OCR Text |
Show Radiative Transport Equations In furnaces and combustion chambers, radiative heat transfer comprises an important mode of heat transfer. We apply the discrete ordinates method as a solution of the radiative transport equations. The balance of energy passing in a specified direction ft through a small differential volume in an emitting-absorbing and scattering gray medium can be written as follows: (ft-v)i (r,ft) = -(K + a)i (r,n) + < Ib (r) + 1^/" I (r,ft')$(ft'->fl) dn" (18) ft' = 4TT where $(ft'-*ft) is the phase function of energy transfer from the incoming ft' direction to the outgoing direction ft; I(r,ft) is the radiation intensity which is a function of position and direction; I^w) is the intensity of blackbody radiation at the temperature of the medium; and < and a are the gray absorption and scattering coefficients of the medium, respectively. The expression on the left-hand side represents the gradient of the intensity in the specified direction ft. The three terms on the right represent the changes in intensity due to absorption and out-scattering, emission, and in-scattering, respectively. If the surface bounding the medium is assumed gray and emits and reflects diffusely, then the radiative boundary condition for Equation 18 is given by: I(r,ft) = eIb(r) + L f\n-$ | Kr.fi') dn' rf.ft>o (19) n -ft <o where I (r,ft) is the intensity of radiant energy leaving a surface at a boundary location, e is the surface emissivity, p is the surface reflectivity, and n is the unit normal vector at the boundary location. -12- |