Volume 47, Issue 3

The formalism of the internal variable theory is applied to extend Navier-Stokes equations. The internal variable theory provides a thermodynamically consistent derivation of constitutive relations and equations of motion without a priori specifying the nature of internal variables. Both single and dual internal variables cases are thoroughly examined. The similarities and differences of the approaches are emphasized. In the single internal variable framework, the elimination of the internal variable results in Maxwell-type constitutive relations and hyperbolic equations of motion. The dual internal variable technique enables us to create even more sophisticated fluid flow models with coupled equations for fluid motion and internal variable evolution.

In this work, an analytical analysis of the dynamics of a van der Waals gas flow passing through a direct shock wave was performed. For this purpose, modified Rankine-Hugoniot conditions were used. The influence of parameters α and β of the van der Waals model and the pressure jump in the shock adiabat was analyzed. Relations for the velocity jump in flow were obtained, and the influence of parameters α and β on the velocity jump was revealed. Calculations made it possible to estimate the limits of applicability of the van der Waals model, within which it adequately describes the physics of the process under consideration.

The aim of this paper is to numerically analyze the hydrothermal behavior of different cross-sectional geometries of microchannel heat sinks (MCHSs) and conduct a comparative analysis of traditional and non-traditional designs using ANSYS Fluent. It is expected that the proposed design discussed in this paper will improve the performance of MCHSs by maximizing the cooling capability and minimizing the thermal resistance and entropy generation rate, thus leading to better energy efficiency. The channel designs include a rectangular microchannel (RMC), a circular microchannel (CMC), an elliptical microchannel (EMC), a trapezoidal microchannel (TMC), a hexagonal microchannel (HMC), and a new microchannel (NMC) which has a plus-like shape. The discussed geometry of the NMC is designed in such a way that it maximizes the cross-sectional area and the wetted perimeter of the channel, keeping the hydraulic diameter constant ( D h = 412{D_{h}}=412 µm). The performance of various channels is compared on the basis of pressure drop, wall temperature, thermal enhancement factor, thermal resistance, thermal transport efficiency, and entropy generation rates. It has been observed that the NMC is capable of cooling effectively and it can achieve a minimum wall temperature of 305 K, thus offering the lowest thermal resistance ( R th {R_{\mathrm{th}}}), irreversible heat loss, and entropy generation rate. Moreover, the NMC has achieved the highest value of the thermal enhancement factor, i. e., 1.13, at Re = 1 , 000\mathrm{Re}=1,000. Similarly, it has the highest thermal transport efficiency of almost 97 % at Re = 1 , 000\mathrm{Re}=1,000, followed by the TMC and the RMC. Overall, the NMC has achieved the best performance in all aspects, followed by the RMC and TMC. The performance of the EMC, the CMC, and the HMC was found to be the worst in this study.

Considering the various irreversibility conditions caused by heat transfer and working processes in a dual cycle, the power density performance is optimized by applying finite-time thermodynamics theory, and multi-objective optimization is performed by using NSGA-II. The effects of cut-off ratio, maximum cycle temperature ratio, and various losses by heat transfer and working processes on the relationships between the power density and the compression ratio and between the power density and the thermal efficiency are analyzed. The thermal efficiency and engine size obtained under the conditions of maximum power output and power density are discussed. The results show that for a dual cycle, the heat engine has a smaller size and higher thermal efficiency under the condition of maximum power density. The cycle compression ratio and cut-off ratio are selected as decision variables, and the dimensionless power output, thermal efficiency, dimensionless ecological function, and dimensionless power density are selected as objective functions. Multi-objective optimization is performed with different objective combinations. The deviation indexes under the LINMAP, TOPSIS, and Shannon entropy approaches are discussed, and the number of generations when the genetic algorithm reaches convergence are obtained. The results show that the genetic algorithm converges at the 341st generation for the quadru-objective optimization, at the 488th generation for the tri-objective optimization, and at the 399th generation for the bi-objective optimization. When the bi-objective optimization is performed with dimensionless power output and dimensionless ecological function as the objective functions, the deviation index obtained based on the LINMAP approach is 0.1400, which is better than those obtained for other single- and multi-objective optimizations.

This work proposes a novel approach for the study of open systems described by completely irreversible reaction mechanisms in non-homogeneous systems and subject to non-equilibrium boundary conditions. Using the non-equilibrium thermodynamics framework, we consider that in an autonomous system of reaction–diffusion equations, the thermodynamic potentials can be constructed from a Lyapunov function that depends directly on the eigenvalues and eigenvectors of the linearized problem. By interpreting this Lyapunov function as the free energy and redefining the chemical potentials, we were able to demonstrate the local stability properties of non-equilibrium stationary states, i. e. , states that do not change with time due to a complex equilibration of internal and external flows. We demonstrate the consistency of our hypotheses with basic thermodynamic principles such as the spectral decomposition of entropy production and the Glansdorff–Prigogine evolution criterion. We discuss how our approach allows us to understand thermodynamic systems without assuming equilibrium or any kind of reversibility.