Boiler's efficiency is one of the important performance indicators of boiler. To keep track of operation cost, efficiency needs to be calculated with adequate accuracy by employing effective mathematical tools. In this work, a new modification in conventional mathematical formulation of efficiency is presented based on time-varying efficiency using time-varying operational variables of boiler. This modification was accomplished using indirect method of efficiency by applying experimental data of variables for certain time span. Moreover a second-order dynamic model of flue gas temperature (FGT) has been derived to construct the mathematical formulation of efficiency only in terms of available inputs. The resulting input–output-based model proved to be in quite agreement with efficiency calculated from experimental data. After modeling, influence of variations in air to fuel ratio (AFR) and fuel flow rate (FFR) upon efficiency has been discussed and it has been shown that time-varying efficiency covers deeper aspect of dynamic relation between efficiency and other input of boiler especially AFR and FFR. Moreover, it has been established that efficiency interacts with the dynamics of boiler, and in this respect, a dynamic relation between combustion process and boiler dynamics has been constructed via efficiency.

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