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There is online calculator for the Lambert's Targeting Problem (LTP) to produce launch and arrival v-infinity pork-chop plots between solar system targets ....
Great efforts have been made on the solidification of phase change nano-capsules (PCNCs). However, the analytical solutions received less attention when its initial temperature is not at the fusion temperature. Therefore, this work aims to analytically study the thermal behavior of PCNC with the same solid-liquid phase density during forced convective cooling when its initial temperature is greater than the fusion temperature. Asymptotic solutions are developed for long- and small-time scale. Asymptic solutions in the limit of large Stefan number to the solid phase temperature and the position of the free boundary were derived using the perturbation method with boundary-fixing transformations. The results predicted by the derived solutions are in good agreement with the data reported in the reference. It is shown that the surface temperature decreases negatively and exponentially under the Robin boundary conditions during the pre-cooling process. Increasing the values of the interfacia ....
Sorption thermal energy storage (STES) has the advantage of high energy storage density and low heat loss, which has been considered as one of the promising solutions to achieve carbon neutrality in buildings. An insight into the thermal energy storage performance of reactors enables the optimization of STES systems. In addition, the analytical solution is concise and understandable in physical significance. In the present work, the perturbation theory was introduced to derive the analytical solutions for the fluid and solid temperatures in the reactor during the discharging process. Subsequently, a zeolite 13X STES system was built to conduct charging and discharging experiments. Based on the derived analytical solution, the fluid temperature at different axial positions in the reactor and energy storage density (ED) of zeolite were calculated and compared with the measured data. The results showed that there was a good agreement between the experimental test and the analytical soluti ....
Analytical solutions play a role in predicting the moisture content of grains in agricultural engineering applications due to their convenience and accuracy. However, most of them ignore evaporation from internal or surface moisture which is not reasonable in real drying. Therefore, this investigation aims to analyse the drying behaviour of a single barley grain analytically. Analytical solutions to the coupled heat and mass transfer equations for spherical particle drying are presented by introducing an auxiliary function through the variable separation approach. Both internal and surface moisture evaporations in barley are fully considered in the equations, which are generally solved with numerical methods. The results reveal that the analytical solution predicted accurately the temperature and moisture content of the barley drying, and the predicted temperatures were lower than that without internal moisture evaporation. The non-linear relationship between the safe storage time (τ) ....
Abstract Fixed and moving boundary problems for the one-dimensional heat equation are considered. A unified approach to solving such problems is proposed by embedding a given initialboundary value problem into an appropriate initial value problem on the real line with arbitrary but given functions, whose solution is known. These arbitrary functions are determined by imposing that the solution of the initial value problem satisfies the given boundary conditions. Exact analytical solutions of some moving boundary problems that have not been previously obtained are provided. Moreover, examples of fixed boundary problems over semi-infinite and bounded intervals are given, thus providing an alternative approach to the usual methods of solution. ....