Effective Thermal Conductivity Tensor Research Articles

Slip and no-slip temperature boundary conditions at interface of porous, plain media: conduction

The phase distribution nonuniformities near bounding surfaces result in anisotropy and nonuniformity of the effective thermal conductivity tensor. For a two-dimensional porous medium made of cylindrical particles, we evaluate the properties of this tensor for cases where the medium is bounded by the fluid saturating it or by a solid surface. The use of a uniform effective conductivity, such as the bulk (far from the surface) value, along with the near surface temperature distribution results in an error in the calculated heat flux. We examine this error and the errors resulting from the use of other approximations of the effective conductivity near the surface. We also point out a slip in the surface temperature occurring when the bulk effective conductivity and the temperature distribution away from the surface are used to extrapolate the temperature at the interface. A slip coefficient is used to account for this slip in temperature.

Effective conductivity and average polarizability of random polycrystals

A third-order expansion for the effective thermal conductivity tensor K* of anisotropic polycrystalline cell materials is derived. The coefficients of the expansion are given in terms of the average polarizability tensor, a nondimensional quantity determined from the grain shape and crystallographic orientation distributions independent of other details of the microgeometry such as two (or more) particle correlation functions. Explicit numerical results for a wide variety of microgeometries made of ellipsoidal cells are obtained. This calculation uses a new method that exploits the symmetry properties of the effective conductivity tensor of a cell material as a function of the single-crystal conductivities.

Effective thermal conductivity of a medium with ellipsoidal particles

The principal components of the effective thermal conductivity tensor, characterizing stationary heat macrotransfer in a dense medium with dispersed ellipsoidal particles of a different material are calculated by a method suggested in [1]. The case of equally oriented ellipsoids and of isotropically distributed ones are considered as examples.

Thermal Conductivity of Partially Degenerate Magnetoplasmas in Stellar Cores

The true, ordinary, and effective thermal-conductivity tensors have been evaluated for a partially degenerate magnetoplasma through the use of a microscepic transport theory with the Boltzmann equation in Chapman and Cowling's second approximation. The formalism provides a smooth transition from the nondegenerate case to full degeneracy. Only electron-ion collisions are considered and ionic lattice conditions arc excluded. The numerical evaluation of the conductivity integrals shows that the effects of magnetic fields lead to a decrease by one to two orders of magnitude in the values of the magnetic components of the effective thermal-conductivity tensor as compared to diminution factors 2 to 3 by inclusion of electron-electron collisions (Hubbard and Lampe). Excellent numerical agreement is obtained with the values of Iben for the nonmagnetic tensor component. As a result of magnetic field effects, the radial thermal flows in degenerate stellar cores with Babcock-type azimuthally coiled magnetic fields should be converted to thermal flows in concentric shells around the core. A possible switch from radial conductive energy transport back to radiative energy transport may take place with attendant instabilities. Finally, a new type of instability is suggested from analogy considerations of observed sign switches in the Hall-type magnetic thermoelectric (Nemst-Ettingshausen flow) andmore » thermal (Righi-Leduc flow) flow components in semiconductors. With heavy- element concentrations (Si, Fe) in stellar core-mantles and again Babcock-type fields, directional reversals in the azimuthal current flows in neighboring shell layers might conceivably lead to powerfully disrupting mechanical forces, and provide a mechanism for stellar pulsationa or explosions. (auth)« less