The modelling of the heat conduction in electrical cables is a complex mathematical problem. To get a quantitative description of the thermo‐electrical characteristics in the electrical cables, one requires a mathematical model for it. It must involve the different physical phenomena occurring in the electrical cables, i.e. heat conduction, convection and radiation effects, description of heat sources due to current transitions. Since the space in mobile systems is limited and weight is always reduced, wire conductor sizes must be kept as small as possible. Thus the main aim is to determine optimal conductor cross‐sections for long standing loads. In this paper we develop and validate a set of mathematical models and numerical algorithms for the heat transfer simulation in cable bundles. The numerical algorithms are targeted to the two‐dimensional transient heat transfer mathematical models. Finally, a validation procedure for the coefficient validation of the differential equations is carried out. Results of numerical experiments are presented.

Tape stripping is a standard measuring method for the investigation of the dermatopharmacokinetics of topically applied substances using adhesive films. These tape strips are successively applied and removed from the skin after application and penetration of topically applied substances. Thus, layers of corneocytes and some amount of topical applied substances are removed. The amount of substances and the amount of stratum corneum removed with a single tape strip has to be determined for the calculation of the penetration profile. The topically applied substances removed from the skin can be determined by classical analytical methods like high-pressure liquid chromatography, mass spectroscopy, and spectroscopic measurements. The amount of corneocytes on the tape strips can be easily detected by their pseudoabsorption. In the present paper, an easy and cheap corneocyte density analyzer is presented that is based on a slide projector. Comparing the results of the measurements obtained by the corneocyte density analyzer and by uv-visible spectrometry, identical results were obtained.

The usual wire rating problem is to compute the permissible conductor current so, that the maximum conductor temperature does not exceed a specified value. When numerical methods are used to determine wire rating, an iterative approach has to be used for this purpose. This is accomplished by specifying a certain conductor current and computing the corresponding conductor temperature. The electrical fuse rating problem is to calculate the melting behavior and to match thermo‐electrical characteristic of the wire and fuse in a way that the wire is protected by a fuse in wanted time and current range. Up to now the selection of wires is based on data, which were not particular optimized for automotive applications, where the wire length is typically short and low weight is important. The same, electrical fuses today are designed for a certain current value and do not protect the wire reliable in a wider current range. So, for automobile applications, fuses have to be re‐designed for every single wire to protect it against short circuit currents. Thus, the investigation of thermo‐electrical characteristics of both wires and fuses is necessary. This paper would like to show some examples how to calculate heat transfer in cylindrical wires (cable rating) and electrical fuses (melting behavior) by implicit Finite Volume Method (FVM) [12]. Such a procedure allows us to obtain simple algorithm to investigate thermo‐electrical behavior of electrical conductors. The key part of the paper is the calculation of the heat transfer by implicit Finite Volume Method. In non‐stationary state 1‐D heat conduction equation is solved for both cylindrical and orthogonal coordinates. In stationary state analytical solutions are presented.

The disadvantage of the pure application of numerical approaches, however, is the fact, that the physicals laws behind are not so easy to visualize, the results art not so easy to generalize, and the storage of the information requires mostly an extensive amount of data. This paper would like to show at some examples the advantages of the combination of both methods. The key part of this approach is the calculation of the heat transfer by the Finite Volume Method (FVM) and the approximation of the calculated data by the so‐called “simplified equations”. These simplified equations were received by analytical solutions of the basic heat conduction equation. The required adaptation of the numerical results was done with properly adapted fitting algorithms on the basis of the elaborated analytical solutions, a process which was leading to an enormous reduction of data. As a result it became possible to describe the applied tasks by a few characteristic constants. Another approach for an analytical solution with a numerical calculation process is the determination of the so‐called “properties of mixed magnitudes”. As an example this principle has been applied for the numerical calculation of electrical multi conductor containing cables. This process allowed the prediction of the thermal behavior of any cable harness with the required precision.