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phsieh2005 September 24, 2007 11:33

how to compute this?
 
Dear CFD experts:

Can someone suggestion a reference site where I can find the formula on how to compute the following:

grad(H^2) where H is a vector field.

Thanks!

phsieh2005

opaque September 24, 2007 13:48

Re: how to compute this?
 
If I am not mistaken, it should be

grad(H^2) = 2 * H dot grad(H)

This typically shows up for ferromagnetic force, or dielectrophoretic forces.

Opaque

phsieh2005 September 24, 2007 14:32

Re: how to compute this?
 
Dear Mr. Opaque:

You are GOOD!

Yes, I am trying to compute the force on paramagnetic particles in the flow field exposed to permanent magnets.

Thanks a lot!

phsieh2005

Q September 25, 2007 09:25

Re: how to compute this?
 
Sorry, I don't believe this is correct:

1/2 GRAD(h^2) = hj hj,i ei = [GRAD h]^T [h]

this derives by the following:

hj,i ei = [GRAD h] ^ T (transpose)

= hj,i (ei Tensor ej)

Applying the tensor product:

hj,i (ei Tensor ej) * hk ek = delta_jk hk hj,i ei

collapsing jk using delta function:

hj,i (ei Tensor ej) * hk ek = hj hj,i ei

In other words: GRAD(h^2) = 2 hj hj,i ei (repeating both i and j)

or

1/2 GRAD(h^2) = h1(h1,1 e1 + h1,2 e2 + h1,3 e3) + ...

h2(h2,1 e1 + h2,2 e2 + h2,3 e3) + ...

h3(h3,1 e1 + h3,2 e2 + h3,3 e3)



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