Surface Integration of vector tensor product

[praban]

Hello,

It may be trivial to many of you, but I am struggling with the following integral involving two spheres i and j separated by a distance mod |rij|

∫ ui (ρ).[Tj (ρ+rij) . nj] d2ρ

The integration is over sphere j. ui is a vector (actually velocity of the fluid around i th sphere)
and Tj (p+rij) is a tensor over the j th sphere. nj is the unit normal on the surface of jth sphere.

I am thinking of doing it by integration by parts. But I am not sure if I can use the same formula for product of two functions in this case as well. Can someone help me? If I can write the correct formula for integration by parts, the rest I should be able to do.

thanks,
Praban

 

[Mandelbroth]

Hello,

It may be trivial to many of you, but I am struggling with the following integral involving two spheres i and j separated by a distance mod |rij|

∫ ui (ρ).[Tj (ρ+rij) . nj] d2ρ

The integration is over sphere j. ui is a vector (actually velocity of the fluid around i th sphere)
and Tj (p+rij) is a tensor over the j th sphere. nj is the unit normal on the surface of jth sphere.

I am thinking of doing it by integration by parts. But I am not sure if I can use the same formula for product of two functions in this case as well. Can someone help me? If I can write the correct formula for integration by parts, the rest I should be able to do.

thanks,
Praban

This link might be helpful.