EXPONENTIAL TRANSFER AND DIFFUSION
The one-dimensional heat equation is solved for exponentially decaying rate of increment and decrement of temperature at the surface of a semi-infinite medium.The diffusion equation is solved for exponentially decaying rate of transfer from a source to a diffusion medium. The two types of sources are: mass initially (a) located at a point, and (b) distributed at interfaces within a porous rectangular parallelepiped or sphere. Solutions for subsequent concentration distribution are stated, and compared with the well-known cases of instantaneous transfer. Numerical evaluation is afforded by the probability integral of complex argument. The treatment is applicable to cases of first-order irreversible chemical reaction and simultaneous diffusion of reaction products.