Convective Diffusion (ubiquitious). Basic Convective Diffusion Model.

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Presentation transcript:

Convective Diffusion (ubiquitious)

Basic Convective Diffusion Model

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.

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

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

Plug Flow

Formal Solution

Cognate Quantities

Straightforward Application

Bizarre Application

The Léveque Problem

A slightly different equation

A somewhat different result But many similarities

Separated Flows

Secondary Flows

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 (With many, many following references that suggest other applications and addition and deletion of factors considered or not considered originally.)

Geometric Model

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)".

Radial Profiles