Entropy generation and Carnot efficiency comparisons of high temperature heat transfer fluid candidates for CSP plants

Heat transfer fluid is a critical component in a concentrating solar power plant. A large quantity of heat transfer fluid is required to transfer heat between the solar collector and the power block, thus it is crucial to select the most appropriate heat transfer fluid in order to maximize the system performance. The present study compared the performances of five molten-salt eutectic mixtures in regarding with the entropy generation rate and the Carnot efficiency of using them as heat transfer fluids. All the five molten-salt eutectic mixtures have thermal stability temperatures above 600 °C. Effects of the tube lengths in the steam generation heat exchanger and the receiver heat exchanger as well as the heat transfer fluid flow rate on both the entropy generation rate and the Carnot cycle efficiency were investigated. The results indicate that the carbonate salts has the worst performances compared to the other eutectic mixtures. The three chloride salts have slightly higher entropy generation rate and 5% higher Carnot efficiency than the Solar Salt. Therefore the three chloride salts are suggested to be used in advanced concentrating solar power tower plants as potential high temperature heat transfer fluids.     

Conflation of ε-Ntu and EGM design methods for heat exchangers with uniform wall temperature

This paper conflates two heat exchanger design approaches – the ε-N_tu (effectiveness–number of transfer units) and the EGM (entropy generation minimization) – focusing on heat exchangers with uniform wall temperature, i.e. condensers and evaporators. An algebraic formulation which expresses the dimensionless rate of entropy generation as a function of the heat exchanger geometry (number of transfer units), the thermal-hydraulic characteristics (friction factor and Colburn j-factor), and the operating conditions (heat transfer duty, core velocity, surface temperature, and fluid properties) is derived. It is shown that there does exist a particular number of transfer units which minimizes the dimensionless rate of entropy generation. An algebraic expression for the optimum heat exchanger effectiveness, based on the working conditions, heat exchanger geometry and fluid properties, is also presented. The theoretical analysis led to the conclusion that a high effectiveness heat exchanger design does not necessarily provide the best thermal-hydraulic performance.     

Optimization for a heat exchanger couple based on the minimum thermal resistance principle

Following the brief introduction to the concept of a physical quantity, entransy, the equivalent thermal resistance of a heat exchanger couple is defined based on the entransy dissipation. The minimum thermal resistance principle is applied to obtain the optimal heat capacity rate of the medium fluid and the optimal allocation of heat exchangers thermal conductance, which correspond to the maximum heat transfer rate in the heat exchanger couple. In addition, analytical expression for the optimal heat capacity rate of the medium fluid is derived, whose reciprocal equals the sum of the reciprocal of the individual heat capacity rate of the hot and cold fluids, just like the case of two electrical capacitors in series. Numerical results in the variation of the thermal resistance and the heat transfer rate with the medium fluid heat capacity rate or the thermal conductance allocation agree with the theoretical analyses. Finally, for comparison, the entropy generation rate is also calculated to obtain its relation with the thermal performance of the heat exchanger couple. The results show that there is no one-to-one correspondence of the minimum entropy generation rate and the maximum heat transfer rate. This indicates that the minimum entropy generation principle cannot be used for optimizing the heat exchanger couple.     

Effect of nanoparticle shape on the heat transfer and thermodynamic performance of a shell and tube heat exchanger

Nanofluid is a heat transfer fluid that can improve the performance of heat exchanger systems. Different parameters such as particle size, shape, and volume concentration affect the performance of these systems. The objective of this paper is to study the effect of different nanoparticle shapes (such as cylindrical, bricks, blades, platelets, and spherical) on the performance of a shell and tube heat exchanger operating with nanofluid analytically. Boehmite alumina (γ-AlOOH) nanoparticles of different shapes were dispersed in a mixture of water/ethylene glycol as the nanofluid. The thermodynamic performance of the shell and tube heat exchanger that is used in a waste heat recovery system was analysed in terms of heat transfer rate and entropy generation. Established correlations were used to measure the thermal conductivity, heat transfer coefficient and rate and entropy generation of nanofluid. The results show an increase in both the heat transfer and thermodynamic performance of the system. However, among the five nanoparticle shapes, cylindrical shape exhibited better heat transfer characteristics and heat transfer rate. On the other hand, entropy generation for nanofluids containing cylindrical shaped nanoparticles was higher in comparison with the other nanoparticle shapes. However, the increased percentage of entropy was below 1%. Therefore, this greater entropy generation could be deemed negligible and cylindrical shaped nanoparticles are recommended to be utilized in heat exchanger systems working with nanofluids.     

Optimization design of shell-and-tube heat exchanger by entropy generation minimization and genetic algorithm

In the present work, a new shell-and-tube heat exchanger optimization design approach is developed, wherein the dimensionless entropy generation rate obtained by scaling the entropy generation on the ratio of the heat transfer rate to the inlet temperature of cold fluid is employed as the objective function, some geometrical parameters of the shell-and-tube heat exchanger are taken as the design variables and the genetic algorithm is applied to solve the associated optimization problem. It is shown that for the case that the heat duty is given, not only can the optimization design increase the heat exchanger effectiveness significantly, but also decrease the pumping power dramatically. In the case that the heat transfer area is fixed, the benefit from the increase of the heat exchanger effectiveness is much more than the increasing cost of the pumping power.     

Thermodynamic optimization of a coiled tube heat exchanger under constant wall heat flux condition

In this paper the second law analysis of thermodynamic irreversibilities in a coiled tube heat exchanger has been carried out for both laminar and turbulent flow conditions. The expression for the scaled non-dimensional entropy generation rate for such a system is derived in terms of four dimensionless parameters: Prandtl number, heat exchanger duty parameter, Dean number and coil to tube diameter ratio. It has been observed that for a particular value of Prandtl number, Dean number and duty parameter, there exists an optimum diameter ratio where the entropy generation rate is minimum. It is also found that with increase in Dean number or Reynolds number, the optimum value of the diameter ratio decreases for a particular value of Prandtl number and heat exchanger duty parameter.     

Effect of maximum and minimum heat capacity rate on entropy generation in a heat exchanger

This paper presents a theoretical analysis of a heat exchanger with a negligible fluid flow pressure drop to determine whether it is better to operate the heat exchanger with the minimum or maximum heat capacity rate of the hot fluid from entropy generation point of view. Entropy generation numbers are derived for both cases, and the results show that they are identical, when the heat exchanger is running at a heat capacity ratio of 0.5 with heat exchanger effectiveness equaling 1. An entropy generation number ratio is defined for the first time, which has a maximum value at ε = 1/(1+R) for any inlet temperature ratio. When R equals 0.1, 0.5 and 0.9, the entropy generation number ratio receives a maximum value at an effectiveness equaling 0.91, 0.67 and 0.526, respectively. When R=0.9, the entropy generation number ratio is the same for all inlet temperature ratios at ε=0.8. The results show that the entropy generation number ratio is far from 1 depending on the inlet temperature ratio of the cold and hot fluid. The results are valid for parallel‐flow and counterflow heat exchangers. Copyright © 2010 John Wiley & Sons, Ltd.     

Comparison of entropy minimization principles in heat exchange and a short-cut principle: EoTD

In this paper the principles called ‘equipartition of forces, EoF’ and ‘equipartition of entropy production, EoEP’ are compared in minimizing the entropy production in heat exchange. Entropy production rates for various cases are calculated according to both principles. The calculations show that entropy productions calculated with EoEP principle are always smaller than those calculated with EoF principle although the differences are considerably small. It is also shown that the heat exchange with EoEP principle implied T_H/T_C=const. Additionally, a new approach, equipartition of temperature difference, EoTD, has been tested comparatively. Although the entropy production rates calculated by this approach are slightly larger than those of two other principles, it can be used as a new principle for quick determination. Copyright © 2003 John Wiley & Sons, Ltd.     

Entropy generation in combined heat and mass transfer

Irreversible entropy generation for combined forced convection heat and mass transfer in a twodimensional channel is investigated. The heat and mass transfer rates are assumed to be constant on both channel walls. For the case of laminar flow, the entropy generation is obtained as a function of velocity, temperature, concentration gradients and the physical properties of the fluid. The analogy between heat and mass transfer is used to obtain the concentration profile for the diffusing species. The optimum plate spacing is determined, considering that either the mass flow rate or the channel length are fixed. For the turbulent flow regime, a control volume approach that uses heat and mass transfer correlations is developed to obtain the entropy generation and optimum plate spacing.     

Theoretical analysis and experimental confirmation of the uniformity principle of temperature difference field in heat exchanger

Theoretical analysis and experimental confirmation for the principle to improve the thermal performance of heat exchangers is performed in this paper. The more uniform the temperature difference field (TDF), the higher the effectiveness of heat exchanger for the fixed N_tu and C_r. The uniformity of the TDF and the effectiveness of 13 types of heat exchangers are studied analytically and numerically, and the results support the uniformity principle of TDF. Further verification is given by the asymptotic solution for TDF in terms of a recurrence formula of heat transfer area distribution for the same kind of heat exchanger. The analysis of entropy generation caused by the heat transfer indicates that the uniformity principle of TDF satisfies the second law of thermodynamics. The results of the experimental setup, governed by the uniformity principle of TDF, show that the effectiveness increases with the increase of the uniformity of TDF. Heat exchanger effectiveness for the best flow distribution was found to be 11.2% greater than that of the conventional flow distribution without associated increase in pressure drop. Two ways, redistributing heat transfer areas and varying the connection between tubes, are presented for improving the uniformity of TDF and increasing effectiveness for the crossflow heat exchangers.     

Thermal characterization of a cross-flow heat exchanger with a new flow arrangement

The objective of the present paper is to thermally characterize a cross-flow heat exchanger featuring a new cross-flow arrangement, which may find application in contemporary refrigeration and automobile industries. The new flow arrangement is peculiar in the sense that it possesses two fluid circuits extending in the form of two tube rows, each with two tube lines. To assess the heat exchanger performance, it is compared against that for the standard two-pass counter-cross-flow arrangement. The two-part comparison is based on the thermal effectiveness and the heat exchanger efficiency for several combinations of the heat capacity rate ratio, C¹, and the number of transfer units, NTU. In addition, a third comparison is made in terms of the so-called “heat exchanger reversibility norm” (HERN) through the influence of various parameters such as the inlet temperature ratio, τ, and the heat capacity rate ratio, C¹, for several fixed NTU values. The proposed new flow arrangement delivers higher thermal effectiveness and higher heat exchanger efficiency, resulting in lesser entropy generation over a wide range of C¹ and NTU values. These metrics are quantified with respect to the arrangement widely used in refrigeration industry due to its high effectiveness, namely, the standard two-pass counter-cross-flow heat exchanger. The new flow arrangement seems to be a promising avenue in situations where cross-flow heat exchangers for single-phase fluid have to be used in refrigeration units.     

Local effects of longitudinal heat conduction in plate heat exchangers

In a plate heat exchanger, heat transfer from the hot to the cold fluid is a multi-dimensional conjugate problem, in which longitudinal heat conduction (LHC) along the dividing walls often plays some role and can not be neglected. Large-scale, or end-to-end, LHC is always detrimental to the exchanger’s effectiveness. On the contrary, if significant non-uniformities exist in the distribution of either convective heat transfer coefficient, small-scale, or local, LHC may actually enhance the exchanger’s performance by improving the thermal coupling between high heat transfer spots located on the opposite sides of the dividing wall.     

Second law analysis and heat transfer in a cross-flow heat exchanger with a new winglet-type vortex generator

In this paper a second law analysis of a cross-flow heat exchanger (HX) is studied in the presence of a balance between the entropy generation due to heat transfer and fluid friction. The entropy generation in a cross-flow HX with a new winglet-type convergent–divergent longitudinal vortex generator (CDLVG) is investigated. Optimization of HX channel geometry and effect of design parameters regarding the overall system performance are presented. For the HX flow lengths and CDLVGs the optimization model was developed on the basis of the entropy generation minimization (EGM). It was found that increasing the cross-flow fluid velocity enhances the heat transfer rate and reduces the heat transfer irreversibility. The test results demonstrate that the CDLVGs are potential candidate procedure to improve the disorderly mixing in channel flows of the cross-flow type HX for large values of the Reynolds number.     

Design and optimization of a downhole coaxial heat exchanger for an enhanced geothermal system (EGS)

The present study considers the design, performance analysis and optimization of a downhole coaxial heat exchanger for an enhanced geothermal system (EGS). The optimum mass flow rate of the geothermal fluid for minimum pumping power and maximum extracted heat energy was determined. In addition, the coaxial pipes of the downhole heat exchanger were sized based on the optimum geothermal mass flow rate and steady-state operation. Transient effect or time-dependent cooling of the Earth underground, and the optimum amount and size of perforations at the inner pipe entrance region to regulate the flow of the geothermal fluid were disregarded to simplify the analysis. The paper consists of an analytical and numerical thermodynamic optimization of a downhole coaxial heat exchanger used to extract the maximum possible energy from the Earth's deep underground (2 km and deeper below the surface) for direct usage, and subject to a nearly linear increase in geothermal gradient with depth. The thermodynamic optimization process and entropy generation minimization (EGM) analysis were performed to minimize heat transfer and fluid friction irreversibilities. An optimum diameter ratio of the coaxial pipes for minimum pressure drop in both limits of the fully turbulent and laminar fully-developed flow regime was determined and observed to be nearly the same irrespective of the flow regime. Furthermore, an optimum geothermal mass flow rate and an optimum geometry of the downhole coaxial heat exchanger were determined for maximum net power output. Conducting an energetic and exergetic analysis to evaluate the performance of binary power cycle, higher Earth's temperature gradient and lower geofluid rejection temperatures were observed to yield maximum first- and second-law efficiencies.     

Second law analysis on the heat transfer of the horizontal concentric tube heat exchanger

In the present study, the theoretical and experimental results of the second law analysis on the heat transfer and flow of a horizontal concentric tube heat exchanger are presented. The experiments setup are designed and constructed for the measured data. Hot water and cold water are used as working fluids. The test runs are done at the hot and cold water mass flow rates ranging between 0.02 and 0.20 kg/s and between 0.02 and 0.20 kg/s, respectively. The inlet hot water and inlet cold water temperatures are between 40 and 50 °C, and between 15 and 20 °C, respectively. The effects of the inlet conditions of both working fluids flowing through the heat exchanger on the heat transfer characteristics, entropy generation, and exergy loss are discussed. The mathematical model based on the conservation equations of energy is developed and solved by the central finite difference method to obtain temperature distribution, entropy generation, and exergy loss. The predicted results obtained from the model are validated by comparing with the present measured data. There is reasonable agreement from the comparison between predicted results and those from the measured data.     

Entropy generation and pumping power in a turbulent fluid flow through a smooth pipe subjected to constant heat flux

In a heat exchange process, heat transfer and pumping power requirements are the two main considerations. Efforts made to increase heat transfer in a fluid flow usually cause increase in the pumping power requirement. In an effort to avoid inefficient utilization of energy through excessive entropy generation, a thermodynamic analysis of turbulent fluid flow through a smooth duct subjected to constant heat flux has been made in this study. The temperature dependence of the viscosity was taken into consideration in determining the heat transfer coefficient and friction factor. It was shown that the viscosity variation has a considerable effect on both the entropy generation and the pumping power. Pumping power to heat transfer ratio and the entropy generation per unit heat transfer can become very large especially for low heat flux conditions.     

Numerical study on a slit fin-and-tube heat exchanger with longitudinal vortex generators

A 3-D numerical simulation is performed on laminar heat transfer and flow characteristics of a slit fin-and-tube heat exchanger with longitudinal vortex generators. Heat transfer enhancement of the novel slit fin mechanism is investigated by examining the effect of the strips and the longitudinal vortices. The structure of the slit fin is optimized and analyzed with field synergy principle. The result coincides with the guideline ‘front coarse and rear dense’. The heat transfer and fluid flow characteristics of the slit fin-and-tube heat exchanger with longitudinal vortex generators are compared with that of the heat exchanger with X-shape arrangement slit fin and heat exchanger with rectangular winglet longitudinal vortex generators. It is found that the Colburn j-factor and friction factor f of the novel heat exchanger with the novel slit fin is in between them under the same Reynolds number, and the factor j/(f^1/3) of the novel heat exchanger increased by 15.8% and 4.2%, respectively.     

The effects of nanofluid on thermophysical properties and heat transfer characteristics of a plate heat exchanger

Improving heat exchanger's performance by increasing the overall heat transfer as well as minimising pressure drop is one of the promising fields of research to focus on. Nanofluids with higher thermal conductivity and better thermophysical properties can be applied in heat exchanger to increase the heat transfer rate. In the present study SiO₂, TiO₂ and Al₂O₃ are applied in a plate heat exchanger and the effects on thermophysical properties and heat transfer characteristics are compared with the base fluid. Since it is desired to minimize the pressure drop, the influence of nanofluid application on pressure drop and entropy generation is investigated. It is concluded that the thermal conductivity, heat transfer coefficient and heat transfer rate of the fluid increase by adding the nanoparticles and TiO₂ and Al₂O₃ result in higher thermophysical properties in comparison with SiO₂. The highest overall heat transfer coefficient was achieved by Al₂O₃ nanofluid, which was 308.69 W/m².K in 0.2% nanoparticle concentration. The related heat transfer rate was improved around 30% compared to SiO₂ nanofluid. In terms of pressure drop, SiO₂ shows the lowest pressure drop, and it was around 50% smaller than the pressure drop in case of using TiO₂ and Al₂O₃.     

Design optimization of heat exchangers with high‐viscosity fluids

The thermal effectiveness and entropy generation of parallel and counter‐flow heat exchangers handling high‐viscosity fluids have been numerically investigated. Both the viscous friction and the viscosity variations with temperature were considered in the analysis. The results show that the thermal effectiveness–NTU curves deviate gradually from the curves obtained using the assumption that the effect of viscosity is negligible. Moreover, the consideration of the viscous frictional heating effect results in a considerable increase in the heat exchanger entropy. An optimum heat exchanger size could be determined from both first law and second law of thermodynamics points of view. The results show also that the effect of viscous friction with variable viscosity becomes more significant for lower inlet temperatures of high‐viscosity fluid. Copyright © 2002 John Wiley & Sons, Ltd.     

Entropy analysis for heat transfer in a rectangular channel with suction

The purpose for this paper is to study heat transfer in a rectangular channel with suction applied at the adjacent two side walls. A two‐dimensional laminar viscous fluid flow is generated due to the application of suction/injection. The other two opposite sides are kept at a constant temperatures, and the walls with suction are maintained at a constant heat flux. The streamlines thus obtained due to the flow and isothermal lines and heat function are analyzed. The regions of high and low frictions are found by drawing contours of the entropy generation number and the Bejan number. The biharmonic equation for stream function is numerically solved by the Finite Difference Method (FDM) using a 13‐point formula, and a five‐point formula is used to solve for all other harmonic equations for temperature, heat function, and pressure. For derivative boundary conditions, the central difference formula with fictitious nodes is used. In the analysis, we note that the corner points are regions of high energy dissipation. The least dissipation of energy is near the wall, where the nondimensional temperature is 1. This paper analyzes heat transfer in the rectangular channel through the heat function and entropy generation number.