Suitability of Embedded Liquid Cooling and Heat Generation for Chips.

Embedded liquid cooling is a preferred solution for dissipating the heat generated by high-power chips. The cooling capacity and pump power consumption of embedded liquid cooling heat sinks differ significantly between different structures. To achieve an accurate match between cooling capacity and heat dissipation requirements, the selection of a liquid-cooled heat sink should be carefully considered in conjunction with the heat dissipation needs of heat sources in real-world thermal management issues. Based on the manufacturing limitations on chip temperature and microchannel pressure, a composite performance index function was developed to assess the cooling capacity and cooling cost of the heat sink. This allowed for the establishment of an evaluation standard to determine the suitability of embedded liquid cooling and heat sink for the heat source. In this study, the suitability of four microchannel heat sinks with the same feature length and fin volume was evaluated under various thermal load conditions. The results show that the best-suited heat sink changes with variations in the thermal load of the chip. In the example, when the heat source was homogeneous at 100 W, the circular section pin fins have an optimal suitability of 0.928 for Re = 500. When the heat source was a heterogeneous heat source with a power of 100 W, the value of Θ was found to be 0.389. Additionally, the optimal suitability of drop section pin fins for Re = 971.5 was determined to be 0.862.

Thermal-Hydrodynamic Behavior and Design of a Microchannel Pin-Fin Hybrid Heat Sink.

A three-dimensional convective heat transfer model of a microchannel pin-fin hybrid heat sink was established. Considering the non-uniform heat generation of 3D stacked chips, the splitting distance of pin-fins was optimized by minimizing the maximum heat sink temperature under different heat fluxes in the hotspot, the Reynolds numbers at the entrance of the microchannel, and the proportions of the pin-fin volume. The average pressure drop and the performance evaluation criteria were considered to be the performance indexes to analyze the influence of each parameter on the flow performance and comprehensive performance, respectively. The results showed that the maximum temperature of the hybrid heat sink attained a minimum value with an increase in the splitting distance. The average pressure drop in the center passage of the microchannel first increased and then decreased. Furthermore, the optimal value could not be simultaneously obtained with the maximum temperature. Therefore, it should be comprehensively considered in the optimization design. The heat flux in the hotspot was positively correlated with the maximum heat sink temperature. However, it had no effect on the flow pressure drop. When the Reynolds number and the pin-fin diameter increased, the maximum heat sink temperature decreased and the average pressure drop of the microchannel increased. The comprehensive performance of the hybrid heat sink was not good at small Reynolds numbers, but it significantly improved as the Reynolds number gradually increased. Choosing a bigger pin-fin diameter and the corresponding optimal value of the splitting distance in a given Reynolds number would further improve the comprehensive performance of a hybrid heat sink.

Efficient Power Characteristic Analysis and Multi-Objective Optimization for an Irreversible Simple Closed Gas Turbine Cycle.

On the basis of the established irreversible simple closed gas turbine cycle model, this paper optimizes cycle performance further by applying the theory of finite-time thermodynamics. Dimensionless efficient power expression of the cycle is derived. Effects of internal irreversibility (turbine and compressor efficiencies) and heat reservoir temperature ratio on dimensionless efficient power are analyzed. When total heat conductance of two heat exchangers is constant, the double maximum dimensionless efficient power of a cycle can be obtained by optimizing heat-conductance distribution and cycle pressure-ratio. Through the NSGA-II algorithm, multi-objective optimizations are performed on the irreversible closed gas turbine cycle by taking five performance indicators, dimensionless power density, dimensionless ecological function, thermal efficiency, dimensionless efficient power and dimensionless power output, as objective functions, and taking pressure ratio and heat conductance distribution as optimization variables. The Pareto frontiers with the optimal solution set are obtained. The results reflect that heat reservoir temperature ratio and compressor efficiency have greatest influences on dimensionless efficient power, and the deviation indexes obtained by TOPSIS, LINMAP and Shannon Entropy decision-making methods are 0.2921, 0.2921, 0.2284, respectively, for five-objective optimization. The deviation index obtained by Shannon Entropy decision-making method is smaller than other decision-making methods and its result is more ideal.

Four-Objective Optimization for an Irreversible Porous Medium Cycle with Linear Variation in Working Fluid's Specific Heat.

Considering that the specific heat of the working fluid varies linearly with its temperature, this paper applies finite time thermodynamic theory and NSGA-II to conduct thermodynamic analysis and multi-objective optimization for irreversible porous medium cycle. The effects of working fluid's variable-specific heat characteristics, heat transfer, friction and internal irreversibility losses on cycle power density and ecological function characteristics are analyzed. The relationship between power density and ecological function versus compression ratio or thermal efficiency are obtained. When operating in the circumstances of maximum power density, the thermal efficiency of the porous medium cycle engine is higher and its size is less than when operating in the circumstances of maximum power output, and it is also more efficient when operating in the circumstances of maximum ecological function. The four objectives of dimensionless power density, dimensionless power output, thermal efficiency and dimensionless ecological function are optimized simultaneously, and the Pareto front with a set of solutions is obtained. The best results are obtained in two-objective optimization, targeting power output and thermal efficiency, which indicates that the optimal results of the multi-objective are better than that of one-objective.

Constructal Optimizations of Line-to-Line Vascular Channels with Turbulent Convection Heat Transfer.

The multi-scale line-to-line vascular channels (LVCs) widely exist in nature because of their excellent transmission characteristics. In this paper, models of LVCs with turbulent convection heat transfer are established. Based on constructal theory and the entropy generation minimization principle, the constructal optimizations of LVCs with any order are conducted by taking the angles at bifurcations as the optimization variables. The heat flux on the channel wall per unit length is fixed and uniform. The areas occupied by vasculature and the total volumes of channels are fixed. The analytical expressions of the optimal angles, dimensionless total entropy generation rate and entropy generation number (EGN) of LVCs with any order versus dimensionless mass flow rate are obtained, respectively. The results indicate that the dimensionless total entropy generation rate of LVCs with any order can be significantly decreased by optimizing the angles of LVCs, which is significantly more when the order of LVCs is higher. As the dimensionless mass flow rate increases, the optimal angles of LVCs with any order remain unchanged first, then the optimal angles at the entrance (root) increase, and the other optimal angles decrease continuously and finally tend to the respective stable values. The optimal angles of LVCs continue to increase from the entrance to the outlet (crown), i.e., the LVCs with a certain order gradually spread out from the root to the crown. The dimensionless total entropy generation rate and EGN of LVCs first decrease and then increase with the growth of the dimensionless mass flow rate. There is optimal dimensionless mass flow rate, making the dimensionless total entropy generation rate and the EGN reach their respective minimums. The results obtained herein can provide some new theoretical guidelines of thermal design and management for the practical applications of LVCs.

Multi-Objective Constructal Design for Quadrilateral Heat Generation Body with Vein-Shaped High Thermal Conductivity Channel.

Based on the quadrilateral heat generation body (HGB) proposed by previous literature, the multi-objective constructal design is performed. Firstly, the constructal design is performed by minimizing the complex function composed of the maximum temperature difference (MTD) and entropy generation rate (EGR), and the influence of the weighting coefficient (a0) on the optimal constructal is studied. Secondly, the multi-objective optimization (MOO) with the MTD and EGR as optimization objectives is performed, and the Pareto frontier with an optimal set is obtained by using NSGA-II. The optimization results are selected from the Pareto frontier through LINMAP, TOPSIS, and Shannon Entropy decision methods, and the deviation indexes of different objectives and decision methods are compared. The research of the quadrilateral HGB shows that the optimal constructal can be gained by minimizing the complex function with the objectives of the MTD and the EGR, the complex function after the constructal design is reduced by up to 2% compared with its initial value, and the complex function of the two reflects the compromise between the maximum thermal resistance and the irreversible loss of heat transfer. The Pareto frontier includes the optimization results of different objectives, and when the weighting coefficient of a complex function changes, the optimization results obtained by minimizing the complex function will also be distributed in the Pareto frontier. The deviation index of the TOPSIS decision method is 0.127, which is the lowest one among the discussed decision methods.

Maximum Efficient Power Performance Analysis and Multi-Objective Optimization of Two-Stage Thermoelectric Generators.

Two-stage thermoelectric generators have been widely used in the aerospace, military, industrial and daily life fields. Based on the established two-stage thermoelectric generator model, this paper further studies its performance. Applying the theory of finite-time thermodynamics, the efficient power expression of the two-stage thermoelectric generator is deduced firstly. The maximum efficient power is obtained secondly by optimizing the distribution of the heat exchanger area, distribution of thermoelectric elements and working current. Using the NSGA-II algorithm, multi-objective optimizations of the two-stage thermoelectric generator are performed thirdly by taking the dimensionless output power, thermal efficiency and dimensionless efficient power as objective functions, and taking the distribution of the heat exchanger area, distribution of thermoelectric elements and output current as optimization variables. The Pareto frontiers with the optimal solution set are obtained. The results show that when the total number of thermoelectric elements is increased from 40 to 100, the maximum efficient power is decreased from 0.308W to 0.2381W. When the total heat exchanger area is increased from 0.03m2 to 0.09m2, the maximum efficient power is increased from 0.0603W to 0.3777W. The deviation indexes are 0.1866, 0.1866 and 0.1815 with LINMAP, TOPSIS and Shannon entropy decision-making approaches, respectively, when multi-objective optimization is performed on three-objective optimization. The deviation indexes are 0.2140, 0.9429 and 0.1815 for three single-objective optimizations of maximum dimensionless output power, thermal efficiency and dimensionless efficient power, respectively.

Four-Objective Optimizations of a Single Resonance Energy Selective Electron Refrigerator.

According to the established model of a single resonance energy selective electron refrigerator with heat leakage in the previous literature, this paper performs multi-objective optimization with finite-time thermodynamic theory and NSGA-II algorithm. Cooling load (R¯), coefficient of performance (ε), ecological function (ECO¯), and figure of merit (χ¯) of the ESER are taken as objective functions. Energy boundary (E'/kB) and resonance width (ΔE/kB) are regarded as optimization variables and their optimal intervals are obtained. The optimal solutions of quadru-, tri-, bi-, and single-objective optimizations are obtained by selecting the minimum deviation indices with three approaches of TOPSIS, LINMAP, and Shannon Entropy; the smaller the value of deviation index, the better the result. The results show that values of E'/kB and ΔE/kB are closely related to the values of the four optimization objectives; selecting the appropriate values of the system can design the system for optimal performance. The deviation indices are 0.0812 with LINMAP and TOPSIS approaches for four-objective optimization (ECO¯-R¯-ε-χ¯), while the deviation indices are 0.1085, 0.8455, 0.1865, and 0.1780 for four single-objective optimizations of maximum ECO¯, R¯, ε, and χ¯, respectively. Compared with single-objective optimization, four-objective optimization can better take different optimization objectives into account by choosing appropriate decision-making approaches. The optimal values of E'/kB and ΔE/kB range mainly from 12 to 13, and 1.5 to 2.5, respectively, for the four-objective optimization.

Four-Objective Optimization of an Irreversible Magnetohydrodynamic Cycle.

Based on the existing model of an irreversible magnetohydrodynamic cycle, this paper uses finite time thermodynamic theory and multi-objective genetic algorithm (NSGA-II), introduces heat exchanger thermal conductance distribution and isentropic temperature ratio of working fluid as optimization variables, and takes power output, efficiency, ecological function, and power density as objective functions to carry out multi-objective optimization with different objective function combinations, and contrast optimization results with three decision-making approaches of LINMAP, TOPSIS, and Shannon Entropy. The results indicate that in the condition of constant gas velocity, deviation indexes are 0.1764 acquired by LINMAP and TOPSIS approaches when four-objective optimization is performed, which is less than that (0.1940) of the Shannon Entropy approach and those (0.3560, 0.7693, 0.2599, 0.1940) for four single-objective optimizations of maximum power output, efficiency, ecological function, and power density, respectively. In the condition of constant Mach number, deviation indexes are 0.1767 acquired by LINMAP and TOPSIS when four-objective optimization is performed, which is less than that (0.1950) of the Shannon Entropy approach and those (0.3600, 0.7630, 0.2637, 0.1949) for four single-objective optimizations, respectively. This indicates that the multi-objective optimization result is preferable to any single-objective optimization result.

Four-Objective Optimization of an Irreversible Stirling Heat Engine with Linear Phenomenological Heat-Transfer Law.

This paper combines the mechanical efficiency theory and finite time thermodynamic theory to perform optimization on an irreversible Stirling heat-engine cycle, in which heat transfer between working fluid and heat reservoir obeys linear phenomenological heat-transfer law. There are mechanical losses, as well as heat leakage, thermal resistance, and regeneration loss. We treated temperature ratio x of working fluid and volume compression ratio λ as optimization variables, and used the NSGA-II algorithm to carry out multi-objective optimization on four optimization objectives, namely, dimensionless shaft power output P¯s, braking thermal efficiency ηs, dimensionless efficient power E¯p and dimensionless power density P¯d. The optimal solutions of four-, three-, two-, and single-objective optimizations are reached by selecting the minimum deviation indexes D with the three decision-making strategies, namely, TOPSIS, LINMAP, and Shannon Entropy. The optimization results show that the D reached by TOPSIS and LINMAP strategies are both 0.1683 and better than the Shannon Entropy strategy for four-objective optimization, while the Ds reached for single-objective optimizations at maximum P¯s, ηs, E¯p, and P¯d conditions are 0.1978, 0.8624, 0.3319, and 0.3032, which are all bigger than 0.1683. This indicates that multi-objective optimization results are better when choosing appropriate decision-making strategies.

Constructal Optimization of Rectangular Microchannel Heat Sink with Porous Medium for Entropy Generation Minimization.

A model of rectangular microchannel heat sink (MCHS) with porous medium (PM) is developed. Aspect ratio of heat sink (HS) cell and length-width ratio of HS are optimized by numerical simulation method for entropy generation minimization (EGM) according to constructal theory. The effects of inlet Reynolds number (Re) of coolant, heat flux on bottom, porosity and volume proportion of PM on dimensionless entropy generation rate (DEGR) are analyzed. From the results, there are optimal aspect ratios to minimize DEGR. Given the initial condition, DEGR is 33.10% lower than its initial value after the aspect ratio is optimized. With the increase of Re, the optimal aspect ratio declines, and the minimum DEGR drops as well. DEGR gets larger and the optimal aspect ratio remains constant with the increasing of heat flux on bottom. For the different volume proportion of PM, the optimal aspect ratios are diverse, but the minimum DEGR almost stays unchanged. The twice minimized DEGR, which results from aspect ratio and length-width ratio optimized simultaneously, is 10.70% lower than the once minimized DEGR. For a rectangular bottom, a lower DEGR can be reached by choosing the proper direction of fluid flow.

Optimal Heat Exchanger Area Distribution and Low-Temperature Heat Sink Temperature for Power Optimization of an Endoreversible Space Carnot Cycle.

Using finite-time thermodynamics, a model of an endoreversible Carnot cycle for a space power plant is established in this paper. The expressions of the cycle power output and thermal efficiency are derived. Using numerical calculations and taking the cycle power output as the optimization objective, the surface area distributions of three heat exchangers are optimized, and the maximum power output is obtained when the total heat transfer area of the three heat exchangers of the whole plant is fixed. Furthermore, the double-maximum power output is obtained by optimizing the temperature of a low-temperature heat sink. Finally, the influences of fixed plant parameters on the maximum power output performance are analyzed. The results show that there is an optimal temperature of the low-temperature heat sink and a couple of optimal area distributions that allow one to obtain the double-maximum power output. The results obtained have some guidelines for the design and optimization of actual space power plants.

Performance Analysis and Four-Objective Optimization of an Irreversible Rectangular Cycle.

Based on the established model of the irreversible rectangular cycle in the previous literature, in this paper, finite time thermodynamics theory is applied to analyze the performance characteristics of an irreversible rectangular cycle by firstly taking power density and effective power as the objective functions. Then, four performance indicators of the cycle, that is, the thermal efficiency, dimensionless power output, dimensionless effective power, and dimensionless power density, are optimized with the cycle expansion ratio as the optimization variable by applying the nondominated sorting genetic algorithm II (NSGA-II) and considering four-objective, three-objective, and two-objective optimization combinations. Finally, optimal results are selected through three decision-making methods. The results show that although the efficiency of the irreversible rectangular cycle under the maximum power density point is less than that at the maximum power output point, the cycle under the maximum power density point can acquire a smaller size parameter. The efficiency at the maximum effective power point is always larger than that at the maximum power output point. When multi-objective optimization is performed on dimensionless power output, dimensionless effective power, and dimensionless power density, the deviation index obtained from the technique for order preference by similarity to an ideal solution (TOPSIS) decision-making method is the smallest value, which means the result is the best.

Performance Optimizations with Single-, Bi-, Tri-, and Quadru-Objective for Irreversible Diesel Cycle.

Applying finite time thermodynamics theory and the non-dominated sorting genetic algorithm-II (NSGA-II), thermodynamic analysis and multi-objective optimization of an irreversible Diesel cycle are performed. Through numerical calculations, the impact of the cycle temperature ratio on the power density of the cycle is analyzed. The characteristic relationships among the cycle power density versus the compression ratio and thermal efficiency are obtained with three different loss issues. The thermal efficiency, the maximum specific volume (the size of the total volume of the cylinder), and the maximum pressure ratio are compared under the maximum power output and the maximum power density criteria. Using NSGA-II, single-, bi-, tri-, and quadru-objective optimizations are performed for an irreversible Diesel cycle by introducing dimensionless power output, thermal efficiency, dimensionless ecological function, and dimensionless power density as objectives, respectively. The optimal design plan is obtained by using three solution methods, that is, the linear programming technique for multidimensional analysis of preference (LINMAP), the technique for order preferences by similarity to ideal solution (TOPSIS), and Shannon entropy, to compare the results under different objective function combinations. The comparison results indicate that the deviation index of multi-objective optimization is small. When taking the dimensionless power output, dimensionless ecological function, and dimensionless power density as the objective function to perform tri-objective optimization, the LINMAP solution is used to obtain the minimum deviation index. The deviation index at this time is 0.1333, and the design scheme is closer to the ideal scheme.

Modeling and Performance Optimization of an Irreversible Two-Stage Combined Thermal Brownian Heat Engine.

Based on finite time thermodynamics, an irreversible combined thermal Brownian heat engine model is established in this paper. The model consists of two thermal Brownian heat engines which are operating in tandem with thermal contact with three heat reservoirs. The rates of heat transfer are finite between the heat engine and the reservoir. Considering the heat leakage and the losses caused by kinetic energy change of particles, the formulas of steady current, power output and efficiency are derived. The power output and efficiency of combined heat engine are smaller than that of single heat engine operating between reservoirs with same temperatures. When the potential filed is free from external load, the effects of asymmetry of the potential, barrier height and heat leakage on the performance of the combined heat engine are analyzed. When the potential field is free from external load, the effects of basic design parameters on the performance of the combined heat engine are analyzed. The optimal power and efficiency are obtained by optimizing the barrier heights of two heat engines. The optimal working regions are obtained. There is optimal temperature ratio which maximize the overall power output or efficiency. When the potential filed is subjected to external load, effect of external load is analyzed. The steady current decreases versus external load; the power output and efficiency are monotonically increasing versus external load.

Power and Thermal Efficiency Optimization of an Irreversible Steady-Flow Lenoir Cycle.

Using finite time thermodynamic theory, an irreversible steady-flow Lenoir cycle model is established, and expressions of power output and thermal efficiency for the model are derived. Through numerical calculations, with the different fixed total heat conductances (UT) of two heat exchangers, the maximum powers (Pmax), the maximum thermal efficiencies (ηmax), and the corresponding optimal heat conductance distribution ratios (uLP(opt)) and (uLη(opt)) are obtained. The effects of the internal irreversibility are analyzed. The results show that, when the heat conductances of the hot- and cold-side heat exchangers are constants, the corresponding power output and thermal efficiency are constant values. When the heat source temperature ratio (τ) and the effectivenesses of the heat exchangers increase, the corresponding power output and thermal efficiency increase. When the heat conductance distributions are the optimal values, the characteristic relationships of P-uL and η-uL are parabolic-like ones. When UT is given, with the increase in τ, the Pmax, ηmax, uLP(opt), and uLη(opt) increase. When τ is given, with the increase in UT, Pmax and ηmax increase, while uLP(opt) and uLη(opt) decrease.

Performance Analysis and Optimization for Irreversible Combined Carnot Heat Engine Working with Ideal Quantum Gases.

An irreversible combined Carnot cycle model using ideal quantum gases as a working medium was studied by using finite-time thermodynamics. The combined cycle consisted of two Carnot sub-cycles in a cascade mode. Considering thermal resistance, internal irreversibility, and heat leakage losses, the power output and thermal efficiency of the irreversible combined Carnot cycle were derived by utilizing the quantum gas state equation. The temperature effect of the working medium on power output and thermal efficiency is analyzed by numerical method, the optimal relationship between power output and thermal efficiency is solved by the Euler-Lagrange equation, and the effects of different working mediums on the optimal power and thermal efficiency performance are also focused. The results show that there is a set of working medium temperatures that makes the power output of the combined cycle be maximum. When there is no heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are parabolic-like ones, and the internal irreversibility makes both power output and efficiency decrease. When there is heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are loop-shaped ones, and the heat leakage loss only affects the thermal efficiency of the combined Carnot cycle. Comparing the power output of combined heat engines with four types of working mediums, the two-stage combined Carnot cycle using ideal Fermi-Bose gas as working medium obtains the highest power output.

Four-Objective Optimizations for an Improved Irreversible Closed Modified Simple Brayton Cycle.

An improved irreversible closed modified simple Brayton cycle model with one isothermal heating process is established in this paper by using finite time thermodynamics. The heat reservoirs are variable-temperature ones. The irreversible losses in the compressor, turbine, and heat exchangers are considered. Firstly, the cycle performance is optimized by taking four performance indicators, including the dimensionless power output, thermal efficiency, dimensionless power density, and dimensionless ecological function, as the optimization objectives. The impacts of the irreversible losses on the optimization results are analyzed. The results indicate that four objective functions increase as the compressor and turbine efficiencies increase. The influences of the latter efficiency on the cycle performances are more significant than those of the former efficiency. Then, the NSGA-II algorithm is applied for multi-objective optimization, and three different decision methods are used to select the optimal solution from the Pareto frontier. The results show that the dimensionless power density and dimensionless ecological function compromise dimensionless power output and thermal efficiency. The corresponding deviation index of the Shannon Entropy method is equal to the corresponding deviation index of the maximum ecological function.

Minimization of Entropy Generation Rate in Hydrogen Iodide Decomposition Reactor Heated by High-Temperature Helium.

The thermochemical sulfur-iodine cycle is a potential method for hydrogen production, and the hydrogen iodide (HI) decomposition is the key step to determine the efficiency of hydrogen production in the cycle. To further reduce the irreversibility of various transmission processes in the HI decomposition reaction, a one-dimensional plug flow model of HI decomposition tubular reactor is established, and performance optimization with entropy generate rate minimization (EGRM) in the decomposition reaction system as an optimization goal based on finite-time thermodynamics is carried out. The reference reactor is heated counter-currently by high-temperature helium gas, the optimal reactor and the modified reactor are designed based on the reference reactor design parameters. With the EGRM as the optimization goal, the optimal control method is used to solve the optimal configuration of the reactor under the condition that both the reactant inlet state and hydrogen production rate are fixed, and the optimal value of total EGR in the reactor is reduced by 13.3% compared with the reference value. The reference reactor is improved on the basis of the total EGR in the optimal reactor, two modified reactors with increased length are designed under the condition of changing the helium inlet state. The total EGR of the two modified reactors are the same as that of the optimal reactor, which are realized by decreasing the helium inlet temperature and helium inlet flow rate, respectively. The results show that the EGR of heat transfer accounts for a large proportion, and the decrease of total EGR is mainly caused by reducing heat transfer irreversibility. The local total EGR of the optimal reactor distribution is more uniform, which approximately confirms the principle of equipartition of entropy production. The EGR distributions of the modified reactors are similar to that of the reference reactor, but the reactor length increases significantly, bringing a relatively large pressure drop. The research results have certain guiding significance to the optimum design of HI decomposition reactors.

Performance of Universal Reciprocating Heat-Engine Cycle with Variable Specific Heats Ratio of Working Fluid.

Considering the finite time characteristic, heat transfer loss, friction loss and internal irreversibility loss, an air standard reciprocating heat-engine cycle model is founded by using finite time thermodynamics. The cycle model, which consists of two endothermic processes, two exothermic processes and two adiabatic processes, is well generalized. The performance parameters, including the power output and efficiency (PAE), are obtained. The PAE versus compression ratio relations are obtained by numerical computation. The impacts of variable specific heats ratio (SHR) of working fluid (WF) on universal cycle performances are analyzed and various special cycles are also discussed. The results include the PAE performance characteristics of various special cycles (including Miller, Dual, Atkinson, Brayton, Diesel and Otto cycles) when the SHR of WF is constant and variable (including the SHR varied with linear function (LF) and nonlinear function (NLF) of WF temperature). The maximum power outputs and the corresponding optimal compression ratios, as well as the maximum efficiencies and the corresponding optimal compression ratios for various special cycles with three SHR models are compared.