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Lecture-4(error-bessel)

# Lecture-4(error-bessel) - Advanced Math Functions Lecture-4...

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Advanced Math Functions Lecture-4

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Error Function When water is poured into a cup that has a heap of salt. Suppose the cup is very tall and you are pouring the water in carefully (i.e. without causing too much turbulence). There is a straw that can be used to sample the water from the top of the cup. What will you observe about the taste of the water that you sample through the straw? The change in concentration that you would observe is expressed in the form of a diffusion equation: With the boundary and initial conditions: 0 1 2 2 = - + D D Pe D D D D x C N x C t C ( 29 I D D C x C = 0 , ( 29 I D D C x C = 0 , ( 29 J D D C t C = , 0
Error Function Diffusion equation: 0 1 2 2 = - + D D Pe D D D D x C N x C t C ( 29 : , D D D t x C Dimensionless concentration (i.e. values are between 0 and 1) : D x Dimensionless distance (i.e. values are between 0 and 1) : D t Dimensionless time (i.e. values are between 0 and 1) : Pe N Reynold’s number is a ratio of inertial to viscous forces. Peclet number measures the ratio of

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