Internal energy transport in adiabatic systems: Thermal Taylor dispersion phenomena (Q1341622)

The authors suggest a concept of homogenization for media which are strongly inhomogeneous on a microscale with respect to the properties controlling heat conduction, i.e. specific heat capacity, density and thermal conductivity. Restricting on the linear case, they use Green function representations of the solutions of the heat conduction differential equations on the microscale as well as on the macroscale. The homogenization is performed by establishing the mean value of Green functions. From this postulate the macroscale material properties are deduced by matching the macroscale moments up to the second-order of both Green functions, i.e. by identifying their long time components. The analysis is made for systems with arbitrarily and with periodically distributed parameters. As examples, a packed bed composed of insulated cylinders in a conducting matrix and a spatially periodic layered medium are treated, and the calculated values of macroscale thermal diffusivity tensor are presented. This interesting study forms the continuation of foregoing papers. Some steps of mathematical deduction could be more transparent.