الفهرس 
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Abstract
the segment focuses on the topic of the hermophoresis migration of an aerosol spherical particle immersed in a porous aterial saturated by a viscous fluid at a tiny non-zero Peclet number Pe is nvestigated using the method of matching asymptotic expansions. In the opposite irection of the z-axis, a uniform temperature gradient is applied to the system in a irection parallel to the particle’s diameter. The Knudsen number is considered to be ompatible with the continuum model’s assumption and to be within the range of the lip fluid flow through the porous medium’s pores. The solid matrix is in thermal quilibrium with the porous medium, which is modeled by the Brinkman equation nd is considered to be homogeneous and isotropic. It is important to consider the urrent asymptotic analytical solutions as a useful technique for validating the umerical approaches for future work on arbitrary Peclet number values.