Nusselt Number dimension question

[Jasones]

So, in

Nu=$\frac{hD}{k}$

h is the heat transfer coefficient, and D is the diameter of the pipe in which heat transfer takes place...

..but what are the dimensions of k in terms of mass (M), length (L), time (T) and temperature ($\theta$)?

So far, I've worked out that the units for h are J/(m² hr C), but I'm having difficulty expressing k in terms of what is given.

Am I wrong is thinking that J/(m² hr C) can be expressed as W/(m² K)? I'm thinking that this is relevant to the end units of k, but I am unsure if the dimensions are correct.

 

[Chestermiller]

The Nussult number is dimensionless, so if you already know the units of h and D, then the units of k should be obvious: J/(m hr C)

 

[Vadar2012]

We could do some major dimensional analysis with this to prove it, but I really don't feel like it. I'm guessing you've done the old pi theorem already though?