Chemical and Biochemical Engineering

Research Advisor

Reed, X. B., Jr.

Advisor's Department

Chemical and Biochemical Engineering


Theoretical calculations have been carried out for forced convective transport for uniform streaming and uniaxial and biaxial extensional axisymmetric flows past single spheres. Homogeneous and heterogeneous chemical reactions, both of first and of second order have also been or are presently being treated. Orthogonality and other properties of Legendre functions have been used, together with introduction of an eigenfunction expansion, to reduce the mathematical description from a partial differential equation with variable coefficients, which is nonlinear for homogeneous second order chemical reactions, to a system of coupled ordinary differential equations for the radial modes. The numerical solutions of the latter have been obtained using the robust, adaptive grid algorithm of Pereyra and Lentini. Plots of the radial functions for given Peclet and Damkohler numbers give insight into the role and interaction of L and of r (the number of terms necessary for convergence of the expansion and the finite radius at which the boundary conditions at infinity are imposed). From the radial modes, local and average Nusselt and Sherwood numbers, as well as the temperature and concentration fields, can be obtained. Plots of radial function families provide new insights that complement physicochemical understanding gained from isocontour plots of the temperature and concentration fields. Plots of local interphase transfer coefficients reflect the behavior of the flux field over the sphere surface and show how the average coefficients arise.

Document Type


Presentation Date

May 1994