Derivation and application of an analytical solution of the mass transfer equation to the case of forced convective flow around a cylindrical and a spherical particle with fluid surface properties

Abstract

The mass and heat transfer to a particle in a flow field have important practical applications in distillation, absorption, spray drying and catalytic reactions. The applications in aerosol science include inhalation dosimetry as well as gas cleaning and filtration processes. To describe any of these applications, however, an analytical or numerical solution must be found for the associated forced convective transfer processes. The objective of this study was to obtain an analytical solution for the partial differential equation (PDE) describing the forced convective mass and heat transfer around a cylindrical and a spherical particle having gaseous (fluid) surface properties by reducing the PDE to a second-order ordinary differential equation using a similarity transformation. Calculations with this solution confirmed that the concentration and temperature gradients were highest at the front stagnant point and that the local mass transfer rates, represented by the Sherwood number, decreased as θ increased from the front stagnation point, θ = 0 to 180°; these results are in agreement with previous observations by others. New observations included: when the convection-to-diffusion transfer rate ratio, the Peclet number, Pe, was finite (Pe < 442 for a cylindrical or <34 for a sphere), the Sherwood number was proportional to Pe 1 2 exp(−1/ωPe) where ω = 3 for a sphere and 1 4.42 for a cylinder; and the mass transfer rate for votex flow at the rear of a cylindrical particle had a weaker dependence on Peclet number (Pe 1 4 . When ku θ or u θ + u′ θ is substituted for u θ in the mass transfer rate expression for a fluid cylinder, the ratio of the new Sherwood number to the old Sherwood number is roughly proportional to √ k or √ u′ θ , respectively.