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1.
With involving innovative swirl flow tapes through the absorber tube in LFR system, the productivity of unit was improved in present study. To grow the thermal feature of water, hybrid nanoparticles (Al2O3 + CuO) were dispersed. For designing current solar unit, 12 mirrors, one absorber tube and secondary reflector have been used. To calculate the heat source in solid zone of tube, SolTrace has been applied. Because of low fraction of each type of nano-sized material, single phase formulation were utilized. For analyzing the 3D turbulent flow of hybrid nanomaterial within the tube, FVM was chosen with incorporating K-ε formulations. Effects of inlet flow rate (Q) and its temperature (Tin), pitch ratio (PR = 0.147059 to 0.5) and height ratio (BR = 0.16 to 0.24), have been examined in outputs. Three important functions which were calculated for all cases were: Nusselt number (Nu), thermal productivity (ηt) and Darcy factor (f). Inclusion of hybrid nanomaterial causes Nu, f and ηt to intensify around 5.26%, 4.67% and 0.316% when Q = 15, PR = 0.5, BR = 0.24. As greater value of PR has been chosen, Nu, f and ηt enhance around 22.27%, 112.45% and 0.514% when Q = 15, BR = 0.16. Intensify of BR creates more secondary flow and Nu, f and ηt augments about 6.36%, 48.7% and 0.06%, when Q = 15, PR = 0.5. With augment of Q and Tin, ηt declines around 15.35% and 0.304%. As Q increases, Nu intensifies about 60.21% but f declines about 11.1% when PR = 0.5, BR = 0.24.  相似文献   

2.
Most of the research work applied to the intensification of heat transfer through convection in turbulent flow, has been devoted to local heat flow and local friction losses. Intensification is obtained by means of turbulators inside smooth channels (fins, steps).In the re-sticking zone of the boundary layer, the heat transfer is maximum and the friction factor is minimum, the latter being maximum in the free flow zone. Maximum values are more than ten times higher than those observed in an undisturbed analogous stream.As early as 1958, those results have been applied to the construction of heat exchangers by which the heat transfer coefficient rises faster than the hydraulic resistance (discovery No 242).Such heat exchangers (water-air) are built from ribbed fin-plates and cross-tubes. The ribs act as turbulators inside the channels which are allowed between plates and tubes.The present paper deals with the influence of geometrical shape and distribution of the turbulator on thermal and hydraulic efficiencies of heat transfer surfaces.The results are presented as graphs
where:Nu,NuR = Nusselt number for channels with and respectively, without, turbulators; ε,εR=friction loss factor for channels with, and respectively, without, turbulators; l'/d = pitch of trottling=ratio between the length of smooth piece l' and its hydraulic diameter d; d1/d=rate of throttling=ratio between hydraulic diameter of the throttled section d1, and that of the smooth piece d.Experimentations have been performed with 16 different combinations of l'/d and d1/d, in channels of the same triangular section and Reynolds number varying between 400 and 5500; in channels with different triangular sections; in channels with rectangular sections.Main results are: the heat transfer intensification depends on the parameters l'/d and d1/d; the maximum intensification depends on the shape of the channel section, the highest values being obtained with triangular shaped channels; the most efficient turbulators
consist of two dimensioned surfaces generated along the channel radius.New radiators for farm tractor-engines have been developed. Their volume and weight are half those of conventional radiators. Their construction does not require any significant modification of the traditional manufacturing technique of such type of equipment and their utilization in dusty environments does not raise any particular difficulty.  相似文献   

3.
Viscous fluids in many processes are mechanically incompressible but experience significant thermally induced volume change. We focus here on models for viscous fluids that impose this behavior through a posited internal constraint, following the formalism which introduces constraint responses that produce no entropy. We investigate four different thermal expansion constraints, whereby the independent mechanical variable in the problem formulation (density ρ or pressure p) is assumed to be specified completely by the independent thermal variable (temperature θ or entropy η). The internal constraint approach yields simpler constitutive relations, and therefore easier material characterization; the resulting model equations are alternatives to the compressible Navier-Stokes equations for simulation and analysis of thermal expansion phenomena. However, whereas the internal constraint formalism preserves consistency with the thermomechanical balance laws, second law, and invariance by fiat, there is no a priori guarantee that stability of the rest state and nonnegativity of specific heat and bulk modulus are preserved. Here we first derive the four possible internal constraint models for thermal expansion. Next we show that each of these four models is equivalent to a specific constitutive limit of the compressible theory, namely two of no pressure dependence of density and their duals of no density dependence of pressure. From this connection, we deduce that two constraints, namely ρ=ρ(η) and p=p(θ), offer physically viable candidates for the modeling of thermal expansion, whereas two others (the customary density-temperature constraint ρ=ρ(θ), as well as p=p(η)) are unphysical in the absence of any other conditions on the process, predicting catastrophic instability of the rest state. This analysis reveals that the internal constraint formalism must be further conditioned to preserve fundamental irreversible (second law) and reversible (stability) inequalities.  相似文献   

4.
The potential of winglet type vortex generator (VG) arrays for air-side heat transfer enhancement is experimentally evaluated by full-scale wind-tunnel testing of a compact plain-fin-and-tube heat exchanger. The effectiveness of a 3VG alternate-tube inline array of vortex generators is compared to a single-row vortex generator design and the baseline configuration. The winglets are placed in a common-flow-up orientation for improved tube wake management. The overall heat transfer and pressure drop performance are assessed under dry-surface conditions over a Reynolds number range based on hydraulic diameter of 220 ≤ Re ≤ 960. It is found that the air-side heat transfer coefficient increases from 16.5% to 44% for the single-row winglet arrangement with an increase in pressure drop of less than 12%. For the three-row vortex generator array, the enhancement in heat transfer coefficient increases with Reynolds number from 29.9% to 68.8% with a pressure drop penalty from 26% at Re = 960 to 87.5% at Re = 220. The results indicate that vortex generator arrays can significantly enhance the performance of fin-tube heat exchangers with flow depths and fin densities typical to those used in air-cooling and refrigeration applications.  相似文献   

5.
In this paper, the development of the tandem reciprocating room-temperature active magnetic regenerative refrigerator and the numerical simulation for the effect of the dead volume are presented. The dead volume effect is analyzed by establishing a one-dimensional time-dependent model for the active magnetic regenerator (AMR). The cooling power at the mass flow rate of 5 g s−1 water and a temperature span of 20 K is reduced from 4 W to 2 W when the length of the dead volume (DDV = 12 mm) is increased from 15 mm to 30 mm. The numerical results indicate that the minimization of dead volume facilitates the improvement of the AMR performance. In particular, the components and the parameters of AMR system are demonstrated. The printed circuit heat exchangers (PCHEs) are employed as the warm end heat exchangers in order to minimize the dead volume of the system. The experimental apparatus includes two active magnetic regenerators containing 186 g of Gd spheres. The maximum no-load temperature span of 26.8 K and a maximum cooling power of 33 W at a zero temperature span were obtained with the frequency of 0.5 Hz under the maximum field of 1.4 T.  相似文献   

6.
Improving the performance of the pulse tube cooler is one of the important objectives of the current studies. Besides the phase shifters and regenerators, heat exchangers also play an important role in determining the system efficiency and cooling capacity. A series of experiments on a 10 W @ 77 K class co-axial type pulse tube cooler with different cold heat exchanger geometries are presented in this paper. The cold heat exchangers are made from a copper block with radial slots, cut through using electrical discharge machining. Different slot widths varying from 0.12 mm to 0.4 mm and different slot numbers varying from around 20–60 are investigated, while the length of cold heat exchangers are kept the same. The cold heat exchanger geometry is classified into three groups, namely, constant heat transfer area, constant porosity and constant slot width. The study reveals that a large channel width of 0.4 mm (about ten times the thermal penetration depth of helium gas at 77 K, 100 Hz and 3.5 MPa) shows poor performance, the other results show complicated interaction effects between slot width and slot number. These systematic comparison experiments provide a useful reference for selecting a cold heat exchanger geometry in a practical cooler.  相似文献   

7.
Entropy generation rates considering particle migration are evaluated for a biologically produced nanofluid flow in a mini double-pipe heat exchanger. The nanofluid is used in tube side and hot water flows in annulus side. Silver nanoparticles synthesized through plant extract method from green tea leaves are utilized. Particle migration causes non-uniform concentration distribution, and non-uniformity intensifies by increase in Reynolds number and concentration. The results indicate that at high concentrations and Reynolds numbers, particle migration can have a great effect on entropy generation rates. For water inlet temperature of 308 K, the contribution of friction in nanofluid entropy generation is much more than that of heat transfer. However, as the water inlet temperature increases to 360 K, the heat transfer contribution increases such that at low Reynolds numbers, the thermal contribution exceeds the frictional one. For total heat exchanger, Bejan number is smaller than 0.2 at water inlet temperature of 308 K, while Bejan number has a large value at water inlet temperature of 360 K. Furthermore, entropy generation at the wall has an insignificant contribution, such that for Re = 1000 and φm = 1%, the total entropy generation rates for the nanofluid, wall, and water are 0.098810, 0.000133, and 0.041851 W/K, respectively.  相似文献   

8.
Most of the research work applied to the intensification of heat transfer through convection in turbulent flow, has been devoted to local heat flow and local friction losses. Intensification is obtained by means of turbulators inside smooth channels (fins, steps).In the re-sticking zone of the boundary layer, the heat transfer is maximum and the friction factor is minimum, the latter being maximum in the free flow zone. Maximum values are more than ten times higher than those observed in an undisturbed analogous stream.As early as 1958, those results have been applied to the construction of heat exchangers by which the heat transfer coefficient rises faster than the hydraulic resistance (discovery No 242).Such heat exchangers (water-air) are built from ribbed fin-plates and cross-tubes. The ribs act as turbulators inside the channels which are allowed between plates and tubes.The present paper deals with the influence of geometrical shape and distribution of the turbulator on thermal and hydraulic efficiencies of heat transfer surfaces.The results are presented as graphs where:Nu,NuR = Nusselt number for channels with and respectively, without, turbulators; ε,εR=friction loss factor for channels with, and respectively, without, turbulators; l'/d = pitch of trottling=ratio between the length of smooth piece l' and its hydraulic diameter d; d*/d=rate of throttling=ratio between hydraulic diameter of the throttled section d*, and that of the smooth piece d.Experimentations have been performed with 16 different combinations of l'/d and d*/d, in channels of the same triangular section and Reynolds number varying between 400 and 5500; in channels with different triangular sections; in channels with rectangular sections.Main results are: the heat transfer intensification depends on the parameters l'/d and d*/d; the maximum intensification depends on the shape of the channel section, the highest values being obtained with triangular shaped channels; the most efficient turbulators
consist of two dimensioned surfaces generated along the channel radius.New radiators for farm tractor-engines have been developed. Their volume and weight are half those of conventional radiators. Their construction does not require any significant modification of the traditional manufacturing technique of such type of equipment and their utilization in dusty environments does not raise any particular difficulty.

Résumé

La réalisation de saillies et de cavités transversales dans la paroi des canaux d'air à section triangulaire ou rectangulaire entraîne une intensification des échanges de chaleur. Cette intensification peut être quantifiée par le nombre caractéristique (Nu/NuR)/(ξ/ξR) dont la valeur est supérieure ou égale à 1 pour des valeurs du rapport Nu/NuR inférieures à 2,15. L'intensification des échanges de chaleur dépend des paramétres géométriques caractéristiques du canal d'air (l'/d) et (d*/d).L'utilisation de plaques-ailettes nervurées dans la construction des radiateurs pour moteurs de machines agricoles entraîne une diminution de deux fois et plus du volume et de la masse de ces appareils, c'est la profondeur qui est réduite.Une grande résistance à l'encrassement et une technique simple de fabrication permettent d'envisager une modernisation rapide du parc de machines agricoles automotrices.  相似文献   

9.
Efficient and compact plate-fin heat exchangers are critical for large-scale helium liquefaction/refrigeration systems as they constitute major part in the cold box. This study experimentally explores the heat transfer and pressure drop behaviors of helium gas at low temperature in four types of plate-fin channels, namely offset-strip and perforated fins, with different geometrical parameters. A series of cryogenic experiments at approximately liquid nitrogen temperature are carried out to measure the Colburn j factors and Fanning friction f factors with a wide range of Reynolds number. Besides, to reveal the performance variations under different operating temperatures, comparative experiments respectively conducted at room temperature and liquid nitrogen temperature are implemented. The results show that in comparison with the performance data at room temperature, most of j factors are relatively smaller perhaps because the lower aluminum thermal conductivity and higher Prandtl Number at low temperature. Meanwhile, the f factors corresponding to cryogenic conditions exhibit slightly larger even though the core pressure drops show considerable reductions. In contrast to the calculated results from the frequently-used performance curves (Chen and Shen, 1993), the Root Mean Squared Errors of j and f values are correlated within 8.38% and 6.97% for one perforated fin core, 41.29% and 34.97% for three OSF cores, respectively. For OSFs, further comparisons with the previous empirical correlations from literatures are conducted to verify the accuracy of each correlation. Generally, most of the calculated results predict acceptably within the deviations of ±25% for the j factors, while the predicted results express relatively large deviations for the f factors. Therefore, it may be revealed that most of the existing correlations were not able to accurately predict the experimental data in consideration of the performance differences under realistic cryogenic operating conditions, which could have significant influences during the design process of cryogenic heat exchangers.  相似文献   

10.
A semiconductor ethanol sensor was developed using ZnO–CuO and its performance was evaluated at room temperature. Hetero-junction sensor was made of ZnO–CuO nanoparticles for sensing alcohol at room temperature. Nanoparticles were prepared by hydrothermal method and optimized with different weight ratios. Sensor characteristics were linear for the concentration range of 150–250 ppm. Composite materials of ZnO–CuO were characterized using X-ray diffraction (XRD), temperature-programmed reduction (TPR) and high-resolution transmission electron microscopy (HR-TEM). ZnO–CuO (1:1) material showed maximum sensor response (S = Rair/Ralcohol) of 3.32 ± 0.1 toward 200 ppm of alcohol vapor at room temperature. The response and recovery times were measured to be 62 and 83 s, respectively. The linearity R2 of the sensor response was 0.9026. The sensing materials ZnO–CuO (1:1) provide a simple, rapid and highly sensitive alcohol gas sensor operating at room temperature.  相似文献   

11.
The performance of high effectiveness (high NTU) perforated plate matrix heat exchangers (MHEs) is dependent on the geometry of the flow channels, as well as the longitudinal heat conduction through the outer walls. The effect of the above factors on the performance of MHEs is investigated in this paper numerically. The results obtained with the present model are validated with our own experimental results as well as those in the literature. The results show a strong influence of longitudinal heat conduction through the outer wall on the performance of MHEs. A parametric study has been carried out to arrive at the optimum flow channel geometry under given operating conditions.  相似文献   

12.
In most domestic and commercial refrigeration systems, frost forms on the air-side surface of the air-to-refrigerant heat exchanger. Frost-tolerant designs typically employ a large fin spacing in order to delay the need for a defrost cycle. Unfortunately, this approach does not allow for a very high air-side heat transfer coefficient, and the performance of these heat exchangers is often air-side limited. Longitudinal vortex generation is a proven and effective technique for thinning the thermal boundary layer and enhancing heat transfer, but its efficacy in a frosting environment is essentially unknown. In this study, an array of delta-wing vortex generators is applied to a plain-fin-and-tube heat exchanger with a fin spacing of 8.5 mm. Heat transfer and pressure drop performance are measured to determine the effectiveness of the vortex generator under frosting conditions. For air-side Reynolds numbers between 500 and 1300, the air-side thermal resistance is reduced by 35–42% when vortex generation is used. Correspondingly, the heat transfer coefficient is observed to range from 33 to 53 W m−2 K−1 for the enhanced heat exchanger and from 18 to 26 W m−2 K−1 for the baseline heat exchanger.  相似文献   

13.
Given their potential to reach higher speed levels than conventional bicycles, the growing market share of e-bikes has been the reason for increased concerns regarding road safety. Previous studies have shown a clear relationship between object approach speed and an observers’ judgment of when the object would reach a predefined position (i.e., time to arrival, TTA), with higher speed resulting in longer TTA estimates. Since TTA estimates have been linked to road users’ decisions of whether or not to cross or turn in front of approaching vehicles, the higher potential speeds of e-bikes might result in an increased risk for traffic conflicts. The goal of the two experiments presented in this paper was to examine the influence of speed and a variety of other factors on TTA estimation for conventional bicycles and for e-bikes. In both experiments, participants from two age groups (20–45 years old and 65 years or older) watched video sequences of bicycles approaching at different speeds (15–25 km/h) and were asked to judge the TTA at the moment the video was stopped. The results of both experiments showed that an increase in bicycle approach speed resulted in longer TTA estimates (measured as the proportion of estimated TTA relative to actual TTA) for both bicycle types (ηp2Exp.1 = .489, ηp2Exp.2 = .705). Compared to younger observers, older observers provided shorter estimates throughout (Exp. I: MDiff = 0.35, CI [0.197, 0.509], ηp2 = .332, Exp. II: MDiff = 0.50, CI [.317, 0.682], ηp2 = .420). In Experiment I, TTA estimates for the conventional bicycle were significantly shorter than for the e-bike (MDiff = 0.03, CI [.007, 0.044], ηp2 = .154), as were the estimates for the elder cyclist compared to the younger one (MDiff = 0.05, CI [.025, 0.066], ηp2 = .323). We hypothesized that the cause for this effect might lie in the seemingly reduced pedaling effort for the e-bike as a result of the motor assistance it provides. Experiment II was able to show that a high pedaling frequency indeed resulted in shorter TTA estimates compared to a low one (MDiff = 0.07, CI [0.044, 0.092], ηp2 = .438). Our findings suggest that both the e-bikes’ potential to reach higher speeds and the fact that they reduce the perceived cycling effort increase the risk of TTA misjudgments by other road users.  相似文献   

14.
Auto refrigerant cascade (ARC) refrigerators operating with zeotropic mixtures provide refrigeration at temperatures less than 173 K (?100 °C) using a single compressor. Different authors have suggested different cascade heat exchangers for ARC refrigerators. There is no study in literature that suggests at what temperature ranges one, two or three cascade heat exchangers are necessary. In this paper the performance of an ARC refrigerator operating in the liquid refrigerant supply mode and operating with optimized hydrocarbon mixtures and different cascade heat exchangers is studied. The optimum number of cascade heat exchangers (stages) to be used for different operating temperatures is suggested.  相似文献   

15.
In present study, heat transfer and turbulent flow of water/alumina nanofluid in a parallel as well as counter flow double pipe heat exchanger have been investigated. The governing equations have been solved using an in-house FORTRAN code, based on finite volume method. Single-phase and standard k-ε models have been used for nanofluid and turbulent modeling, respectively. The internal fluid has been considered as hot fluid (nanofluid) and the external fluid, cold fluid (base fluid). The effects of nanoparticles volume fraction, flow direction and Reynolds number on base fluid, nanofluid and wall temperatures, thermal efficiency, Nusselt number and convection heat transfer coefficient have been studied. The results indicated that increasing the nanoparticles volume fraction or Reynolds number causes enhancement of Nusselt number and convection heat transfer coefficient. Maximum rate of average Nusselt number and thermal efficiency enhancement are 32.7% and 30%, respectively. Also, by nanoparticles volume fraction increment, the outlet temperature of fluid and wall temperature increase. Study the minimum temperature in the solid wall of heat exchangers, it can be observed that the minimum temperature in counter flow has significantly reduced, compared to parallel flow. However, by increasing Reynolds number, the slope of thermal efficiency enhancement of heat exchanger gradually tends to a constant amount. This behavior is more obvious in parallel flow heat exchangers. Therefore, using of counter flow heat exchangers is recommended in higher Reynolds numbers.  相似文献   

16.
06Cr19Ni10 austenitic stainless steel sheet square butt joints without filler metal addition were fabricated using EBW (electron beam welding) processes. Fatigue properties, tensile properties and microstructure of the welded joints were studied. It was found that the yield strength, tensile strength, elongation and Vickers hardness of EBW joint can reach the level of base material performance. Fusion zones consist of coarse columnar dendritic grains, which are perpendicular to the weld pool boundary. The hardness of heat affected zone is lower than weld centreline. The reason is that the grain of heat affected zone under the action of electron beam heat source happened recovery and recrystallization. The present work suggests that S–N curve slope of welding joint should be revised to m = 10 under the condition of high stress levels, and S–N curve slope is still m = 3.0 under the condition of low stress levels. Fatigue cracks did not extend along the minimum thickness of the section. On the contrary, fatigue cracks extended along the maximum height of the section.  相似文献   

17.
Nanofluids and helical tubes are among the best methods for heat transfer enhancement. In the present study, laminar, developing nanofluid flow in helical tube at constant wall temperature is investigated. The numerical simulation of Al2O3-water nanofluid with temperature dependent properties is performed using the two-phase mixture model by control volume method in order to study convective heat transfer and entropy generation. The numerical results is compared with three test cases including nanofluid forced convection in straight tube, velocity profile in curved tube and Nusselt number in helical tubes that good agreement for all cases is observed. Heat transfer coefficient in developing region inside a straight tube using mixture model shows a better prediction compared to the homogenous model. The effect of Reynolds number and nanoparticle volume fraction on flow and temperature fields, local and overall heat transfer coefficient, local entropy generation due to viscous dissipation and heat transfer, and the Bejan number is discussed in detail and compared with the base fluid. The results show that the nanofluid and the base fluid have almost the same axial velocity profile, but their temperature profile has significant difference in developing and fully developed region. Entropy generation ratio by nanofluid to the base fluid in each axial location along the coil length showed that the entropy generation is reduced by using nanofluid in at most length of the helical tube. Also, better heat transfer enhancement and entropy generation reduction can be achieved at low Reynolds number.  相似文献   

18.
《Advanced Powder Technology》2020,31(5):2092-2100
Tapered wire coil insert is proposed as a novel enhancer in the double tube heat exchanger and experimental studies on Al2O3 + MgO hybrid nanofluid flowing under the turbulent condition are performed to investigate the hydrothermal characteristics. Effects of using tapered wire coil turbulator and hybrid nanofluid on the hydrothermal behaviors are examined for different coil configurations (Converging (C) type, Diverging (D) type and Conversing-Diverging (C-D) type) and hybrid nanofluid inlet temperatures and volume flow rates. Results show that D-type wire coil insert promotes better hydrothermal performance as compared to C-type and C-D type. Nusselt number and friction factor of hybrid nanofluid using D-type, C-D type and C-type wire coil inserts enhance up to 84%, 71% and 47%, and 68%, 57% and 46%, respectively than that of water in tube without insert. The entropy generation of hybrid nanofluid is lower than that of base fluid in all cases. The thermal performance factor for hybrid nanofluid is found more than one with all inserts. The thermal performance factor is observed a maximum of 1.69 for D-type coil. The study reveals that the hybrid nanofluid and tapered wire coil combination is promising option for improving the hydrothermal characteristics of double pipe heat exchanger.  相似文献   

19.
The objective of this paper is to investigate the influence of nanoparticles on the heat transfer characteristics of refrigerant-based nanofluid flow boiling inside a horizontal smooth tube, and to present a correlation for predicting heat transfer performance of refrigerant-based nanofluid. For the convenience of preparing refrigerant-based nanofluid, R113 refrigerant and CuO nanoparticles were used. Experimental conditions include an evaporation pressure of 78.25 kPa, mass fluxes from 100 to 200 kg m−2 s−1, heat fluxes from 3.08 to 6.16 kW m−2, inlet vapor qualities from 0.2 to 0.7, and mass fractions of nanoparticles from 0 to 0.5 wt%. The experimental results show that the heat transfer coefficient of refrigerant-based nanofluid is larger than that of pure refrigerant, and the maximum enhancement of heat transfer coefficient is 29.7%. A heat transfer correlation for refrigerant-based nanofluid is proposed, and the predictions agree with 93% of the experimental data within the deviation of ±20%.  相似文献   

20.
A combined cycle has been proposed for the production of power and refrigeration simultaneously. The cycle can be driven by low grade heat sources such as solar, geothermal and waste heat sources. In the first part of this paper, a model has been developed to perform a parametric analysis to evaluate the effects of important parameters on the performance of the cycle, which is a combination of Rankine and absorption refrigeration cycle. Propane–decane has been used as an organic dual working fluid. In the second part, multi objective genetic algorithm is applied for Pareto approach optimization of the cycle. There are three important conflicting objectives namely, turbine work (Wt), cooling capacity (Qc) and thermal efficiency (ηth) which have been selected to find the best possible combination of these performance parameters. Optimization has been carried out by varying turbine inlet pressure, superheated temperature and condenser temperature as design variables. Among optimum design parameters, a trade-off point is selected. Turbine inlet pressure, superheated temperature and condenser temperature are assumed to be 29.5 bar, 410 K and 386.6 K respectively as the values assigned to this point. Furthermore, it has been shown that some interesting and important relationships can be discovered among optimal objective functions and decision variables involved, consequently.  相似文献   

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