Physics-informed neural network models of industrial systems often fail to provide accurate predictions consistently over time because of temporal variations in raw material characteristics, plant operating and environmental conditions, and asset health. This necessitates updating of model parameters, which, in turn, requires exploration of the parameter space and identification of accurate values of model parameters regularly to enhance the reliability of models. To address this need, we present a sequential training and tuning methodology consisting of solving both forward and inverse problems of PINNs and parameter discovery via optimization. This methodology is tested for modeling of heat transfer in a rotary kiln, a common equipment in many process industries such as chemicals, steel, cement and materials. The proposed approach not only uncovers accurate model parameters but also helps in building a robust PINN model. Model predictions using parameters obtained through the proposed approach are in fairly good agreement with data from an industrial rotary kiln. This method can update model parameters as needed, offering more reliable and accurate predictions compared to traditional approaches.