By Carlo Ferrari
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Additional resources for Lectures on Radiating Gasdynamics: General Equations and Boundary Conditions
Sample text
22) .. = "j 8 J dnf _i_ d B "j (Tm) 3c 41r 41r (vfv. J )= "· J 0 ~ B 3c v. J B,. 23) Thus the relative importance of the radiative pressure and thermal pression appears to be measured by the product of the reciprocal of the Boltzmann number and the ratio U /c. 24) ~ 0 --= (t) ap (B;u U;-) 0 """dX'" Since U111 /c ~ 1 generally, it appears that the force effect of the radiation can be generally neglected, except in the case B0 u /B0 • > 1 ; in any case, by comparison of the rei. 24) with the rei.
2) that (10. ' = 1. 4) Let be 1 the unit vector in the propagation direction of the radiation -+ striking ~ ; (} the angle that s forms with the x axis, and I{) the angle that the is used to projection of ~in the plane (y, z) forms with the y axis. _' denote st the corresponding angles; finally p. is used to denote p. ' = cos (). n'. ' (hVf 1 r+ (O,P. dV Sll II and the total number of photons II reflected within ds-2' results to be -fp. ',l{)~ = v J P. r- (P. Q <10. B) being llihe hemisphere of radius one, centered at 0 (the point of incidence).
1 r:ll (IJ. ,V') 1 ~ I ~ =-, u (P. 14) being 6 (x-a)the Dirac function: this function has the property that a ... x the symbol b 11 denotes a constant. Thus the ftrst term at the right-hand side of eq. 10) becomes _ 1 2, -~ f<. '1'; p',op') I~(~ ,op) dU = n- ff b, o ? 14) is that of the specular reflection. Suppose now that a canst. 14 ') II The eq. 12') gives 1 r 811 = a II 1r and therefore r·»= r 1 /7r . Thus the first term at the right-hand side of eq. 1 fr II 811 rv (P. , ,, • n- 0 r; 0 (P.