| Title:
|
Optimal Convective Heat-Transport (English) |
| Author:
|
Dalík, Josef |
| Author:
|
Přibyl, Oto |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
50 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
13-18 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The one-dimensional steady-state convection-diffusion problem for the unknown temperature $y(x)$ of a medium entering the interval $(a,b)$ with the temperature $y_{\min }$ and flowing with a positive velocity $v(x)$ is studied. The medium is being heated with an intensity corresponding to $y_{\max }-y(x)$ for a constant $y_{\max }>y_{\min }$. We are looking for a velocity $v(x)$ with a given average such that the outflow temperature $y(b)$ is maximal and discuss the influence of the boundary condition at the point $b$ on the “maximizing” function $v(x)$. (English) |
| Keyword:
|
convective heat-transport |
| Keyword:
|
two-point convection-diffusion boundary-value problem |
| Keyword:
|
optimization of the amount of heat |
| MSC:
|
34B05 |
| MSC:
|
65L10 |
| idZBL:
|
Zbl 1244.76022 |
| idMR:
|
MR2920704 |
| . |
| Date available:
|
2011-12-16T14:42:32Z |
| Last updated:
|
2013-09-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141749 |
| . |
| Reference:
|
[1] Deuflhard, P., Weiser, M.: Numerische Matematik 3, Adaptive Lösung partieller Differentialgleichungen. De Gruyter, Berlin, 2011. MR 2779847 |
| Reference:
|
[2] Ferziger, J. H., Perić, M.: Computational Methods for Fluid Dynamics. Springer, Berlin, 2002, 3rd Edition. Zbl 0998.76001, MR 1384758 |
| Reference:
|
[3] Kamke, E.: Handbook on Ordinary Differential Equations. Nauka, Moscow, 1971, (in Russian). |
| Reference:
|
[4] Roos, H.-G., Stynes, M., Tobiska, L.: Numerical Methods for Singularly Perturbed Differential Equations. Springer, Berlin, 1996. Zbl 0844.65075, MR 1477665 |
| . |
