Transient convection due to the sudden change of the temperature gradient

Changing the imposed angular temperature distribution suddenly into another angular temperature yields a transient convection due to the thermal Marangoni effect inside the liquid column until the final velocity distribution is reached. This transient has been determined analytically for a liquid bridge, for which no axial dependency exists,i.e. for the two-dimensional case. The method may also be applied to time-periodic temperature fields.