The one-dimensional steady-state convection-diffusion problem for the unknown temperature $y\left(x\right)$ of a medium entering the interval $(a,b)$ with the temperature $y_{min}$ and flowing with a positive velocity $v\left(x\right)$ is studied. The medium is being heated with an intensity corresponding to $y_{max}-y\left(x\right)$ for a constant $y_{max}>y_{min}$. We are looking for a velocity $v\left(x\right)$ with a given average such that the outflow temperature $y\left(b\right)$ is maximal and discuss the influence of the boundary condition at the point $b$ on the “maximizing” function $v\left(x\right)$.

Advanced building design is a rather new interdisciplinary research branch, combining knowledge from physics, engineering, art and social science; its support from both theoretical and computational mathematics is needed. This paper shows an example of such collaboration, introducing a model problem of optimal heating in a low-energy house. Since all particular function values, needed for optimization are obtained as numerical solutions of an initial and boundary value problem for a sparse system...

In the contribution we present a problem of shape optimization of the cooling cavity of a plunger that is used in the forming process in the glass in dustry. A rotationally symmetric system of the mould, the glass piece, the plunger and the plunger cavity is considered. The state problem is given as a stationary heat conduction process. The system includes a heat source representing the glass piece that is cooled from inside by water flowing through the plunger cavity and from outside by the environment surrounding...