</i> reaches the maximum value of 27.5. At this point, the impact of the roughness on the flow rate reaches its maximum. Similarly, in the case of triangular corrugation, when the <i>λ</i> reaches 15 and the <i>Ha</i> is 0, <i>ζ</i> reaches the maximum value of 18.7. In addition, the sinusoidal corrugation has a stronger influence on the flow rate under the same values of <i>Ha</i> and <i>λ</i> compared with triangular corrugation. |
| first_indexed | 2024-03-09T16:36:34Z |
| format | Article |
| id | doaj.art-c6343f3e6c374f319fe6c06c841ca041 |
| institution | Directory Open Access Journal |
| issn | 2072-666X |
| language | English |
| last_indexed | 2024-03-09T16:36:34Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Micromachines |
| spelling | doaj.art-c6343f3e6c374f319fe6c06c841ca0412023-11-24T14:56:23ZengMDPI AGMicromachines2072-666X2023-11-011411205410.3390/mi14112054The Effect of Random Roughness on the Electromagnetic Flow in a MicropipeZhili Wang0Yanjun Sun1Yongjun Jian2School of Mathematical Science, Inner Mongolia University, Hohhot 010021, ChinaSchool of Mathematical Science, Inner Mongolia University, Hohhot 010021, ChinaSchool of Mathematical Science, Inner Mongolia University, Hohhot 010021, ChinaThe features of stationary random processes and the small parameter expansion approach are used in this work to examine the impact of random roughness on the electromagnetic flow in cylindrical micropipes. Utilizing the perturbation method, the analytical solution until second order velocity is achieved. The analytical expression of the roughness function <i>ζ</i>, which is defined as the deviation of the flow rate ratio with roughness to the case having no roughness in a smooth micropipe, is obtained by integrating the spectral density. The roughness function can be taken as the functions of the Hartmann number <i>Ha</i> and the dimensionless wave number <i>λ</i>. Two special corrugated walls of micropipes, i.e., sinusoidal and triangular corrugations, are analyzed in this work. The results reveal that the magnitude of the roughness function rises as the wave number increases for the same Ha. The magnitude of the roughness function decreases as the <i>Ha</i> increases for a prescribed wave number. In the case of sinusoidal corrugation, as the wave number <i>λ</i> increases, the Hartmann number <i>Ha</i> decreases, and the value of <i>ζ</i> increases. We consider the <i>λ</i> ranging from 0 to 15 and the <i>Ha</i> ranging from 0 to 5, with <i>ζ</i> ranging from −2.5 to 27.5. When the <i>λ</i> reaches 15, and the <i>Ha</i> is 0, <i>ζ</i> reaches the maximum value of 27.5. At this point, the impact of the roughness on the flow rate reaches its maximum. Similarly, in the case of triangular corrugation, when the <i>λ</i> reaches 15 and the <i>Ha</i> is 0, <i>ζ</i> reaches the maximum value of 18.7. In addition, the sinusoidal corrugation has a stronger influence on the flow rate under the same values of <i>Ha</i> and <i>λ</i> compared with triangular corrugation.https://www.mdpi.com/2072-666X/14/11/2054random roughnesselectromagnetic flowroughness functionmicropipe |
| spellingShingle | Zhili Wang Yanjun Sun Yongjun Jian The Effect of Random Roughness on the Electromagnetic Flow in a Micropipe Micromachines random roughness electromagnetic flow roughness function micropipe |
| title | The Effect of Random Roughness on the Electromagnetic Flow in a Micropipe |
| title_full | The Effect of Random Roughness on the Electromagnetic Flow in a Micropipe |
| title_fullStr | The Effect of Random Roughness on the Electromagnetic Flow in a Micropipe |
| title_full_unstemmed | The Effect of Random Roughness on the Electromagnetic Flow in a Micropipe |
| title_short | The Effect of Random Roughness on the Electromagnetic Flow in a Micropipe |
| title_sort | effect of random roughness on the electromagnetic flow in a micropipe |
| topic | random roughness electromagnetic flow roughness function micropipe |
| url | https://www.mdpi.com/2072-666X/14/11/2054 |
| work_keys_str_mv | AT zhiliwang theeffectofrandomroughnessontheelectromagneticflowinamicropipe AT yanjunsun theeffectofrandomroughnessontheelectromagneticflowinamicropipe AT yongjunjian theeffectofrandomroughnessontheelectromagneticflowinamicropipe AT zhiliwang effectofrandomroughnessontheelectromagneticflowinamicropipe AT yanjunsun effectofrandomroughnessontheelectromagneticflowinamicropipe AT yongjunjian effectofrandomroughnessontheelectromagneticflowinamicropipe |