Journal of Thermal Science Vol.25, No.4 (2016) 380388 Received: May 2016 Piotr Dzierwa: Dr. www.springerlink.com DOI: 10.1007/s11630-016-0874-7 Article ID: 1003-2169(2016)04-0380-09 Optimum Heating of Thick-Walled Pressure Components Assuming a Quasi-steady State of Temperature Distribution Piotr Dzierwa 1 , Marcin Trojan 1 , Dawid Taler 2 , Katarzyna Kamińska 3 , Jan Taler 1 1. Institute of Thermal Power Engineering, Cracow University of Technology, Cracow, Poland, 2. Institute of Thermal Engineering and Air Protection, Faculty of Environmental Engineering, Cracow, Poland 3. Department of Hydraulic Engineering and Geotechnics, Agricultural University of Cracow © Science Press and Institute of Engineering Thermophysics, CAS and Springer-Verlag Berlin Heidelberg 2016 As a result of the development of wind farms, the gas – steam blocks, which shall quickly ensure energy supply in case the wind velocity is too low, are introduced to the energy system. To shorten the start-up time of the gas – steam and conventional blocks, the structure of the basic components of the blocks are changed, e.g. by reducing the diameter of the boiler, the thickness of its wall is also reduced. The attempts were also made to revise the cur- rently binding TRD 301 regulations, replacing them by the EN 12952-3 European Standard, to reduce the allowa- ble heating and cooling rates of thick walled boiler components. The basic assumption, on which the boiler regu- lations allowing to calculate the allowable temperature change rates of pressure components were based, was the quasi – steady state of the temperature field in the simple shaped component, such as a slab, cylindrical or spher- ical wall. Keywords: pressure component, thermal stress, quasi-steady state, optimum heating Introduction The quasi – steady state occurs in structural compo- nents of boilers and turbines during a long heating or cooling process running at a constant rate of change of temperature. In this paper, a more detailed analysis of the quasi – steady state was conducted for non – weakened walls and for walls weakened by openings. The use of formulas for circumferential stress at the edges of the openings to determine the allowable heating and cooling rates for the assumed pressure was also presented. Those formulas can be used in real life, as the analysis of the temperature and stress fields in the quasi – steady state can be quickly conducted with the use of the Finite Elements Method (FEM), even for components of a complex structure. The quasi – steady state can be characterized by the following factors:  constant temperature difference between the se- lected points of the component (Fig. 1)  constant, time independent, thermal stress (Fig. 2). The results presented in Figs. 1 and 2 were obtained for the following data: r in = 0.85 m, r o = 0.94 m, c = 511 J/(kgK),  = 7775 kg/m 3 , k = 47.3 W/(mK), E = 201105 MPa, β = 1.21×10 ‒5 1/K,  = 0.288. Let's consider the simplifying assumption that the thermo-physical properties of the wall material: k ,c, , E, and  are constant and determined for the average tem- perature over time and the wall thickness. The transient heat transfer equation in the quasi – steady state can be then simplified to form [1, 2] 2 T v T    (1)