Viscous dissipation effects on thermal entrance region heat transfer in pipes with uniform wall heat flux
| ISSN: |
1573-1987
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|---|---|
| Source: |
Springer Online Journal Archives 1860-2000
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| Topics: |
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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| Notes: |
Abstract The analytical solution to Graetz problem with uniform wall heat flux is extended by including the viscous dissipation effect in the analysis. The analytical solution obtained reduces to that of Siegel, Sparrow and Hallman neglecting viscous dissipation as a limiting case. The sample developing temperature profiles, wall and bulk temperature distributions and the local Nusselt number variations are presented to illustrate the viscous dissipation effects. It is found that the role of viscous dissipation on thermal entrance region heat transfer is completely different for heating and cooling at wall. In the case of cooling at wall, a critical value of Brinkman number, Br c=−11/24, exists beyond which (−11/24〈Br〈0) the fluid bulk temperature will always be less than the uniform entrance temperature indicating the predominance of cooling effect over the viscous heating effect. On the other hand, with Br 〈 Br c the bulk temperature T b will approach the wall temperature T w at some downstream position and from there onward the bulk temperature T b becomes less than the wall temperature T w with T w 〉 B b 〉 T 0 indicating overall heating effect for the fluid. The numerical results for the case of cooling at wall Br 〈 0 are believed to be of some interest in the design of the proposed artctic oil pipeline.
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| Type of Medium: |
Electronic Resource
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| URL: |
| _version_ | 1798296630058811392 |
|---|---|
| autor | Ou, J. W. Cheng, K. C. |
| autorsonst | Ou, J. W. Cheng, K. C. |
| book_url | http://dx.doi.org/10.1007/BF00413074 |
| datenlieferant | nat_lic_papers |
| hauptsatz | hsatz_simple |
| identnr | NLM192986422 |
| issn | 1573-1987 |
| journal_name | Flow, turbulence and combustion |
| materialart | 1 |
| notes | Abstract The analytical solution to Graetz problem with uniform wall heat flux is extended by including the viscous dissipation effect in the analysis. The analytical solution obtained reduces to that of Siegel, Sparrow and Hallman neglecting viscous dissipation as a limiting case. The sample developing temperature profiles, wall and bulk temperature distributions and the local Nusselt number variations are presented to illustrate the viscous dissipation effects. It is found that the role of viscous dissipation on thermal entrance region heat transfer is completely different for heating and cooling at wall. In the case of cooling at wall, a critical value of Brinkman number, Br c=−11/24, exists beyond which (−11/24〈Br〈0) the fluid bulk temperature will always be less than the uniform entrance temperature indicating the predominance of cooling effect over the viscous heating effect. On the other hand, with Br 〈 Br c the bulk temperature T b will approach the wall temperature T w at some downstream position and from there onward the bulk temperature T b becomes less than the wall temperature T w with T w 〉 B b 〉 T 0 indicating overall heating effect for the fluid. The numerical results for the case of cooling at wall Br 〈 0 are believed to be of some interest in the design of the proposed artctic oil pipeline. |
| package_name | Springer |
| publikationsjahr_anzeige | 1973 |
| publikationsjahr_facette | 1973 |
| publikationsjahr_intervall | 8029:1970-1974 |
| publikationsjahr_sort | 1973 |
| publisher | Springer |
| reference | 28 (1973), S. 289-301 |
| search_space | articles |
| shingle_author_1 | Ou, J. W. Cheng, K. C. |
| shingle_author_2 | Ou, J. W. Cheng, K. C. |
| shingle_author_3 | Ou, J. W. Cheng, K. C. |
| shingle_author_4 | Ou, J. W. Cheng, K. C. |
| shingle_catch_all_1 | Ou, J. W. Cheng, K. C. Viscous dissipation effects on thermal entrance region heat transfer in pipes with uniform wall heat flux Abstract The analytical solution to Graetz problem with uniform wall heat flux is extended by including the viscous dissipation effect in the analysis. The analytical solution obtained reduces to that of Siegel, Sparrow and Hallman neglecting viscous dissipation as a limiting case. The sample developing temperature profiles, wall and bulk temperature distributions and the local Nusselt number variations are presented to illustrate the viscous dissipation effects. It is found that the role of viscous dissipation on thermal entrance region heat transfer is completely different for heating and cooling at wall. In the case of cooling at wall, a critical value of Brinkman number, Br c=−11/24, exists beyond which (−11/24〈Br〈0) the fluid bulk temperature will always be less than the uniform entrance temperature indicating the predominance of cooling effect over the viscous heating effect. On the other hand, with Br 〈 Br c the bulk temperature T b will approach the wall temperature T w at some downstream position and from there onward the bulk temperature T b becomes less than the wall temperature T w with T w 〉 B b 〉 T 0 indicating overall heating effect for the fluid. The numerical results for the case of cooling at wall Br 〈 0 are believed to be of some interest in the design of the proposed artctic oil pipeline. 1573-1987 15731987 Springer |
| shingle_catch_all_2 | Ou, J. W. Cheng, K. C. Viscous dissipation effects on thermal entrance region heat transfer in pipes with uniform wall heat flux Abstract The analytical solution to Graetz problem with uniform wall heat flux is extended by including the viscous dissipation effect in the analysis. The analytical solution obtained reduces to that of Siegel, Sparrow and Hallman neglecting viscous dissipation as a limiting case. The sample developing temperature profiles, wall and bulk temperature distributions and the local Nusselt number variations are presented to illustrate the viscous dissipation effects. It is found that the role of viscous dissipation on thermal entrance region heat transfer is completely different for heating and cooling at wall. In the case of cooling at wall, a critical value of Brinkman number, Br c=−11/24, exists beyond which (−11/24〈Br〈0) the fluid bulk temperature will always be less than the uniform entrance temperature indicating the predominance of cooling effect over the viscous heating effect. On the other hand, with Br 〈 Br c the bulk temperature T b will approach the wall temperature T w at some downstream position and from there onward the bulk temperature T b becomes less than the wall temperature T w with T w 〉 B b 〉 T 0 indicating overall heating effect for the fluid. The numerical results for the case of cooling at wall Br 〈 0 are believed to be of some interest in the design of the proposed artctic oil pipeline. 1573-1987 15731987 Springer |
| shingle_catch_all_3 | Ou, J. W. Cheng, K. C. Viscous dissipation effects on thermal entrance region heat transfer in pipes with uniform wall heat flux Abstract The analytical solution to Graetz problem with uniform wall heat flux is extended by including the viscous dissipation effect in the analysis. The analytical solution obtained reduces to that of Siegel, Sparrow and Hallman neglecting viscous dissipation as a limiting case. The sample developing temperature profiles, wall and bulk temperature distributions and the local Nusselt number variations are presented to illustrate the viscous dissipation effects. It is found that the role of viscous dissipation on thermal entrance region heat transfer is completely different for heating and cooling at wall. In the case of cooling at wall, a critical value of Brinkman number, Br c=−11/24, exists beyond which (−11/24〈Br〈0) the fluid bulk temperature will always be less than the uniform entrance temperature indicating the predominance of cooling effect over the viscous heating effect. On the other hand, with Br 〈 Br c the bulk temperature T b will approach the wall temperature T w at some downstream position and from there onward the bulk temperature T b becomes less than the wall temperature T w with T w 〉 B b 〉 T 0 indicating overall heating effect for the fluid. The numerical results for the case of cooling at wall Br 〈 0 are believed to be of some interest in the design of the proposed artctic oil pipeline. 1573-1987 15731987 Springer |
| shingle_catch_all_4 | Ou, J. W. Cheng, K. C. Viscous dissipation effects on thermal entrance region heat transfer in pipes with uniform wall heat flux Abstract The analytical solution to Graetz problem with uniform wall heat flux is extended by including the viscous dissipation effect in the analysis. The analytical solution obtained reduces to that of Siegel, Sparrow and Hallman neglecting viscous dissipation as a limiting case. The sample developing temperature profiles, wall and bulk temperature distributions and the local Nusselt number variations are presented to illustrate the viscous dissipation effects. It is found that the role of viscous dissipation on thermal entrance region heat transfer is completely different for heating and cooling at wall. In the case of cooling at wall, a critical value of Brinkman number, Br c=−11/24, exists beyond which (−11/24〈Br〈0) the fluid bulk temperature will always be less than the uniform entrance temperature indicating the predominance of cooling effect over the viscous heating effect. On the other hand, with Br 〈 Br c the bulk temperature T b will approach the wall temperature T w at some downstream position and from there onward the bulk temperature T b becomes less than the wall temperature T w with T w 〉 B b 〉 T 0 indicating overall heating effect for the fluid. The numerical results for the case of cooling at wall Br 〈 0 are believed to be of some interest in the design of the proposed artctic oil pipeline. 1573-1987 15731987 Springer |
| shingle_title_1 | Viscous dissipation effects on thermal entrance region heat transfer in pipes with uniform wall heat flux |
| shingle_title_2 | Viscous dissipation effects on thermal entrance region heat transfer in pipes with uniform wall heat flux |
| shingle_title_3 | Viscous dissipation effects on thermal entrance region heat transfer in pipes with uniform wall heat flux |
| shingle_title_4 | Viscous dissipation effects on thermal entrance region heat transfer in pipes with uniform wall heat flux |
| sigel_instance_filter | dkfz geomar wilbert ipn albert fhp |
| source_archive | Springer Online Journal Archives 1860-2000 |
| timestamp | 2024-05-06T09:55:08.844Z |
| titel | Viscous dissipation effects on thermal entrance region heat transfer in pipes with uniform wall heat flux |
| titel_suche | Viscous dissipation effects on thermal entrance region heat transfer in pipes with uniform wall heat flux |
| topic | ZL |
| uid | nat_lic_papers_NLM192986422 |