Stochastic exergy and entropy generation in heat-recovery channels under correlated wall heating

Abstract

Abstract Industrial flue-gas waste-heat recovery is affected not only by the amount of recovered heat but also by the stability and thermodynamic quality of the recovered energy. In furnace operation, load variation, combustion fluctuation, flow redistribution, and wall fouling can generate spatially non-uniform and temporally correlated wall-temperature disturbances. This study develops a stochastic thermodynamic framework for a three-dimensional flue-gas waste-heat-recovery channel subjected to random wall heating. The heated-wall temperature fluctuation is modeled as an Ornstein-Uhlenbeck random field, and the recovery-side fluid temperature is governed by a convection-diffusion equation with a stochastic Robin boundary condition. The temperature response is decomposed into a deterministic mean field and a zero-mean fluctuation field. A boundary-to-outlet transfer formulation is then used to propagate the wall disturbance to an outlet-layer temperature variance, while the same fluctuation statistics are used to evaluate second-order corrections to recovered heat rate, recovered exergy, entropy generation, and exergy destruction. The analysis shows that the channel behaves as a thermal low-pass filter: slowly varying wall-temperature fluctuations are transmitted more effectively to the outlet than rapidly varying fluctuations. The recovered-exergy correction is positive but small for the investigated baseline case because it depends mainly on the smoothed outlet-temperature variance. By contrast, the entropygeneration correction is much larger because it depends on local fluctuation, gradient, and wall-covariance terms near the heated boundary. These results indicate that outlet-based energy or exergy indicators alone may underestimate the thermodynamic impact of random heat-source nonuniformity, whereas stochastic entropy-generation analysis captures the associated local irreversibility.