1. Convective Diffusion (ubiquitious)

2. Basic Convective Diffusion Model

3. The basic problem  Convective movement within the fluid (liquid)  Diffusive movement.  The 'local' balance with the fluid.  The (many) different velocity profiles  The (many) different boundary conditions.

4. Geometries & Velocity Profiles  Geometries  Cylindrical  Sheet  Velocity Profiles (fully developed)  "Plug" flow  Parabolic profile (Graetz-Nusselt)  Linear approximation (Léveque)

5. Boundary conditions  Specified permeability  Specified concentration  Specified flux  Matching  Impermeable wall

6. Plug Flow

7. Formal Solution

8. Cognate Quantities

9. Straightforward Application

10. Bizarre Application

11. The Léveque Problem

12. A slightly different equation

13. A somewhat different result But many similarities

14. Separated Flows

15. Secondary Flows

16. The Krogh Tissue Cylinder Krogh, A., 1919, "The number and the distribution of capillaries in muscle with the calculation of the oxygen pressure necessary for supplying the tissue," Journal of Physiology (Cambridge, Eng), Vol. 52, pp. 409-515. (With many, many following references that suggest other applications and addition and deletion of factors considered or not considered originally.)

17. Geometric Model

18. Emphasis is on metabolism in the tissue  The problem depends on convective diffusion but emphasizes what happens in the tissue. The convective flow is a "line source (or sink)".

19. Radial Profiles