This paper proposes a mathematical model with distributed parameters that allows to simulate the heat transfer processes in combustion chamber waterwalls of supercritical steam boilers. The model comprises solving the one-dimensional mass, momentum and energy conservation equations. The Forward Time Backward Space scheme is applied to discretize the governing equations. Two types of computational verification are performed for the proposed model. At first the model is validated with the analytical solution. The computational accuracy of the proposed model was tested for different time steps and grid size. At second, the results produced by the model were compared with those obtained when the Crank-Nicolson scheme is used to discretize the energy equation. In this case of results comparison the fluid flow and heat transfer phenomena were modeled for spirally wounded waterwall tubes of the combustion chamber in a supercritical boiler. A good agreement was found between the results produced by the proposed model and those obtained by using the analytical and Crank-Nicolson approaches. Therefore, the proposed model can be regarded as a useful tool for the design and monitoring of this type of heated surfaces. Moreover, the model can be applied in power units simulators. (C) 2015 Elsevier Ltd. All rights reserved.