Transient thermal Marangoni convection in a liquid bridge

By a sudden change of an imposed axial temperature field at the liquid surface of an infinite cylindrical liquid bridge, a transient convection is initiated inside the liquid. This is due to the sudden change in surface tension causing a transient flow from an original velocity distribution to a final one by means of the thermal Marangoni effect. This transient has been determined analytically for linear, quadratic, sinusoidal and exponential axial temperature fields. Some special cases have been evaluated numerically. It should be noted that the method presented may also be used if any periodic axial temperature distribution is suddenly changed into any other periodic temperature field. It is also valid for time-periodic temperature fields.