By K K Sen, S J Wilson
Lots of the tools defined during this e-book can be utilized with beauty differences to unravel move difficulties of better complexity. All makes an attempt were made to make the publication self-contained.
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Additional resources for Radiative transfer in curved media : basic mathematical methods for radiative transfer and transport problems in participating media of spherical and cylindrical geometry
However, more complex cases will be considered and basic deductions made when we take up special problems in Chapter VI. Integral equation for source function in cylindrical geometry : We consider an infinite cylindrical medium of radius R with a net flux TTF. incident on the bounding surface at an angle cos vertical and cos rj with the \x with the outward drawn normal to the surface. The distribution of internal sources other than scattering may be given by B ^ r ) , r being the distance measured from the axis of the 45 cylinder.
U by the reduction factor iro J R/x exp I * a(r')ds' , r where ru = s. rr )2n- * R/x 2 I ^5(/i - /i )dji = n nF. 28) assuming axial symmetry of the radiation field. -uo ) = . 29) ru *>„ Then the contribution to source function from the reduced incident radiation B (r) is given by B o(r) " +1 * * w(r) r ^ ! I0(r,M')5(M0+M')dM' u(r)F. 30) )ds' r M„ Furthermore, if o> and a are constants, that is when the medium is homogeneous, ti>F. r V > - -IT [cf. 472]. 31) 44 I f 0 < fi < 1, we have UJF. 2 "R " r) = - ^ B (r) rr Vo - -IT 4 (_ : uF.
8) where ^,o,(0,—/i) , the neutron angular density at the free surface in the inward direction is equal to a given incident distribution of neutrons. Boundary conditions in spherical medium : In radiative transfer problems in spherical geometry one generally deals with spherical media with point source, with spherical shells or spherical media with absorbing and emitting cores etc. In all these cases statements of boundary conditions are fairly straight forward. 30). Fig. 2 (A) A sphere of finite radius with a point source of energy : The boundary condition that is generally used is the absence of angular distribution of intensity at free surface.