HEAT-FLUX SOLUTIONS OF THE 13-MOMENT APPROXIMATION TRANSPORT-EQUATIONS IN A MULTISPECIES GAS

A steady state analytical solution of the heat flux equation in the 13 -moment approximation is obtained, where temperature gradient, regimes changing from subsonic to supersonic flow situations, and effects of drift velocity between species, say diffusion-thermal effects, are tak en into account. From such a general solution, validity conditions of Fourier's law are examined. A solution for a collisionless regime base d upon the above solution is achieved. Then, the high-latitude topside ionosphere with a mixture of the ionized constituents O+ and H+ and n eutrals is studied. Heat flux is derived for the two ionized constitue nts in a regime where the gradient of the aligned velocity component i s less important than collision frequencies. Heat fluxes of O+ and Hions in this situation are further simplified considering that H+ ion concentration is smaller than O+ ion concentration. With the help of t he European incoherent scatter (EISCAT)-VHF data, O+ and H+ heat fluxe s in the high-latitude topside ionosphere are calculated with the abov e solutions. Results are compared to those obtained with Fourier's law . We find that Fourier's law underestimates significantly heat fluxes in this case, especially for H+. Thermal conduction is calculated, bot h with our general solution and with the Fourier's law. For the H+ ion thermal conduction, Fourier's law may lead to an inverse variation wi th altitude when compared to our solution, which gives an inverse cont ribution to the H+ ion energy balance and to the H+ temperature. H+ io n heat flux is upward not only in the supersonic regime shown by DE 1 data but also in the subsonic regime at lower altitude in the high-lat itude topside ionosphere, as shown by EISCAT data.