Nanocrystals with orange‐reddish luminescence based on the pyrochlore‐type complete solid solutions with cube‐like morphology in the Eu2Sn2O7–Gd2Sn2O7 system were directly formed from the precursor solutions of SnCl4, GdCl3, and EuCl3 under weakly basic hydrothermal conditions at temperatures higher than 180°C for 5 h. The crystallite of Gd2Sn2O7 pyrochlore gradually grew from 10 to 37 nm as the hydrothermal treatment temperature rose from 180°C to 240°C. The lattice parameter of cubic phase linearly increased with increased europium concentration according to the Vegard's law. The characteristic orange‐reddish photoluminescence spectra of Gd2Sn2O7:Eu3+ cubelike nanocrystals with crystallite size from 34 to 37 nm that were formed at 240°C for 5 h were attributed to the most sharp orange (586 nm) luminescence with high intensity and quite broad red (610–630 nm) emission with weak intensity, according to the 5D0→7F1 and 5D0→7F2 transitions of Eu3+, respectively. At a composition of (Eu0.09Gd0.91)2Sn2O7, the intensity of orange emission reached the maximum. The Red‐to‐Orange (5D0→7F2/5D0→7F1) (R/O) emission intensity ratio was in the low range from 0.10 to 0.14, which was a characteristic of Gd2Sn2O7:Eu3+.

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In this study, the authors attempted to introduce a simulation technique for radiation-convection heat transfer in the high-temperature fields of industrial furnaces, boilers, and gas turbine combustors. The convection effect was analyzed by a differential equation, but the radiation effect was analyzed by an integral equation. Thus, it was not easy to arrange both effects using the same type of equations. Then, the authors introduced the zone method and Monte Carlo method for the integral equation of the radiation effect and the finite difference method for the differential equation of the convection effect. A three-dimensional analysis of the high-temperature furnace was performed by this simulation technique to obtain its temperature distribution. Furthermore, another radiation-convection heat transfer analysis in the low-temperature living room was performed by the same technique. Finally, the authors tried to develop a computer software for radiation-convection heat transfer and described their idea of software construction for the above.

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