A compact difference scheme for numerical solutions of second order dual-phase-lagging models of microscale heat transfer

Dual-phase-lagging (DPL) models constitute a family of non-Fourier models of heat conduction that allow for the presence of time lags in the heat flux and the temperature gradient. These lags may need to be considered when modeling microscale heat transfer, and thus DPL models have found application in the last years in a wide range of theoretical and technical heat transfer problems. Consequently, analytical solutions and methods for computing numerical approximations have been proposed for particular DPL models in different settings. In this work, a compact difference scheme for second order DPL models is developed, providing higher order precision than a previously proposed method. The scheme is shown to be unconditionally stable and convergent, and its accuracy is illustrated with numerical examples.

Successful functionalization of superporous zeolite templated carbon using aminobenzene acids and electrochemical methods

A novel and selective electrochemical functionalization of a highly reactive superporous zeolite templated carbon (ZTC) with two different aminobenzene acids (2-aminobenzoic and 4-aminobenzoic acid) was achieved. The functionalization was done through potentiodynamic treatment in acid media under oxidative conditions, which were optimized to preserve the unique ZTC structure. Interestingly, it was possible to avoid the electrochemical oxidation of the highly reactive ZTC structure by controlling the potential limit of the potentiodynamic experiment in presence of aminobenzene acids. The electrochemical characterization demonstrated the formation of polymer chains along with covalently bonded functionalities to the ZTC surface. The functionalized ZTCs showed several redox processes, producing a capacitance increase in both basic and acid media. The rate performance showed that the capacitance increase is retained at scan rates as high as 100 mV s−1, indicating that there is a fast charge transfer between the polymer chains formed inside the ZTC porosity or the new surface functionalities and the ZTC itself. The success of the proposed approach was also confirmed by using other characterization techniques, which confirmed the presence of different nitrogen groups in the ZTC surface. This promising method could be used to achieve highly selective functionalization of highly porous carbon materials.