Heat conduction in cylinders: Entropy generation and mathematical inequalities. (June 2018)

• Record Type: Journal Article
• Authors: Tian, Xiaowei; Wang, Liqiu
• Is Part Of: International journal of heat and mass transfer. Volume 121(2018)
• Page Start: 1137
• Page End: 1145
• Publication Date: 2018-06
• Subjects: Entropy generation -- Heat conduction -- Mathematical inequalities -- Second law of thermodynamics; Heat -- Transmission -- Periodicals; Mass transfer -- Periodicals; Chaleur -- Transmission -- Périodiques; Transfert de masse -- Périodiques; Electronic journals; 621.4022
• DOI: 10.1016/j.ijheatmasstransfer.2018.01.055
• Languages: English
• ISSNs: 0017-9310

Abstract

Highlights: Entropy generation and its limit as time tends to infinity. Mathematical inequalities from the second law of thermodynamics being applied to heat conduction in adiabatic cylinders. Bounded entropy generation if the heat conduction is initiated by the initial temperature distribution. Unbounded entropy generation if the heat conduction involves a heat source with positive volume average. The relation between the second law of thermodynamics and mathematical inequalities. Some fundamental insights of universe and our future. Abstract: We examine the entropy generation regarding its magnitude and the limit as time tends to infinity and apply the second law of thermodynamics to develop mathematical inequalities with heat conduction in adiabatic cylinders. The former shows a bounded entropy generation if the heat conduction is initiated by the initial temperature distribution, but unbounded if the heat conduction involves a heat source with positive volume average over the cylinder. The latter yields various innovative relations that are useful both for studying differential equations and for examining accuracy of analytical, numerical and experimental results. The work not only builds up the relation between the second law of thermodynamics and mathematical inequalities, but also offers some fundamental insights of universe and our future.