Volume 46, Issue 3

The authors presented a time-independent plasticity approach, where a typical plastic-loading process is viewed as an infinitesimal state change of two neighboring equilibrium states, and the yield and consistency conditions are formulated based on the conjugate forces of the internal variables. In this paper, a stability condition is proposed, and the yield, consistency, and stability conditions are reformatted by the inelastic differential form of the Gibbs free energy. The Gibbs equation in thermodynamics with internal variables is a representation to the differential form of the Gibbs free energy by a single Gibbs free energy function. In this paper, we propose the so-called extended Gibbs equation, where the differential form may be represented by multiple potential functions. Various associated and nonassociated plasticity with a single or multiple yield functions can be derived from various representations based on the reformulated approach, where yield and plastic potential functions are in the form of inelastic differentials of the potential functions. The generalized Drucker inequality can only be derived from the one-potential representation as a stability condition. For a multiple-potential representation, the stability condition can be ensured if the multiple potentials are concave functions and possess the same stationary point.

Numerical studies have been performed to analyze the fluid flow and heat transfer characteristics of nine microchannel heat sinks (MCHS) with different shapes and different arrangements of the ribs and cavities on the sidewalls, using three common shapes (square, triangle, and circular) of ribs or cavities as the basic structure in this work. The boundary conditions, governing equations, friction factor ( f ), Nusselt number (Nu), and performance evaluation criteria ( ξ ) were considered to determine which design was the best in terms of the heat transfer, the pressure drop, and the overall performance. It was observed that no matter how the circular ribs or cavities were arranged, its heat sink performance was better than the other two shapes for Reynolds number of 200–1000. Therefore, circular ribs or cavities can be considered as the best structure to improve the performance of MCHS. In addition, the heat sink performance of the microchannel heat sink with symmetrical circular ribs (MCHS-SCR) was improved by 31.2 % compared with the conventional microchannel heat sink at Re = 667. This was because in addition to the formation of transverse vortices in the channel, four symmetrical and reverse longitudinal vortices are formed to improve the mixing efficiency of the central fluid (low temperature) and the near-wall fluid (high temperature). Then, as the Reynolds number increases, the heat sink performance of MCHS-SCR dropped sharply. The heat sink performance of microchannel heat sinks with staggered ribs and cavities (MCHS-SCRC, MCHS-STRC, and MCHS-SSRC) exceeded that of MCHS-SCR. This indicated that the microchannel heat sink with staggered ribs and cavities was more suitable for high Reynolds number (Re > 800).

In the present study, conjugate heat transfer and fluid flow performance of microchannel heat sink has been investigated using dimensionless parameters. Novel ribs of four different types are introduced on the side walls of channel, which include trapezoidal ribs, rectangular ribs, hydrofoil ribs, and elliptical ribs. The performance evaluation has been conducted by comparing friction factor ( f ), Nusselt number (NuNu), fluid bulk temperature (Tf{T_{f}}), wall shear stress ( τ ), field synergy number (FcFc), irreversible heat loss (Qd{Q_{d}}), and Bejan number (BeBe) in a Reynolds number, ranging from Re=100\mathit{Re}=100 to Re=1000\mathit{Re}=1000. The results revealed that the addition of these novel ribs are helpful in improving the overall thermal and hydraulic performance of microchannel heat sink. From the results of Bejan number, it has been revealed that more than 96 % of losses are because of heat transfer. However, at low Reynolds number, the frictional losses can be neglected, because of very low fluid velocity. Moreover, it has been revealed that synergetic relation between velocity and temperature gradient becomes weaker at higher Reynolds number. Furthermore, it is clear from this study that elliptical ribs performed better in thermal aspects, whereas hydrofoil ribs performed better at hydrodynamic aspects.

In this paper, a new model of the three-electron reservoir energy selective electronic cooling device applying double-resonance energy filters is proposed by using finite time thermodynamics. The analytical formulas of the main performance parameters for the double-resonance three-electron reservoir cooling device are derived. The optimal cooling load and coefficient of performance of the cooling device varying with major structure design parameters are explored and the optimal operation regions are further determined. Moreover, detailed analyses are conducted to reveal the influences of center energy level difference, chemical potential difference, energy level width, energy spacing and the phonon transmission induced heat leakage on the optimal performance characteristics of the cooling device. Finally, a performance comparison is made between the double-resonance and single-resonance three-electron reservoir electronic cooling devices. It is shown that through reasonable structure design, the optimal performance characteristics of the double-resonance device can be controlled to be much higher than those of the single-resonance cooling device.

The complex time-dependent heat and electromagnetic energy transfer in a new type of reverse thermal engine is analyzed. The reverse thermal engine consists of a cold body, a Peltier element and an electric circuit containing an inductor with controllable inductance. This system allows cooling a body below the ambient temperature. The inductor acts as an accumulator of magnetic energy, receiving electrical work from the Peltier element during some time intervals and supplying the Peltier element with electrical work during other time intervals. The system is named self-driven reverse thermal engine since one of its subsystems (the inductor) receives and releases work. The new type of engine has features which make it different from classical reverse thermal engines: it cannot operate in steady state and it operates for a finite time interval. Instead of usual indicators of performance such as the coefficient of performance, other performance indicators should be used, such as the minimum cooled body temperature and the interval of time needed to reach a given cooled body temperature. Significant cooling effects do not necessarily need high inductance values. The operation of the new engine has been optimized by using direct optimal control procedures. The open-source program package BOCOP has been used to transform the optimal control problem into a non-linear dynamic problem. The minimum temperature reached by the cooled body depends on its mass. There exists, however, a global minimum temperature, for a specified optimum mass of the cooled body. The minimum temperature decreases by increasing the value of the Seebeck coefficient and by decreasing the thermal conductance. Thermal damped oscillations may arise under special circumstances. This implies a very small difference between the initial temperatures of the cold and cooled bodies and a specific range of variation for the conductance of the Peltier element.

The entropy generation rate in a low dimensional film is formulated incorporating the heat flux and effective thermal conductivity of the film material. In the analysis, the mathematical formulation employed is kept the same as that used in the diffusive regime. However, the entropy generation rate is corrected by replacing the bulk thermal conductivity with an effective thermal conductivity evaluated from the Boltzmann equation. The entropy generation rate using the phonon distribution from the equation of phonon radiative transport in the film material is employed. The results show that both formulations result in a very close match for the entropy generation rates.