SIMILARITY OF A PROBLEM IN CONCENTRATION-DEPENDENT DIFFUSION AND FLOW IN A FREE BOUNDARY LAYER
ARNOLD ENGINEERING DEVELOPMENT CENTER ARNOLD AFB TN
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The mathematical similarity of a problem in one-dimensional diffusion in a semi-infinite medium when the diffusion coefficient varies linearly with concentration to the problem of the fully developed boundary layer between two fluid streams was demonstrated. By applying the von Mises transformation in reverse, the one-dimensional diffusion equation was transformed to the Prandtl boundary-layer equations, which were subsequently transformed to a single non- linear ordinary differential equation. The transformed boundary and initial conditions of the diffusion problem were shown to correspond to the boundary conditions for the mixing of two uniform fluid streams. Numerical results for the diffusion problem were obtained from existing solutions to the fluid mechanics problem.
- Fluid Mechanics