Fundamental heat and entropy transfer mechanisms of convection underlying the first and second laws for an unsteady multiport system and their applications in parallel flow heat exchangers

Abstract

Although thermal convection is ubiquitous in nature and technology, it has long been argued whether convection can be considered as an independent mode of heat transfer. Here, we show that pure convection mode is generally recognized from the classical first and second laws via mass flow by rooting the unsteady mass conservation relation through an equivalent multiport system. The fundamental distinction is made between convection driven by the thermal and entropy potential differences and mass flow accompanied by zero potential difference. The constitutive relations of the convective heat and entropy fluxes and their thermodynamic relationship are developed in terms of their potential differences with the exponential distribution of temperature difference in a compressible flow. In the absence of work transfer, the first and second laws are simply expressed by the standard Maxwell’s electromagnetic type equations via the total heat and entropy flux vectors. The pure convection theory is applied to a parallel-flow heat exchanger and the linear temperature difference distribution is obtained for both streams via the first-law definitions of the convective and overall heat transfer coefficients in an internal flow. The entropy generation rate inside a heat exchanger is recalculated and indicated to be driven by the difference between the reciprocal of outlet temperatures of two streams, from which the entropy generation number between outlets is developed to eliminate the entropy generation paradox. The present linear temperature difference profiles agree well with the experimental data, and the outlet entropy generation number is also justified by comparing with the previous nondimensionalizing entropy generation numbers.