# how to compute this?

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 September 24, 2007, 11:33 how to compute this? #1 phsieh2005 Guest   Posts: n/a 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

 September 24, 2007, 13:48 Re: how to compute this? #2 opaque Guest   Posts: n/a 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

 September 24, 2007, 14:32 Re: how to compute this? #3 phsieh2005 Guest   Posts: n/a 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

 September 25, 2007, 09:25 Re: how to compute this? #4 Q Guest   Posts: n/a 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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