ABSTRACT
Now let us introduce a change of variable and a change of unknown making the analysis of equation (2.1) easier in Section 3. We define the variable ^and the function \j/ by :
then substituting in equation (2.1) the expression of R given by (2.8) and by using the previous relations the equations (2.1) and (2.3) become
i) 3t\j/-otx3x\j/+ ocy3y\|/-y(T,Y)3^\j/ = 0 ; (2.9)
ii) co = - 4 i i n Pt y(T, Y) J \\f VT d£. o
We assume the variations with respect to y of the functions \j/, T and Y are negligible compared to the variations with respect to the other variables (at least in a neighbourhood of the plane x equals zero). Then using the relations (2.5) and (2.9) ii), the Boltzmann's equation (2.9) i) for the function \|/ and the conservation equations (2.4), (2.6) for the function Y and for the function T respectively, read :
3t \j/ - a x 3X y - y(T, Y) 3^ \j/ = 0, (2.10) + oo
The last step of the derivation of the mathematical model consists in using a boundary layer approximation for the equations (2.10), (2.11) and (2.12).
