Abstract A general methodology of incorporating physical constraints into applications of bracket theory in nonequilibrium thermodynamics is introduced at the macroscopic level expressed in terms of a set of local field variables. Constraints on the state variables are incorporated into the system description by suitably modifying the functional derivatives due to the presence of constraints through an extension of Lagrange’s method of undetermined multipliers to local field variables, whereby the dynamics of conserved quantities are restricted to submanifolds that are compatible with the imposed constraints. This article presents the mathematical prerequisites of the general methodology and a classification of constraints, along with a discussion of characteristic applications to microstructured materials.

Abstract The classical Hertz–Knudsen–Schrage (HKS) relations for mass and heat transfer across liquid-vapor interfaces are valid for ideal gas vapors only. We propose a generalization of the HKS relations towards non-ideal vapors based on equilibrium and non-equilibrium property relations for a van-der-Waals-like gas obtained from the Enskog–Vlasov kinetic equation, and determine the corresponding dimensionless resistivities for mass and heat transfer across an interface. Considering constant evaporation and accommodation coefficients, it is found that all resistivities decay towards the critical point.

Abstract This work provides numerical solution for the dual-phase lag (DPL) theory, which accounts for non-equilibrium heating transfer in cylindrical living tissue during laser irradiation by finite element method. Given the complexity of the governing equation, the solution to such problems is pursued through the implementation of the finite element approach. The assessment of tissue thermal injuries includes determining the span of denatured proteins through the application of the Arrhenius formulation. The results of the finite element method are confirmed as valid by comparing its numerical solution with the data available from the existing experimental data. Furthermore, a comparison with validated experimental data confirms the efficacy of the mathematical model in assessing bioheat transfer in living tissues. The present findings highlight the importance of incorporating dual-phase lags in predictive thermal models to accurately capture the transient response of biological tissues under short-pulse laser exposure.

Abstract In a rigid crystal, phonons are quasiparticles that carry heat, and they can be seen at various levels of description like phonon kinetic theory, phonon hydrodynamics, Guyer–Krumhansl equation, or Fourier heat conduction. In a previous paper, we extended the Guyer–Krumhansl equation by adding two internal state variables, a symmetric tensor and an antisymmetric tensor. These internal variables express the viscous and vortical motion of phonons. In the present paper, we analyze the model by means of asymptotic expansion, and we find a geometric analogue of the model. While the zeroth-order expansion reduces the model to the Guyer–Krumhansl equation, the first-order expansion gives a more complicated heat flux evolution equation, of which the stability conditions of equilibrium solutions are studied. The geometric formulation of the model gives the heat flux as a functional of the entropy flux, in contrast to the usual setting of Extended Irreversible Thermodynamics, and also the two fluxes cease to be proportional via the temperature (in contrast to the Clausius formula for entropy flux).

Abstract Sustainable cooling is critical for climate change mitigation and energy resilience, potentially reducing global greenhouse gas emissions while addressing rising demand for cooling. Solar refrigeration technologies offer alternatives to electricity-intensive refrigeration systems but remain underutilised in industrial applications where thermal energy is required for many manufacturing processes. Specifically, Vuilleumier refrigerators – heat-driven devices with mechanical simplicity – show unexplored potential when powered by concentrated solar energy, as no existing models integrate a solar concentrator with the refrigeration cycle irreversibilities. Here, we develop an endoreversible thermodynamic model of a solar-driven Vuilleumier refrigerator, coupling optical concentration, absorber design, and regeneration effect. Numerical analysis reveals that the coefficient of performance ( β ) exhibits concentration-dependent thresholds ( ξ > 0.18 at 273 K; ξ > 0.11 at 253 K), with asymptotic plateaus at β ≈ 9 and β ≈ 4 respectively. Normalised sensitivity analysis identifies regenerator effectiveness ( ɛ ) as the dominant parameter (12–16 times more influential), compared with the solar-specific parameters. These results resolve a critical gap in solar-thermal refrigeration by demonstrating that regenerator design – not concentrator scaling – limits maximum coefficient of performance. This work provides a thermodynamic blueprint delineating the fundamental performance boundaries of solar-Vuilleumier technology, governed by irreversibility constraints and asymptotic efficiency limits.

Abstract An endoreversible-model of air-standard modified Atkinson-cycle via isothermal-heat-addition is built in this study, power ( P ), efficiency ( η ), power-density ( P d ), ecological-function ( E ), and efficient-power ( E p ) performances of modified Atkinson-cycle are analyzed and compared firstly. Taking P ̄ $\bar{P}$ , η , P d , E and E ̄ p ${\bar{E}}_{p}$ as objective-functions (OFs), and compression-ratio ( γ ) as optimization variable, the one five-objective optimization, five quadru-objective optimizations, ten tri-objective optimizations, ten bi-objective optimizations and five single-objective optimizations are completed by using NSGA-II furtherly. To find optimal solution, deviation indices ( Ds ) of three decision-making-methods (DMMs) which include Shannon Entropy, LINMAP and TOPSIS are utilized to compare optimization results. Results show that curves P versus η and P d versus η are loop-shaped ones, and curves P versus γ and P d versus γ are parabolic-like ones. With the increases of pre-expansion-ratio ( ρ ) and the maximum-temperature-ratio ( τ ), P d is improved. Modified Atkinson-cycle designed with P d as the OF has smaller size and higher η . Compared with traditional Atkinson-cycle, isothermal heating modified Atkinson-cycle performance is evidently improved, P ̄ $\bar{P}$ , η , E ̄ $\bar{E}$ , P ̄ d ${\bar{P}}_{d}$ , E ̄ p ${\bar{E}}_{p}$ are improved by 30.18 %, 7.31 %, 39.57 %, 32.27 %, 47.60 %, respectively. When optimized with 5, 4, 3, or two objectives, the more the number of objectives is, modified Atkinson-cycle has more reasonable design plan and better trade-off design performance . The major contributions herein are establishment of modified Atkinson-cycle and accomplishment of MOOs for it with five OFs.

Abstract This study develops a novel thermoelectric generator system to utilize vehicle exhaust gas waste heat and convert it into electrical energy. A three-dimensional thermoelectric generator system with innovative heat sinks on both the hot and cold sides is designed to boost the thermoelectric generator’s output power and conversion efficiency. Three novel heat sink models for both sides of the thermoelectric generator are generated according to the square-pin fin size and the gaps between the fins to investigate the effects of the exhaust gas temperature and its flow rate. According to the findings, the highest temperature difference between both sides of the thermoelectric generator and the highest hot side heat transfer rate are obtained as 185.56 K and 113.69 W for Model C, and the maximum output power reached up to 4.44 W with a conversion efficiency of 3.90 % for the same model. As a result, the net output power is maximized with Model C at 4.07 W concerning the pressure drop and the pumping power. Considering waste heat recovery systems, Model C yields an increase in thermoelectric power generation by 23.3 % from 3.6 W to 4.44 W compared to the systems in the literature.

Abstract In this work, a theoretical study is carried out on the effects of the thickness of a semiconductor thin film on the transport of heat and particles under the action of an external temperature difference. The dependence of the Seebeck effect on the thickness is considered. The thickness film is introduced through the transport coefficients of the material, namely, the thermal and electrical conductivities and the intrinsic Seebeck coefficient, by resorting to known results of irreversible thermodynamics. Graphs of the generated electric potential difference by an external temperature difference versus film thickness are obtained in the range 0.1 µm–1 µm. We compare the results of two slightly doped materials, namely, silicon and bismuth telluride of the n- and p- types. The n-type silicon shows an optimal thickness where the generated electric potential difference is maximum, while the electric potential difference in the n-type bismuth telluride decreases with decreasing thickness. The electric response of p-type silicon and p-type bismuth telluride also worsens as the thickness decreases. The results presented may be useful in the design of thermoelectric devices on the sub-micrometer length scale.

Abstract We studied planar compressible Poiseuille flows of an ideal gas, both in steady and unsteady states, to identify the minimal number of state parameters required to describe changes in internal energy. In previous work (Phys. Rev. E 104, 055107 (2021)), five parameters were needed for steady flows. Here, using global non-equilibrium thermodynamics, we reduce this number to three: non-equilibrium entropy S * , volume V , and number of particles N . The internal energy U ( S * , V , N ) of such systems in stationary and non-stationary states is the function of non-equilibrium entropy S * , volume V and number of particles N in the system irrespective of any processes, number of boundary conditions or imposed constraints. We tested this by placing a cylinder inside the channel, finding that U depends on the cylinder’s location y c only via the state parameters S * ( y c ) and N ( y c ) for V = const. Moreover, in cases where the flow becomes unstable and parameters such as velocity and pressure oscillate, U depends on time t only through S * ( t ) and N ( t ) for V = const. These results demonstrate that this formulation of internal energy remains robust and consistent, even in unsteady flows with varying boundary conditions.