text: Another form of dimensional analysis that will result in the Grashof number is known as the Buckingham π theorem. This method takes into account the buoyancy force per unit volume,  due to the density difference in the boundary layer and the bulk fluid.
  This equation can be manipulated to give,
  The list of variables that are used in the Buckingham π method is listed below, along with their symbols and dimensions.
  With reference to the Buckingham π theorem there are  dimensionless groups. Choose ,  ,  and  as the reference variables. Thus the  groups are as follows:
  Solving these  groups gives:
  From the two groups  and  the product forms the Grashof number:
  Taking  and  the preceding equation can be rendered as the same result from deriving the Grashof number from the energy equation.
  In forced convection the Reynolds number governs the fluid flow. But, in natural convection the Grashof number is the dimensionless parameter that governs the fluid flow. Using the energy equation and the buoyant force combined with dimensional analysis provides two different ways to derive the Grashof number.