Minimum Entropy Generation Number Research Articles

Numerical analysis of flow and heat transfer characteristics of double-layer heterogeneous single crystal diamond microchannel heat sinks

In order to solve the heat dissipation problems associated with highly integrated and high heat flux microelectronic devices, in this work, a novel type double-layer heterogeneous single crystal diamond microchannel heat sink (DLH-SCD-MCHS) is designed and numerically analyzed, in which the upper channel is rectangular and the lower channel consists of various cavities and rib combinations. The comprehensive performance of the DLH-SCD-MCHS was analyzed by the correlation with pumping power and thermal resistance, and the enhanced heat transfer factor (η). The outcome shows that the DLH-SCD-MCHS significantly enhances the heat transfer while appropriately sacrificing part of the pressure drop. Compared with the traditional double-layer microchannel heat sink (DL-MCHS), the pressure drop of DLH-SCD-MCHS is increased by 23.8–43.5 %, the heat transfer coefficient is enhanced by 74.5–117.1 %, and the η is improved by 62.5–87.4 %. The DLH-SCD-MCHS can reduce the irreversible loss, and the minimum augmentation entropy generation number is 0.64 for the DLH-SCD-MCHS with rectangular cavity and rectangular rib (Model V). As Re = 874, the relative rib width, the relative rib length and the relative position of the ribs of the Model V are 0.5, 0.571 and 0.5, respectively, the maximum η is 1.97. The DLH-SCD-MCHS provides new insights for the management of the heat transfer system of microelectronic devices.

Thermodynamic performance study on the novel efficient flow pattern global construction evaporator

Based on the fluid-efficient flow pattern global construction heat transfer enhancement mechanism, a novel evaporator, called the efficient flow pattern global construction evaporator (EFGE), is presented to improve the in-tube evaporation heat transfer at low quality. The numerical analysis and experimental study of EFGE's thermodynamic performance are performed. Results show that the temperature distribution characteristic of the fluid-efficient heat transfer flow pattern construction is better than that of the initial fluid. The evaporation heat transfer coefficient (HTC) of EFGE is 0.34–1.04 times that of a common parallel flow evaporator (PFE), and the pressure drop of EFGE is only 80%–116 % of that of a common PFE at the quality of 0.9. The theoretical nonuniformity of the evaporation HTC between low- and high-quality flow is approximately 12%–67 %, which is 55%–72 % of the pressure drop. The numerical analysis results agree with the finding that EFGE has better thermodynamic performance than PFE in terms of friction power reduction and minimum entropy generation number.

Optimization of inserted coiled tube three-fluid heat exchanger using genetic algorithms

The three-fluid heat exchanger is a multi-stream heat exchanger that provides three streams at different temperatures for certain usage objectives. Recently, optimizing heat exchangers generally and three-fluid heat exchangers especially have received great attention in the energy field. The current study objective is to get the optimal mass flow rate of the three streams to minimize the entropy generation number and maximize effectiveness. Optimization is performed on the inserted coiled tube type for 24 cases with different usage objectives and different mass flow rate constraints. The optimization is done using an analytical approach for the temperature profiles and a regressed model for the overall heat transfer coefficients. Single-objective and multi-objective genetic algorithms are the optimization algorithms. The result shows that cooling the hot fluid is the most efficient usage objective; however, heating the intermediate-temperature fluid is the less efficient usage objective. Also, the study shows that the entropy generation number is dependent on the mass flow rate constraint. The maximum effectiveness of 0.693 occurs when the usage objective is cooling the hot fluid. In this case, the mass flow rate of the cold and the intermediate-temperature fluids are maxima while the mass flow rate of the hot fluid is minimum. The minimum entropy generation number 0.0486 occurs when the mass flow rate of the cold fluid is maximum while the mass flow rate of the hot fluid and intermediate-temperature fluid are minimal.

The effects of staggered triangular ribs induced vortex flow on hydrothermal behavior and entropy generation in microchannel heat sink

For dissipating the increasing heat in high flux microelectronic device, an original microchannel heat sink with staggered triangular ribs induced vortex flow is designed. In this work, the width (Wch) and height (Hch) of a single microchannel with staggered triangular ribs (MC-STR) are both 0.2 mm, as well as the width (Wr), height (Hr) and length (Lr) of the triangular rib are in ranges of 0.025–0.15 mm, 0.012–0.072 mm and 0.06–0.16 mm, respectively. The influences of the relative rib width (Wr/Wch), relative rib height (Hr/Wch) and relative rib length (Lr/Wch) on the hydrothermal behavior and entropy generation in MC-STR are numerically analyzed at the Reynolds number (Re) of 243–639. The results show that the increases in Wr/Wch and Hr/Wch can effectively improves the thermal performance, and reduce augmentation entropy generation number, but increase the flow resistance. In addition, the rise of Lr/Wch has weak effect on hydrothermal behavior and entropy generation. Overall, the MC-STR with Wr/Wch = 0.5, Hr/Wch = 0.3 and Lr/Wch = 0.5 at Re = 639 yields the highest performance evaluation criterion (1.502). Moreover, the minimum augmentation entropy generation number (0.236) is achieved at MC-STR with Wr/Wch = 0.5, Hr/Wch = 0.36 and Lr/Wch = 0.4 as Re = 639.

Energy and exergy analyses of solar drying of black cardamom (Amomum subulatom Roxburgh) using indirect type flat plate collector solar dryer

AbstractThis study has summarized the energy and exergy analyses of flat plate collector solar dryer. The study involves a fundamental method for the design of the solar collector based on minimum entropy generation number (Ns) and mass flow number (M). The optimal performance parameters of the solar collector were determined using thermodynamic optimization procedure. Black cardamom was dried in the solar dryer at the drying air temperature range of 26–62°C. The amount of useful energy varied between 0.07 and 0.63 kW based on the degree of solar insolation. Subsequently, it was observed that the useful energy accumulated by the solar dryer was sufficient to dry black cardamom samples to 8.2% moisture content from an initial moisture content of 80.6%. The range of energy utilization values inside the cabinet was between 7.53 and 74.61 W for a period of 24 hr. It was observed that the energy utilization ratio (EUR) varied from 22.12–80.73%, 22.62–97.71%, and 14.25–77.81%, respectively, for the three consecutive days. The increase in the inlet air temperature led to an increase in the EUR values. Furthermore, during the drying studies, the exergy efficiency of the drying chamber was ranged from 31.19% to 93.28%, with an average of 72.08%. The developed solar dryer incorporates a free energy source, sustainability, increased drying capacity, and the creation of high‐quality products. This dryer can be promoted as beneficial and sustainable equipment for drying agro products by small and marginal farmers.Practical applicationsFree energy sources and sustainability are the benefits of this solar dryer system. Agricultural producers are considering the use of renewable energy, such as solar energy, in the drying of agricultural goods. The design of the solar collector was based on the minimum entropy generation number. In this study, a dynamic model was provided in which the kinetics of moisture reduction are calculated based on the quantity of solar energy received in the collector and the temperature fluctuation in the collector. The exergy input and exergy loss of the dryer are affected by solar radiation. The quantity of energy received and consumed is included in the energy analysis.

Local thermal non-equilibrium conjugate forced convection and entropy generation in an aircraft cabin with air channel partially filled porous insulation

PurposeThe purpose of this study is to numerically investigate heat transfer and entropy generation between airframe and cabin-cargo departments in an aircraft. The conjugate forced convection and entropy generation in a cylindrical cavity within air channel partly filled with porous insulation material as simplified geometry for airframe and cabin-cargo departments are considered under local thermal non-equilibrium condition.Design/methodology/approachThe non-dimensional governing equations for fluid and porous media discretized by finite volume method are solved using the SIMPLE algorithm with pressure and velocity correction.FindingsThe effects of the following parameters on the problem are investigated; Reynolds number, Darcy number, the size of inlet and exit cross-section, thermal conductivity ratio for solid and fluid phases, angle between the vertical symmetry axis and the end of channel wall exit and the gap between adiabatic channel wall and horizontal adiabatic wall separating cabin and cargo sections.Originality/valueThis paper can provide a basic perspective and framework for thermal design between the fuselage and cabin-cargo sections. The minimum total entropy generation number is calculated for various Reynolds numbers and thermal conductivity ratios. It is observed that the channel wall temperature increases for high Reynolds number, low Darcy number, narrower exit cross-section and wider the gap between channel wall and horizontal.

Designing of microsink to maximize the thermal performance and minimize the Entropy generation with the role of flow structures

Designing a novel microsink with geometric structures for better cooling of compact tiny-sized electronic devices at lower pressure drop is the utmost desire of recent technological development. A three-dimensional numerical study of conjugate heat transfer has been carried out to propose a microsink with the disruptive structures placed symmetrically about the vertical midplane in a rectangular microchannel. The channels are made of silicon with the structures like triangular cavity (TC), secondary branches (SB) and blockage (B) with water as a working fluid. The effects of these structures are illustrated by heat transfer, friction factor, thermal performance (TP), entropy generation (EG) due to heat transfer, entropy generation (EG) due to pressure drop and entropy generation number (EGN) over the range of Reynolds number (Re) from 146 to 618. The best channel has been identified from the rigorous analysis among the microchannels with the only triangular cavity (TC), triangular cavity with the secondary branch (TCSB) and triangular cavity along with secondary branch and blockage (TCSBB) from the highest TP and minimum EGN. These two models have been chosen to find out a best channel as criteria of highest heat transfer with the same pumping power from the highest TP and minimum temperature of electronic sink from the lowest EGN. The highest TP and lowest EGN are obtained from the channel TCSBB compared to other three channels. The parametric variation of relative angle of the secondary branch, length of cavity, width of secondary branch and cavity, pitch distance have been varied to find the maximum TP and the minimum EGN. The values have been obtained equal to 2.01 and 0.41 respectively at Re of 480. The significant roles of longitudinal vortex on the augmentation of heat transfer and minimizations of EG mechanism with the alteration of geometrical parameters are exploited and described explicitly. Finally, the correlations of heat transfer enhancement and rise in pressure drop dependent on geometric parameter have been inscribed based on Response surface methodology.

Effects of truncated and offset pin-fins on hydrothermal performance and entropy generation in a rectangular microchannel heat sink with variable fluid properties

A rectangular microchannel with truncated and offset pin-fins is designed, and investigated using numerical simulation. The width (Wc) and height (Hc) of a single smooth microchannel are 0.1 mm and 0.2 mm, respectively. The pin-fin length, width and height (Hr) are 0.06 mm, 0.03 mm and 0–0.2 mm, respectively. The offset value (Wr) of two adjacent pin-fins in width direction of microchannel ranges from 0 to 0.07 mm. The effects of relative height (Hrc = Hr/Hc) and relative offset value (Wrc = Wr/Wc) on hydrothermal performance and entropy generation are analyzed. Results show that increasing pin-fin height usually results in both higher thermal enhancement and flow resistance. Increasing pin-fin offset value properly can enhance heat transfer, but extremely larger offset value leads to decrease of thermal enhancement. The microchannel with Hrc = 0.75 and Wrc = 0.6 yields the maximum overall thermal performance factor of 1.43. The minimum augmentation entropy generation number of 0.31 is obtained in microchannel with Hrc = 0.75 and Wrc = 0.4. From comparison of variable and constant fluid properties, variable fluid properties significantly affect flow and heat transfer performance. Particularly, fluid viscosity plays a key role in fluid properties while others have unobvious effect.

Design optimization of a cross-flow He-Xe recuperator through second law analysis

Nuclear power conversion in space has been approached by various means since the first space missions, with the advent of concepts such as thermoelectric, thermionic and thermodynamic conversion. Nowadays, thermal cycles are under greater focus for being capable of providing higher conversion efficiencies. In this context, one of the main concerns of engineers is the trade-off between power and mass. Therefore, this work aims the optimization of a recuperator used in a regenerative closed Brayton cycle applied for power conversion in the project of a small-scale nuclear reactor. The recuperator consists of a cross-flow, shell-and-tube heat exchanger with a matrix of tubes distributed in a staggered configuration. In this work, the number of tubes and the mass flow rate are varied. The number of tubes distributed axially is fixed as 4, whereas the quantity around the axis can be 5, 7, 9, 12 and 16 tubes. The working fluid considered in this study is a mixture of noble gases He-Xe with a molecular weight of 40 g/mol, whereas Inconel alloy 617 is applied as the recuperator material. The optimization procedure was based on the entropy generation minimization and the heat exchanger effectiveness, using the Computational Fluid Dynamics (CFD) technique to obtain the flow field. Optimum mass flow rates are obtained for all the geometries at the points of minimum entropy generation number, around which lie the ranges of tested mass flow rates. The ratio between the entropy generation number and effectiveness associated with the optimum mass flow rate is considered a performance evaluation criterion, and the dependence of this parameter with exchanger mass is assessed in order to select the most suitable geometry for the studied application. This analysis leads to the optimum design point at the geometry of 9 tubes around the recuperator axis, yielding a lost available work of 929.76 W for an ambient temperature of 298 K.

Effect of surface roughness on the performance of heat exchanger

In this research work, double-pipe counter flow heat exchanger has been analyzed with various roughnesses of steel, aluminum and copper pipes and also with two different cold fluids: water and ammonia at same flow rates. Dimensions of the heat exchanger are inner and outer diameters of inner pipe being 0.034 and 0.042 m, whereas diameters of outer pipe are 0.054 and 0.06 m, respectively, and length of heat exchanger is 1.8 m. In K-ℇ modeling, computational fluid dynamics tool has been used for performance analyses and this computational work has been validated by entropy, exergy and entransy analyses. After computational numerical analyses, this investigation has concluded that maximum rate of heat transfer through heat exchanger has been found with copper–ammonia combination with smooth surface. Minimum rates of entropy generation, exergy destruction, entransy dissipation-based thermal resistance and entransy dissipation number have been obtained with copper–water combination, and minimum entropy generation number and maximum effectiveness have been obtained with copper–ammonia combination. Percentage changes in the parameters/properties have also been calculated at different operating conditions. Copper as inner pipe material with smooth surface and ammonia as cold fluid have been recommended for counter flow double-pipe heat exchanger. Computer software has been developed for hassle-free analyses of heat exchanger.

Constructal optimization for line-to-line vascular based on entropy generation minimization principle

Constructal optimizations of the first to fifth order line-to-line vascular channels (LVCs) with convective heat transfer are carried out in this paper by taking minimum entropy generation rate (EGR) and minimum entropy generation number (EGN) as the optimization objectives, respectively. The angles of the LVCs are taken as the optimization variables, and the fixed vascular channel areas and total volumes of LVCs are taken as the constraints. The optimal constructs corresponding to minimum EGR and minimum EGN are obtained, respectively. The influences of the mass flow rate (MFR) on the optimal results are analyzed. The results show that the EGR of the LVCs decreases when the angle freedom increases with the constant dimensionless MFR, which is more obvious when the order increases. When the order increases, the EGR increases but the EGN decreases. Both the EGR and the EGN increase with the increase of the dimensionless MFR. The results obtained herein can provide some thermal design and management guidelines for the applications of LVCs.

Optimization of heat sink of thermoelectric cooler using entropy generation analysis

In the present study, an optimization model is developed for a thermoelectric cooler (TEC) based on the entropy generation minimization method. In the model, the total entropy generation rate, the entropy generation number and the exergetic efficiency are proposed as optimization objective functions, respectively, while the number of transfer units of the heat sink is considered as a constraint. The heat capacity rate of cooling fluid in the heat sink is optimized under other given conditions. The results show that a minimum total entropy generation rate and a minimum entropy generation number can be achieved by optimally selecting the heat capacity rate of the cooling fluid. In addition, the minimum total entropy generation rate and corresponding optimal heat capacity rate of the cooling fluid are both dominated by the number of transfer units and the electrical current. Furthermore, the effects of the heat capacity rate of cooling fluid and the electric current in terms of the exergetic efficiency are also evaluated.

Entropy generation analysis of a microchannel-condenser for use in a vapor compression refrigeration cycle

Dimensionless entropy generation number in the microchannel condenser of a vapor compression refrigeration cycle is investigated. An air cooled, brazed aluminum parallel flow heat exchanger is considered as the condenser with R-134a as the refrigerant. While the effects of the fin pitch, fin height, louver angle and the air mass flow rate are investigated for the air side, the effect of the channel diameter is examined for the refrigerant side. The analysis is performed segment by segment for the superheated, two phase and subcooled regions using well-established empirical correlations. A mapping study is presented for the variation of entropy generation number with the mentioned parameters. The optimum air mass flow rate interval is found to be between 0.055 and 0.1 kgs−1 for a given fin pitch interval of 1–1.6 mm. This range is within the operating limits of air fans in the market for this size. In this operating range, the optimal dimensions giving the minimum entropy generation numbers are presented. The entropy generation number distribution is given based on the pressure drop, heat transfer or the refrigerant state in the heat exchanger considering superheated, two phase, and subcooled regions. The entropy generation number due to pressure drop on the air side becomes dominant after a mass flow rate around 0.08 kgs−1. Hence, an optimum air mass flow rate generating the minimum entropy generation number is sought for different sizes of the condenser. The condenser length is variable in the range of 84.3–80.6 mm for the mentioned optimal air mass flow rate interval. The condenser height changes depending on desired operational conditions, and it is determined to be 112.5 mm for the fixed values given in the study. The study is unique in the literature in pursuing an entropy generation number mapping study for microchannel two-phase flow in air cooled heat exchangers.

Experimental investigation on the thermodynamic performance of double-row liquid–vapor separation microchannel condenser

A double-row liquid–vapor separation microchannel condenser (D-LSMC) was presented, and its tube pass scheme was optimized using the theoretical method. A series of experiments were conducted to investigate the heat load, average heat transfer coefficient (AHTC), and pressure drop of the optimal D-LSMC. Experimental results were compared with an optimal common double-row parallel-flow microchannel condenser (D-PFMC). The findings showed that, at the inlet mass flux of 585 kgm−2 s−1 to 874 kgm−2 s−1, the AHTC of the D-LSMC was 3.3%–14.4% higher than that of the D-PFMC. However, the pressure drop of the D-LSMC was only 43.4%–52.1% of that of the D-PFMC. The heat exchange capacity of the back row was weaker by almost half of that of the front row. In addition, the tube wall temperature of the back row decreased faster than that of the front row, which indicated that the back row had a larger pressure drop. The minimum entropy generation number (Ns) was used to evaluate the D-LSMC and the D-PFMC, which indicated the greater thermodynamic performance of the D-LSMC.

Heat transfer enhancement in a novel internally grooved tube by generating longitudinal swirl flows with multi-vortexes

In this paper, turbulent flow characteristics and heat transfer performance in a novel internally grooved tube are analyzed numerically. The objective of this work is to enhance heat transfer performance without causing a considerable increase in the pressure drop by generating longitudinal swirl flows with multi-vortexes according to the optimum velocity field obtained from the heat transfer optimization. Visualization of the flow in the grooved tubes shows that longitudinal swirl flows with multi-vortexes are generated in the inclined grooved tube but not in the straight grooved tube. This kind of flow pattern results in a long flow path and relatively intense flow mixing between the wall and the core flow regions, which significantly improves the synergy between the velocity and temperature fields, and thereby enhances the heat transfer performances. Moreover, entropy generation analysis shows entropy generation number decreases with the increment of groove inclination angle as the inclination angle is no more than 30°, while beyond this inclination angle entropy generation number starts to increase. The minimum entropy generation number and maximum overall thermal-hydraulic performance are achieved with the groove inclination angle of 30° at the lowest Reynolds number. Therefore, we conclude that groove inclination angles have a profound effect on the heat transfer performances, and the mechanism of heat transfer enhancement is mainly due to the effect of the longitudinal swirl flows with multi-vortexes generated in the grooved tube.

Entransy analyses of thermal processes with variable thermophysical properties

Entransy method is developed for the analyses of thermal processes with variable thermophysical properties. The entransy and enthalpy entransy balance equations for thermal processes with variable thermophysical properties are derived based on the definitions of differential entransy and enthalpy entransy. The definitions of the entransy and enthalpy entransy for an object are presented. The optimization principles for heat transfer and heat-work conversion processes with variable thermophysical properties are discussed with the concept of entransy. Entransy analyses for a two-stream heat exchanger and a closed Brayton cycle with variable thermophysical properties are conducted and compared with the entropy generation analyses. For the heat exchanger, the results show that both the minimum entransy-dissipation-based thermal resistance and the minimum revised entropy generation number correspond to the maximum heat exchanger effectiveness when the inlet condition of the heat exchanger is prescribed, but the minimum entropy generation rate and the minimum entropy generation number do not. For the closed Brayton cycle, the results show that both the maximum entransy loss rate and the minimum entropy generation rate correspond to the maximum output power and both the maximum entransy loss coefficient and the minimum entropy generation number correspond to the maximum heat-work conversion efficiency when the inlet conditions of the streams and the environmental temperature are prescribed. When the inlet temperature of the hot stream increases, larger entransy loss rate and larger entransy loss coefficient still correspond to larger output power and larger heat-work conversion efficiency respectively.

Entropy generation assessment of shell and tube latent heat storage unit

Thermodynamic optimisation for latent heat thermal energy storage unit (LHSU) is carried out using the theory of minimisation of entropy generation number. The influence of key parameters like heat transfer fluid (HTF) inlet temperature, initial temperature of phase change material (PCM) and mass flow rates of HTF on entropy generation number is analysed. Analysis is carried out for two PCMs, i.e., paraffin wax and stearic acid, with different melting temperature to establish the influence of melting temperature of PCM on entropy generation number. The results show that minimum HTF inlet temperature provides minimum entropy generation number. The results also demonstrate that higher initial temperature of PCM provides minimum entropy generation number during solidification process. The mass flow rate of HTF has negligible influence on the entropy generation number compared with the influence of fluid inlet temperature and initial temperature of PCM.

Experimental investigation on microchannel condensers with and without liquid–vapor separation headers

To enhance heat transfer in microchannels during condensation by improving the refrigerant average quality, a new liquid–vapor separation microchannel condenser (LSMC) is presented in this paper. Compared with the common parallel flow microchannel condenser (PFMC), the LSMC has a pair of headers that can drain away the condensate after each pass. The in-tube heat transfer coefficient and pressure drop of the two kinds of microchannel condensers with similar heat transfer areas are compared under mass fluxes that range from 450 kg/(m2s) to 770 kg/(m2s), heat fluxes that range from 1.5 kW/m2 to 2.45 kW/m2, and condensing temperatures that range from 45 °C to 50 °C. Results show that the average heat transfer coefficient (AHTC) of the LSMC exceeds that of the PFMC when the mass flux is more than 590 kg/(m2s) or the average quality is more than 0.57. The pressure drop of the LSMC greatly reduces by 30.5%–52.6% of the PFMC. The combined thermodynamic performance of the LSMC is better than that of the PFMC based on the ranking through the penalty factor and minimum entropy generation number.

In-tube performance evaluation of an air-cooled condenser with liquid–vapor separator

This study evaluates the thermal hydraulic performance of a novel liquid–vapor separation condenser (LSC). A series of experiments was performed to investigate the in-tube heat transfer coefficient and pressure drop of the LSC with varying average refrigerant quality at constant mass flux. The results were compared with the performance of a serpentine condenser (SC) and a parallel-flow condenser (PFC), with R134a as the refrigerant. Findings showed a very small change in the wall temperature of the LSC. The LSC had the lowest average condensation heat transfer coefficient among the three condensers at lower heat flux, but exceeded that of the PFC at higher heat flux. The pressure drop of the LSC was 77.1–81.4% lower than that of the SC and 57.5–64.6% lower than that of the PFC at a heat flux of 6.45kWm−2. Moreover, heat flux and condensing temperature had little influence on the pressure drop of the LSC. Based on these experimental data, the three evaluation criteria (friction power ratio, penalty factor, and minimum entropy generation number) applied to the three condensers proved that the LSC had the best thermal hydraulic performance. The lowest irreversibility of the LSC resulted from the entropy generation rate of the refrigerant side, which was the lowest among the three condensers.

Entropy Generation of Natural Convection Heat Transfer in a Square Cavity Using Al2O3–Water Nanofluid

Entropy generation of an Al2O3–water nanofluid due to heat transfer and fluid friction irreversibility has been investigated in a square cavity subject to different side‐wall temperatures using a nanofluid for natural convection flow. This study has been carried out for the pertinent parameters in the following ranges: Rayleigh number between 104 and 107 and volume fraction between 0 and 0.05. Based on the obtained dimensionless velocity and temperature values, the distributions of local entropy generation, average entropy generation, and average Bejan number are determined. The results are compared for a pure fluid and a nanofluid. It is totally found that the heat transfer, and entropy generation of the nanofluid is more than the pure fluid and minimum entropy generation and Nusselt number occur in the pure fluid at any Rayleigh number. Results depict that the addition of nanoparticles to the pure fluid has more effect on the entropy generation as the Rayleigh number goes up.