Abstract: An algebraically explicit analytical solution is derived for the partial differentical equation set describing the thermal dynamic process of boiler economizer heating surface. The expression of temperatures of flue gas, metal tube and working substance in this analytical solution only consist of linear terns and exponential terms of independent variables as well as constants. The physical meaning of this analytical solution is clear and typical. An extraordinary method is proposed to obtain the analytical solution; instead of the ordinary method of separating variables assuming the unknown solution, another method of separating variables assuming, is applied. It is found out that the latter (perhaps can be named method of separating variables with addition) is able to solve the thermal dynamic process equation set but the former is not. Then, it is worth developing further this extraordinary method.

Key words: Analytical solution, Boiler, Dynamic process, Heating surface