Wednesday, 8 October 2014

Prandtl Number

The Prandtl number \mathrm{Pr} is a dimensionless number that is defined as the ratio of momentum diffusivity (kinematic viscocity) to thermal diffusivity.
It is defined as:
\mathrm{Pr} = \frac{\nu}{\alpha} = \frac{\mbox{viscous diffusion rate}}{\mbox{thermal diffusion rate}} = \frac{c_p \mu}{k}
where:
  • \nu : kinematic viscocity, \nu = \mu/\rho, (SI units : m2/s)
  • \alpha : thermal diffusivity, \alpha = k/(\rho c_p), (SI units : m2/s)
  • \mu : dynamic viscocity, (SI units : Pa s = N s/m2
  • k: thermal conductivity, (SI units : W/(m K) )
  • c_p : specific heat capacity, (SI units : J/(kg K) )
  • \rho : density, (SI units : kg/m3 ).

Pr < 1 means thermal diffusivity dominates and Pr >1 means momentum diffusivity dominates.
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