Critical components in coal-fired power plants such as final superheater heat exchangers experience severe conditions associated with high metal temperatures and high temperature gradients during base load and transient operations. Such adverse conditions could significantly reduce the life span of the components, especially due to the requirement of greater plant flexibility that is an essential part of the global power system transformation. Integrated thermofluid process models can be employed to obtain a better understanding of the relationship between the operational conditions and the metal temperatures. Thus, a methodology was developed to model radiant superheater heat exchangers in steady state and transient operations. The methodology is based on a network approach which entails solving the transient one-dimensional forms of the conservation equations for mass, energy and momentum. The model building blocks account for the convective thermal resistance on the steam side, the conductive thermal resistances of the tube wall and scaling or fouling on the tube walls, as well as the convective and radiative thermal resistances and direct radiation on the flue gas side. The model captures the physical layout of the tube passes in a tubesheet via the arrangement of the network building blocks. It is also possible to connect tubesheets together across the width of the boiler as per the arrangement in a real plant. The modelling methodology was first used to develop a process model of a convective cross-flow primary superheater heat exchanger with complex flow arrangement. The dual-tube 12-pass superheater was discretized along the flue gas flow path as well as along the steam flow path. The model was qualitatively validated using real plant data from literature and for reference purposes also systematically compared to conventional lumped parameter models. The ability of the model to analyse the effect of ramp rate during load changes on the tube metal temperature was demonstrated, as well as the ability to determine the maldistribution of flow and temperature on the steam and flue gas sides. The methodology was also applied to model a U-shaped radiant superheater heat exchanger. Due to the challenges associated with obtaining comprehensive real plant data in an industrial setting, a validation methodology was proposed that is based on a combination of plant design C-schedules and a boiler mass and energy balance, as well as limited plant measurements. The consistent comparisons with C-schedule data provide evidence of the validity of the model, which was further demonstrated via the comparisons with real plant data. The model allows prediction of the steam mass flow and temperature distribution going into the outlet stub headers as well as the main outlet headers for different inlet flow and temperature distributions on the steam and flue gas sides. These results were compared to detail real-plant measurements of the outlet header temperatures. The model also allows prediction of the metal temperatures along the length of the tubes which cannot readily be measured in the plant. The model was applied to demonstrate the impact of different operational conditions on the tube metal temperatures. Such integrated process models can be employed to study complex thermofluid process phenomena that may occur during intermittent, transient and low load operation of power plants. In addition, such models could be useful for predictive and preventative maintenance as well as online condition monitoring.