A detailed numerical investigation of pattern selection for thermocapillary flow in rectangular containers in microgravity is presented. These dynamics are studied for liquid $n$-octadecane, an alkane with high Prandtl number $(\text{Pr}=52.53)$, due to its relevance to recent microgravity experiments. Pattern selection is analyzed in terms of the aspect ratio, $\mathrm{\Gamma }$, and the applied Marangoni number, Ma. In short containers, the bifurcation picture is characterized by a transition from steady thermocapillary flow to a standing wave (SW) oscillatory mode as Ma is varied. This transition takes the form of a primary subcritical Hopf bifurcation accompanied by a secondary saddle node; these two bifurcations delimit a region of bistability. In large containers, the dynamics is characterized by a supercritical Hopf bifurcation that marks the transition from steady flow to a traveling wave (TW) mode. The critical Ma for this transition increases with $\mathrm{\Gamma }$. In intermediate containers, a complex pattern selection scenario is found, where both steady and oscillatory convection, in the form of either TWs or SWs, can appear depending on $\mathrm{\Gamma }$ and Ma. Finally, we apply this bifurcation analysis to help explain recent results on thermocapillary flows during the melting of phase change materials in microgravity [Salgado Sánchez et al., Int. J. Heat Mass Transf. 163, 120478 (2020); Salgado Sánchez et al., J. Fluid Mech. 908, A20 (2021)]. The temporal evolution of the phase change is characterized by an effective $\mathrm{\Gamma }$ and Ma in the liquid phase. We find very good agreement between the flow transitions observed during melting and those predicted for the equivalent rectangular containers over the explored range of $1.5\le \mathrm{\Gamma }\le 16$.

A rigorous analytical study of the global error of panel methods is presented. The analysis is performed for a wide variety of body shapes and different panel geometries to fully understand their effect on the convergence of the method. In particular, we study the global error associated with panel methods applied to thin or thick bodies with purely convex parts or with both convex and concave parts, and with smooth or non-smooth boundaries. Most previous studies focused on the analysis of local error, considering only the influence of the nearest panels and excluding the rest. The difference is shown to be appreciable in many configurations. Generally, there is a lack of consensus concerning the order of magnitude of the error for panel methods even in the simplest case with flat panels and a constant distribution of doublets along them. This paper clarifies apparently different or inconsistent results obtained by other authors.

This paper describes a laboratory set-up designed to support hands-on learning of heat transfer principles in aerospace engineering education. Developed within the framework of experiential and project-based learning, the set-up enables students to experimentally characterize the convective coefficient of a cooling fan and the thermo-optical properties of aluminum plates with different surface coatings, specifically their absorptivity and emissivity. A custom-built, LED-based radiation source (the ESAT Sun simulator) and a calibrated temperature acquisition system are used to emulate and monitor radiative heating under controlled conditions. Simplified physical models are developed for both the ESAT Sun simulator and the plates that capture the dominant thermal dynamics via first-order energy balances. The laboratory workflow includes real-time data acquisition, curve fitting, and thermal model inversion to estimate the convective and thermo-optical coefficients. The results demonstrate good agreement between the model predictions and observed temperatures, which supports the suitability of the set-up for education. The proposed activities can strengthen the student’s understanding of convective and radiative heat transport in aerospace applications while also fostering skills in data analysis, physical and numerical reasoning, and system-level thinking. Opportunities exist to expand the material library, refine the physical modeling, and evaluate the long-term pedagogical impact of the educational set-up described here.