The Analysis of Thermomechanical Periodic Motions of a Drinking Bird

Abstract

A water drinking bird or simply drinking bird (DB) is discussed in terms of a thermomechanical model. A mathematical expression of motion derived from the thermomechanical model of a drinking bird and numerical solutions are explicitly shown, which is helpful in understanding physical meanings and fundamental difference between mechanical and thermomechanical periodic motion. The mathematical and physical differences between mechanical and thermomechanical motions are clearly examined, resulting in time-independent and time-dependent coupling constants of equations of motion and continuous transitions between bifurcation solutions. The thermodynamical and irreversible process of a drinking bird motion could be theoretically examined and practically applied to energy harvesting technologies by way of the current modeling. As an example of irreversible thermodynamics, the thermomechanical model of DB will help understand heat engines manifested from microscopic to macroscopic systems.

Thermodynamic Consistency and Thermomechanical Dynamics (TMD) for Nonequilibrium Irreversible Mechanism of Heat Engines

“…It demonstrates thermodynamic phenomena, or more precisely, irreversible thermodynamic phenomena. We have discussed the equation of motion and solution to the thermomechanical DB model and practical applications through thermoelectric energy conversions [4] [5]. Based on the papers, the irreversible thermodynamic DB system and thermodynamic consistency, time-evolution to thermodynamic equilibrium, the concept of coupling and decoupling of mechanical and thermodynamic systems will be discussed and numerically evaluated in the current paper.…”

“…The change of the thermal state is related to time-evolution of the internal energy, ( ) where the time c t is a "critical time" (onset time) for the transition, and d t is the corresponding drinking (dipping) time. The transition from a NIS to an equilibrium state after dipping is similarly investigated by: Though detailed heat conduction mechanisms should be introduced for transitions at c t and d t shown by arrows in (1.2) and (1.3), the transitions are mathematically simplified and expressed by using piecewise continuous function (the step function) in the thermomechanical model [4]. The "thermodynamic consistency of irreversible processes" is examined by conditions: (1.1)- (1.3).…”

“…After a DB's dipping, the volatile water in the glass tube is artificially returned to the lower bulb by a mechanical trick. The mathematical technicality corresponding to the mechanical trick is produced with the step function and termed as "initialization" [4].…”

Improving Heat-Engine Performance via High-Temperature Recharge

“…In Section 4, we discuss the work outputs, efficiencies, and entropy productions of Carnot and Curzon-Ahlborn heat engines operating with frictional dissipation of a heat engine's work output at the highest practicable temperature-which we dub as high-temperature recharge (HTR)-and the improvements thereof over those obtainable (as per Section 3) without HTR. Cases wherein HTR is practicable include, but are not necessarily limited to, (a) hurricanes, which via HTR are rendered more powerful than they would otherwise be [27][28][29][30][31][32][33][34][35][36][37], (b) thermoelectric generators [38], and (c) heat engines powered by a cold reservoir, employing ambient as the hot reservoir, for example, heat engines powered by the evaporation of water [39][40][41][42][43][44][45][46][47][48][49][50][51] or by liquid nitrogen [52], ocean-thermal-energy-conversion (OTEC) heat engines [53][54][55][56], and heat engines powered by the cold of outer space [57].…”

“…Hence for these cyclic heat engines, HTR at the temperature of the hot reservoir could increase efficiency, but HTR at a still higher temperature probably would not be practicable. By contrast, consider cyclic heat engines powered by a cold reservoir, employing ambient as the hot reservoir, for example, cyclic heat engines powered by the evaporation of water [39][40][41][42][43][44][45][46][47][48][49][50][51] or by liquid nitrogen [52], ocean thermal-energy-conversion (OTEC) heat engines [53][54][55][56], and heat engines powered by the cold of outer space [57]. For these cyclic heat engines, HTR at a higher temperature than ambient probably would be practicable.…”