text: Free convection is caused by a change in density of a fluid due to a temperature change or gradient. Usually the density decreases due to an increase in temperature and causes the fluid to rise. This motion is caused by the buoyancy force. The major force that resists the motion is the viscous force. The Grashof number is a way to quantify the opposing forces.
  The Grashof number is:
  : for vertical flat plates
  : for pipes and bluff bodies
  where:
  *   is gravitational acceleration due to Earth
  *  is the coefficient of volume expansion (equal to approximately  for ideal gases)
  *  is the surface temperature
  *  is the bulk temperature
  *  is the vertical length
  *  is the diameter
  *  is the kinematic viscosity.
  The  and  subscripts indicate the length scale basis for the Grashof number.
  The transition to turbulent flow occurs in the range  for natural convection from vertical flat plates. At higher Grashof numbers, the boundary layer is turbulent; at lower Grashof numbers, the boundary layer is laminar, that is, in the range .