Geodesic
Optimal Convective Heat-Transport
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 50 (2011) no. 2, pp. 13-18 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $v(x)$.
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 $v(x)$.
Classification : 34B05, 65L10
Keywords: convective heat-transport; two-point convection-diffusion boundary-value problem; optimization of the amount of heat 
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     title = {Optimal {Convective} {Heat-Transport}},
     journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
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Dalík, Josef; Přibyl, Oto. Optimal Convective Heat-Transport. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 50 (2011) no. 2, pp. 13-18. http://geodesic.mathdoc.fr/item/AUPO_2011_50_2_a1/