- #1
seaspecies
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Hello.
I am interested in learning the mathematical derivation from Cartesian coordinates Navier-Stokes equation to cylindrical coordinates Navier-Stokes equation. These equations have similar forms to the basic heat and mass transfer differential governing equations. I’ve tried looking online and at a variety of fluid mechanics books and heat transfer books and they all simply skip the math and go straight into just stating the equations. It seems like it is too complicated that it is not worth saying. Or it might be so trivial that I might be missing something. Maybe it is not worth it but I am curious of how it is done.
I attached the part the I am most confused about as a jpeg. How do they equal?
[tex]
\frac{\partial T^2}{\partial x^2}+\frac{\partial T^2}{\partial y^2}=\frac{1}{r}\frac{\partial}{\partial r}r\frac{\partial T}{\partial r}+\frac{1}{r^2}\frac{\partial T^2}{\partial\theta^2}
[/tex]
Thanks. I am sorry if I had any errors I am new here.
I am interested in learning the mathematical derivation from Cartesian coordinates Navier-Stokes equation to cylindrical coordinates Navier-Stokes equation. These equations have similar forms to the basic heat and mass transfer differential governing equations. I’ve tried looking online and at a variety of fluid mechanics books and heat transfer books and they all simply skip the math and go straight into just stating the equations. It seems like it is too complicated that it is not worth saying. Or it might be so trivial that I might be missing something. Maybe it is not worth it but I am curious of how it is done.
I attached the part the I am most confused about as a jpeg. How do they equal?
[tex]
\frac{\partial T^2}{\partial x^2}+\frac{\partial T^2}{\partial y^2}=\frac{1}{r}\frac{\partial}{\partial r}r\frac{\partial T}{\partial r}+\frac{1}{r^2}\frac{\partial T^2}{\partial\theta^2}
[/tex]
Thanks. I am sorry if I had any errors I am new here.
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