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Homework Help: Dimensions of k in Nusselt Number

  1. Sep 8, 2012 #1
    1. The problem statement, all variables and given/known data
    A common dimensionless group used in heat transfer calculations is defined as:


    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 ([itex]\theta[/itex]) and in terms of SI units.
    2. Relevant equations


    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. jcsd
  3. Jun 21, 2015 #2
    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.
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