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

The mass and heat transfer to a particle in a flow held have important practical applications in distillation, absorption, spray drying and catalytic reactions. The applications in aerosol science include inhal ation dosimetry as well as gas cleaning and filtration processes. To d escribe 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 sol ution for the partial differential equation (PDE) describing the force d convective mass and heat transfer around a cylindrical and a spheric al particle having gaseous (fluid) surface properties by reducing the PDE to a second-order ordinary differential equation using a similarit y transformation. Calculations' with this solution confirmed that the concentration and temperature gradients were highest at the front stag nant point and that the local mass transfer rates, represented by the Sherwood number, decreased as a increased from the front stagnation po int, theta = 0 to 180 degrees; these results are in agreement with pre vious observations by others. New observations included: when the conv ection-to-diffusion transfer rate ratio, the Peclet number, Pe, was fi nite (Pe < 442 for a cylinder or <34 for a sphere), the Sherwood numbe r was proportional to Pe(1/2) exp(-1/pi Pe) where pi = 3 for a sphere and 1/4.42 for a cylinder; and the mass transfer rate for vortex how a t the rear of a cylindrical particle had a weaker dependence on Peclet number (Pe(1/4)). When ku(theta) or u(theta) + u(theta)' is substitut ed for u(theta) in the mass transfer rate expression for a fluid cylin der, the ratio of the new Sherwood number to the old Sherwood number i s roughly proportional to root k or root u(theta)', respectively.