Grashof Number - Derivation of Grashof Number

Derivation of Grashof Number

The first step to deriving the Grashof Number Gr is manipulating the volume expansion coefficient, as follows:

$\mathrm{\beta}=\frac{1}{v}\left(\frac{\partial v}{\partial T}\right)_p \mathrm=\frac{-1}{\rho}\left(\frac{\partial\rho}{\partial T}\right)_p$

This partial relation of the volume expansion coefficient, with respect to fluid density, and constant pressure can be rewritten as

and

- bulk fluid density - boundary layer density - temperature difference between boundary layer and bulk fluid

There are two different ways to find the Grashof Number from this point. One involves the energy equation while the other incorporates the buoyant force due to the difference in density between the boundary layer and bulk fluid.

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