Instantaneous Point Source on an Infinite Plane Emitting into Half Space

2 Instantaneous Point Source on an Infinite Plane Emitting into Half Space 

The case of a continuous source is another example of interest. We would expect intuitively that the solution to this problem could in principle be obtained by integrating over time the result obtained for an instantaneous source. This is indeed the case and leads to the emergence of a special type of integral, termed the error function erf x, which is defined as 

The error function can be viewed as a partial area under the Gaussian distribution curve (2/n )exp -u ). It has the value 0 at x = 0, and a value of 1 at X = oo. The latter case corresponds to the full area under the distribution curve. A related expression is the complementary error function erfc x, which is defined as 

The error function integral has to be evaluated numerically and can be found tabulated in texts on diffusion or conduction, or in mathematical tables. An abbreviated listing appears in Table 4.2, and some important properties of the function are summarized in Table 4.3. 

With these definitions in place, we can now proceed to present the solution to the continuous point source problem. It is given by the following (see Item 5 of Table 4.1). 

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INSTANTANEOUS POINT SOURCE ON AN INFINITE PLANE EMITTING INTO HALF SPACE... 

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