The Kudryashov and Sinelshchikov (KS) equation address pressure waves in liquid-gas bubble mixtures while considering heat transport and viscosity. This study mainly includes two types of generalized solutions: polynomial function traveling wave solutions and rational function traveling wave solutions. In this study, we constructed the KS equation's exact traveling and solitary wave solutions with variable coefficients by the generalized unified method (GUM). These newly created solutions play a significant role in mathematical physics, optical fiber physics, plasma physics, and other applied sciences disciplines. We illustrated the dynamical behavior of the discovered solutions in three dimensions. We proposed the possibility of discussing wave interaction and other wave structures using bilinear form related to the Hirota method for the fractional solution.

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This paper describes a real-time performance-monitoring method based on PTC 4-2013 that was developed for determining and reporting the annual heat rate for fossil fuel power plants. Unlike for the PTC 4 test, the coal composition is typically not known in real-time, so the procedure uses a modified output-loss approach applied to a control volume that closely conforms to the boiler. A calibration approach utilizes an ultimate analysis to describe the coal being burned during the calibration, while holding the plant load and other factors steady. This permits the calculation of correction factors used during real-time performance monitoring. Based on several assumptions that are justified within, a real-time estimate of coal composition is obtained. The losses are calculated in a similar manner to PTC 4-2013. However, the losses are expressed on a per-pound of as-fired coal basis, as opposed to a percentage of higher heating value of the coal, which is not known in real-time.

This paper describes a modified F-factor approach for real-time performance monitoring of heat rate and CO2 emissions for fossil fuel power plants. The calculation protocol introduced in the present investigation is a modification of the F-factor method mandated by the U.S. Environmental Protection Agency (EPA). It utilizes Continuous Emissions Monitoring Systems (CEMS) data to evaluate an F-factor based on actual conditions prevailing in the combustion process, and therefore is less reliant on the use of empirical correction factors. The proposed method is intended to be used in combination with a real-time output-loss performance monitoring approach described herein. It was shown that when modified F-factors were corrected back to standard conditions of stack pressure and temperature, and stoichiometric combustion was assumed, standard EPA F-factors were comparable in magnitude to the values generated by the real-time algorithm. The modified F-factor method was used to evaluate the gross heat rate. The resulting heat rate values were identical to those obtained by a real-time performance monitoring algorithm for the same input data. The modified F-factor method was likewise used to calculate the mass flow rate of CO2 as a function of gross plant generation. Those resulting values were compared to similar data reported to EPA. The real-time CO2 mass flow rate data obtained using the modified F-factor method agreed more closely with the EPA F-factor values as the plant load increased.