×

Optimal convective heat-transport. (English) Zbl 1244.76022

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 \(v(x)\).

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76R10 Free convection
65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
80A20 Heat and mass transfer, heat flow (MSC2010)
PDFBibTeX XMLCite
Full Text: EuDML

References:

[1] Deuflhard, P., Weiser, M.: Numerische Matematik 3, Adaptive Lösung partieller Differentialgleichungen. De Gruyter, Berlin, 2011. · Zbl 1230.65093
[2] Ferziger, J. H., Perić, M.: Computational Methods for Fluid Dynamics. Springer, Berlin, 2002, 3rd Edition. · Zbl 0998.76001 · doi:10.1007/978-3-642-56026-2
[3] Kamke, E.: Handbook on Ordinary Differential Equations. Nauka, Moscow, 1971)
[4] Roos, H.-G., Stynes, M., Tobiska, L.: Numerical Methods for Singularly Perturbed Differential Equations. Springer, Berlin, 1996. · Zbl 0844.65075
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.