A computational method is developed to evaluate the cooling effectiven
ess of a tangential slot in a particle-laden flow. The physical proble
m analyzed involves the tangential injection of a coolant at a wall su
bjected to convective heating from a turbulent boundary layer and radi
ative heating from hot particles. Previous published analyses did not
include radiative or particle effects. The boundary-layer equations, i
ncluding energy and species conservation, are solved using a finite di
fference scheme. The particle transport equation is also solved by a f
inite difference technique. A two-dimensional formulation for the solu
tion of the radiative equation of transfer is developed using the sphe
rical harmonics method. This formulation is different from those previ
ously published in that it solves for an azimuthally integrated form o
f the intensity. This approach reduces the number of unknowns in the s
olution and is therefore more computationally efficient. Particle opti
cal properties are obtained using the Mie scattering theory. A paramet
ric study is performed to determine the effects of wall emissivity and
other parameters on cooling effectiveness and particle deposition on
the wall.