# Dimensions of k in Nusselt Number

1. Sep 8, 2012

### Jasones

1. The problem statement, all variables and given/known data
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.
2. Relevant equations

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

3. 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.

2. Jun 21, 2015

### 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.