In the event of turbo-generator set participating into the peak-regulating operation

the thermal expansion of turbine casing is one of the most important factors affecting flexibility and safety of the steam turbine.Starting from unstable differential equation of heat conduction for a two-dimentional(2-D) cylindrical wall

in which the internal steam is linearly distributing along the axial direction

and varying along with the time

and external wall is adiabatic

has been obtained from deduction

and a comparison with the result from finite-element calculation being carried out.It shows that the obtained model has high precison and rapid calculation.Directing against steam cylinders with different structure

and through some reasonable assumptions

a complicated cylinder structure can be decomposed into simple sub-structures

and a cylinder model of axial expansion has been obtained.The said model can also be used for real-time monitoring of axial expansion for the steam cylinder.The deducing method applied and the expansion calculating formula obtained can also used for other correlative analysis of cylindrical components with thick wall having similar boundary conditions.