IS THE THERMAL DIFFUSIVITY OF UNSATURATED SOILS A MONO-MAXIMUM FUNCTION OF THEIR MOISTURE CONTENT

The conductive heat transfer in the three-dimensional medium water–air–solid grain was investigated on the basis of the exact analytical solution of the problem on the steady harmonic 2D temperature fi eld in a composite having a doubly periodic chequered structure in the form of an isogonal tiling. An explicit expression for the diff usivity of the indicated composite depending on its volumetric moisture content has been constructed. It was established that the diff usivity of this composite reaches a physically meaningful maximum at a certain degree of its saturation with water. It is shown that the expression obtained is analogous to the solution of the classical Muscat problem on the fi ltration of oil in a doubly periodic array of production and injection wells.
The conductive heat transfer in the three-dimensional medium water–air–solid grain was investigated on the basis of the exact analytical solution of the problem on the steady harmonic 2D temperature fi eld in a composite having a doubly periodic chequered structure in the form of an isogonal tiling. An explicit expression for the diff usivity of the indicated composite depending on its volumetric moisture content has been constructed. It was established that the diff usivity of this composite reaches a physically meaningful maximum at a certain degree of its saturation with water. It is shown that the expression obtained is analogous to the solution of the classical Muscat problem on the fi ltration of oil in a doubly periodic array of production and injection wells.
Author:  A. R. Kacimov, Yu. V. Obnosov
Keywords:  porous medium, thermal diff usivity, eff ective thermal conductivity, steady heat conduction, singlemaximum function, solid fi bers, doubly periodic chequered structure, Maxwell refraction, composite four-sector square, upscaling, holomorphic functions, R-linear conjugation problem
Page:  1350