# Johannes Kepler Symposium on Mathematics

As part of the Johannes Kepler symposium on mathematics doc. RNDr. Jaroslav Mlynek CSc., Department of Mathematics and Didactics of Mathematics, TU Liberec, will give a public talk (followed by a discussion) on Wed, May 18, 2011 at 15:15 o'clock at HS 13 on the topic of "Optimization of the heat radiation intensity on a mould surface in the car industry" . The organziers of the symposium,

O.Univ.-Prof. Dr. Ulrich Langer,
Univ.-Prof. Dr. Gerhard Larcher
A.Univ.-Prof. Dr. Jürgen Maaß, and
die ÖMG (Österreichische Mathematische Gesellschaft),

hereby cordially invite you.

Series A - General Colloquium:

The intention is to present general information not only to experts, but also to students and guests from outside the mathematical institutes.

### Optimization of the heat radiation intensity on a mould surface in the car industry

This lecture is focused on the calculation of the heat radiation intensity on an aluminium mould surface. The moulds are intended for the production of artificial leather in the car industry (e.g. artificial leather on a car dashboard).

The mould is warmed by infra heaters located above the mould up to temperature 250°C. It is necessary to carry out the configuration of the infra heaters in such way that the heat radiation intensity on the whole mould surface is approximately the same (within the given tolerance) and in such way the same material structure and colour of the artificial leather are ensured. The practical realisation of suitable positioning of the infra heaters above the mould upon the basis of the experience of technicians is rather time-consuming. We will construct a heat radiation model. The mould surface is described by its elementary surfaces. The procedure of heat radiation intensity calculating on a particular mould surface for the respective location of infra heaters will be described in this lecture. Experimental measured values of heat radiation intensity in the surroundings of an infra heater are used for the calculation procedure.

Subsequently we will concentrate on finding suitable locations for the infra heaters to achieve approximately the same heat radiation intensity on the whole mould surface. We will find suitable location for the infra heaters on the basic of genetic algorithm. One individual of a population will represent one possible location of heaters. We will create a specimen and an initial population of individuals in the beginning of genetic algorithm. Subsequently we will generate new individuals of population and we will search individual with suitable evaluation (fitness). We will observe accuracy of the solution in dependence on number of generated individuals.