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Titanium represents an important biomaterial for implantable medical devices. During medical device manufacturing by means of welding, implant structures are partially exposed to high temperatures. Additionally, active implants such as pacemakers can heat up during operation. Therefore, numerical studies of heat propagation within titanium structures represent an essential tool to assess functionality and safety of medical devices. The current study focusses on the development of a method for experimental validation of numerical heat transfer analysis of biomaterials such as titanium. Numerical heat transfer analysis was performed using the software Abaqus. A finite-element model was established including material properties such as density, thermal conductivity und specific heat capacity. Temperature distribution among a locally applied thermal load was calculated. Furthermore, effects such as convection were considered. For validation, an experimental setup was implemented according to the numerical calculation using a local heating tool. Heat propagation in the sample was determined, respectively. Radiation-based heat determination was performed using an infrared thermographic camera aligned parallel to the sample surface. Contact-based heat determination was performed using thermocouples fixed to the surface at defined distances from the point of local heat input. For evaluation of numerical and experimental results, temperature- time curves were compared for five distinct measuring points, respectively. While infrared thermography offers the advantage of non-contact measurements, difficulties may arise from the definition of correct emissivity and challenging sample surface characteristics, such as metallic reflectance and surface texture. The thermocouple-based temperature measurement shows a high sensitivity to local temperature changes, but it is not always suitable due to the influence on the sample by thermocouple fixation. Infrared thermography and thermocouple based temperature measurements represent suitable procedures for experimental validation of numerical heat transfer analysis of titanium. An individual decision for the most suitable method must be made considering the specific sample and its further application.

The parameter dependence of the various attractive solutions of the three variable nonlinear Lorenz equations is studied as a function of r, the normalized Rayleigh number, and of σ, the Prandtl number. Previous work, either for fixed σ and all r or along σ ∝ r and $\sigma \propto \sqrt{r}$, is extended to the entire (r, σ) parameter plane. An onion-like periodic pattern is found which is due to the alternating stability of symmetric and nonsymmetric periodic orbits. This periodic pattern is explained by considering non-trivial limits of large r and σ and thus interpolating between the above mentioned cases. The mathematical analysis uses Airy functions as introduced in previous work, but instead of concentrating on the Lorenz map we analyze the trajectories in full phase space. The periodicity of the Airy function allows to calculate analytically the periodic onion structure in the (r, σ)-plane. Previous observations about sequences of bifurcations are confirmed, and more details regarding their symmetry are reported. [ABSTRACT FROM AUTHOR]