Dimensions of k in Nusselt Number

[Jasones]

Homework Statement

A common dimensionless group used in heat transfer calculations is defined as:

Nu=\frac{hD}{k}

where h is the heat transfer coefficient, and D is the diameter of the pipe in which heat transfer takes place. Please determine the dimensions of the quantity k in terms of mass (M), length (L), time (T) and temperature (\theta) and in terms of SI units.

Homework Equations

Nu=\frac{hD}{k}

The Attempt at a Solution

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.

 

[Carlos Gouveia]

Well, in SI units h, the heat transfer coefficient is given in J/(m² s K), or W/(m² K) as 1 W = 1 J/s. Hour (hr) is not one of the SI system's base units.

Therefore, k, the thermal conductivity, should be expressed as W/(m K) and in MLTΘ notation it is expressed as MLT⁻³Θ⁻¹.