To resolve the inconsistencies associated with entropy production rates in convective heat transfer for unsteady compressible flows, the novel formulae for overall entropy generation rate and entropy generation rates per unit length and per unit volume are developed with a common driving force of inverse temperature differences complying with the Onsager's relation including the contributions of conduction and pure convection. The intrinsic relationships among three entropy generation rates are established and the difference between entropy generation rate and entransy dissipation rate is distinguished. To measure the relative utilization quantity and quality of an enhanced heat transfer wall, a wall temperature effectiveness (w) is defined as the ratio of thermal conductance to capacity rate and a wall entropy transfer efficiency (ηw) based on the second law is introduced for convective heat transfer devices. It is shown that w is the nondimensionalized convective heat transfer coefficient and ηw is the ratio of bulk fluid temperature to wall surface temperature with the relation associated with a pressure-drop (pumping power) duty parameter (a) and inlet fluid-to-wall temperature ratio (ϕ) between w and ηw. The validity of proposed entropy generation rates and the concepts of w and ηw is demonstrated by the heat transfer rate−temperature diagrams and by comparing to previous formulations. As an alternative criterion of performance evaluation, a wall effectiveness–wall entropy transfer efficiency method is developed to simultaneously gauge the figures of merit of the first- and second-law performances combining the influences of temperature difference and pressure drop, and the actual lower and upper limits of ηw and w dependent only on a and ϕ are obtained for practical operation. The w−ηw method is applied to typical heat exchangers (for the single-side case) to demonstrate its usefulness and sensitivity.
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