Absorptances and deposited energy profiles are calculated for thin layers of metallic powder placed on a reflective substrate at normal incidence of collimated radiation. Radiation transfer equation is analytically solved by the two-flux method. The effective optical parameters of the powder are estimated in geometrical optics approximation taking into account dependent scattering. The cases of specularly and diffusely reflecting particles are studied. Due to multiple reflections in an open pore system, laser radiation can penetrate in powder to considerable depths, much greater than the characteristic particle diameter. Total laser energy absorbed in a thin powder layer on a reflective substrate increases with its thickness but the deposited energy density decreases. Generally, the absorptance and the energy density for specular reflection are slightly greater than these values for diffuse reflection. The results obtained in the limit of deep powder bed essentially agree with known ray tracing simulations. The present model is in good agreement with experimentally observed correlation between effective absorptance of metallic powders and absorptance of corresponding dense metals.
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