Nusselt Number Equation Simplification?

[dillonmhudson]

Homework Statement

See the picture for the homework problem:
http://i41.tinypic.com/2drk2x.png

Homework Equations

I'm having trouble converting between the first equation and the second one.

I understand that Nu_x=h_x*x/k
Re = rho*v*x/visc
Pr = c_p*visc/k

But how the heck do I convert all that to the second equation?

Thanks

The Attempt at a Solution

As above, I combined the equations together but I don't know where the T (temperature) comes in, or how you can simplify an equation when you have a square root and a cube root.

 

[KataKoniK]

Hello,

It looks like you are trying to convert between the Nusselt number (Nu), Reynolds number (Re), and Prandtl number (Pr) equations. The second equation you have shown is the definition of the Nusselt number, which is used to calculate heat transfer coefficients in fluid flow. The first equation is a combination of the Reynolds and Prandtl numbers, which are also important in determining heat transfer coefficients.

To convert between the two equations, you can use the definitions of the Reynolds and Prandtl numbers to substitute into the first equation. This will give you an expression for the Nusselt number in terms of the velocity (v), density (ρ), heat capacity (c_p), thermal conductivity (k), and viscosity (μ) of the fluid. You can then rearrange this equation to solve for the temperature (T) and simplify as needed.

I hope this helps. Good luck with your homework!