Deriving an equation for a function of two variables for a simulation

Aug 2015

I am having difficulty deriving an equation for a simulation for a moving laser on a test piece.

The problem is:

I have three different variables, Heat flux (h), time (t) and displacement in the y coordinate. The y axis ranges from y=0 to d, where d is the length of the test piece. At time = 0, the Heat flux = maximum, and y= 0. At time = t final, y=d and h= maximum only at the point d. i.e. d=0 at every other point along the y axis.

In other words, I need an equation that determines h to be max at a point along the y axis and zero at all other points, where h is a function of time and distance y.

Please help!
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