Transformation of Coordinates for Zones in Uniform Translation

The basic transport expression of Eq. 3.34 can be written in the partial derivative form 

The translation and diffusion processes can be separated and the mathematics simplified by a change in coordinates. We define a coordinate system moving with the center of gravity of the zone, located at x = X, and thus in the case under consideration, moving forward at a velocity of W with respect to the old coordinate system. The distance along the axis of translation in the new coordinate system y is related to x by 

Our object is to describe concentration c (and its derivatives) in this new coordinate system. 

We make the transformation of coordinates by first obtaining the exact differential 

From this we obtain dcldi)M, needed as the term on the left of Eq. 3.35 

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