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- A little clarification with regard to the natural boundary condition.

Hi, I'd like to be clarified regarding the general natural/Neumann boundary condition for a PDE.

1. The natural boundary condition is generally defined as:

(1)

and can be expressed as, according to this resource:

(2)

But apparently, according to this resource (posted by Dr. Fan):

(3)

Which is which? Is it supposed to be positive, or negative? When should it be positive or negative?

2. If I apply the derivative boundary condition, on say, the bottom of a square plate, I can state:

(4)

or for simplicity,
(5)

Obviously, comparing it with (2), n

Thanks!

1. The natural boundary condition is generally defined as:

and can be expressed as, according to this resource:

But apparently, according to this resource (posted by Dr. Fan):

Which is which? Is it supposed to be positive, or negative? When should it be positive or negative?

2. If I apply the derivative boundary condition, on say, the bottom of a square plate, I can state:

or for simplicity,

Obviously, comparing it with (2), n

_{y}is equal to 0. Why is this so? Why is n_{y}= 0?Thanks!