Second law analysis for optimal thermal design of radial fin geometry by convection

This paper presents a second law analysis for the optimal geometry of fin array by forced convection. The analytical analysis involves the achievement of a balance between the entropy generation due to heat transfer and entropy generation due to fluid friction. In the design of a thermal system, it is important to minimize thermal irreversibilities because the optimal geometry will be found when the entropy generation rate is minimized. In this paper, the entropy generation rate is discussed and optimum thickness for fin array is determined on the basis of entropy generation minimization subjected to the global constraint. In addition, the influence of cost parameters on the optimum thickness of fin array is also considered and presented in graphical form. It has been found that the increase in cross flow fluid velocity will enhance the heat transfer rate that will reduce the heat transfer irreversibility.     

Entropy analysis of a flow past a heat‐generated bluff body

Cooling of a bluff body is a topic of interest for many engineers and scientists. Forced convection over the bluff body generates flow separation, which in turn affects the heat transfer characteristics and increases the irreversibilities involved in the system. In the present study, flow over a rectangular solid body with constant heat flux is considered. The governing flow and energy equations are solved in two‐dimensional space numerically using a control volume approach. In order to investigate the effect of the fluid properties on the heating process, three different fluids are taken into account. These are air, ethylene glycol and therminol. To determine the irreversibilities involved in the system, entropy analysis is carried out. It is found that fluid properties have considerable effect on the entropy generation. The entropy generation due to heat transfer well exceeds the entropy generation due to fluid friction. The surface temperature of the solid body highly depends on the cooling fluid employed. Copyright © 1999 John Wiley & Sons, Ltd.     

Costs of Irreversibilities in Heat Exchanger Design

Abstract

An operationally convenient methodology is presented for relating economic costs to entropy generation. This methodology, in the hands of the heat exchanger designer, allows an interaction with the system designer to gain insights into the trade-offs allowed between the thermodynamic irreversibilities of flow friction, heat transfer, heat leakage, and mixing. The methodology starts with a recognition of the appropriate individual irreversibilities, then relates the individual costs to system rating and energy penalties by thermodynamic arguments. The analysis loop is closed by considerations related to reduction of the individual irreversibilities in a cost-effective way. In contrast, the usual energy or “exergy” analysis provides an answer for the overall costs of the collective irreversibilities. This does not provide the engineer with the insight needed to minimize the individual irreversibilities in a cost-effective manner,     

Effects of the Dipole Position on Thermomagnetic Convection in a Locally Heated Shallow Enclosure: Thermodynamic and Transport Analysis

Steady-state thermomagnetic convection in a shallow cavity under zero-gravity conditions is numerically investigated for different positions of the field-source. Two symmetrically placed, discrete, flush-mounted heaters of identical strengths represent power-dissipaters in electronics/MEMS applications. The sidewalls are isothermal heat sinks. Correlations between the field-source position and the flow morphology have been established. The distribution patterns of maximum heater temperatures and pertinent heat transfer parameters are explained. The local entropy generation due to heat transfer and fluid friction irreversibilities are determined. The total entropy generation is found to be almost entirely dependent on heat transfer irreversibility. The dipole position that minimizes the total entropy generation also produces the lowest average temperature on the heaters.     

Local entropy generation and exergy analysis of the condenser in a direct methanol fuel cell system

This paper aims to identify the irreversibilities in the condenser of a direct methanol fuel cell (DMFC) system and present possible enhancements in its design through local entropy generation analysis (L-EGA). For this purpose, the local entropy generation terms originating from heat and mass calculated from results of a pseudo two-phase computational fluid dynamic (CFD) model of the condenser. Through this analysis, the total irreversibilities due to heat and mass transfer are calculated locally (e.g., film boundary layer, vapour-gas boundary layer) under the variable operating conditions of a DMFC (undersaturated, saturated, and supersaturated conditions of the cathode exhaust gas). Moreover, the exergy destruction ratio of condenser is found to estimate the exergy performance of the condenser. The results show that in the case of supersaturated cathode exhaust gas (CEG) flow, the entropy generation rate due to mass transfer in the film region is found as 0.032 W/(m·K) which is 18 times higher than that for the undersaturated CEG flow. However, entropy generation rate due to mass transfer decreases significantly when the hot flow is just over the film region. In the film region, the entropy generation rates originating from heat transfer are found as 0.0055 W/(m·K) (for the undersaturated case), 0.0032 W/(m·K) (for the saturated case), and 0.0015 W/(m·K) (for the supersaturated case). Moreover, the maximum exergy destruction ratio is found as 0.72 when the CEG is undersaturated and the CEG velocity is 0.18 m/s, while the lowest exergy destruction ratio is calculated as 0.28 when the CEG is saturated.     

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.     

Entropy generation through hexagonal cross‐sectional duct for constant wall temperature in laminar flow

Second law analysis of heat transfer in laminar flow for hexagonal cross‐section duct was analysed analytically. Geometrical effect of hexagonal duct was considered. The variation of total entropy generation was studied along the duct length. As a working fluid water and unused engine oil were used to compare the effect of fluid in the duct. Results were compared with circular cross‐section duct. It is found that the non‐dimensional entropy generation in a hexagonal cross‐section duct can be as high as a factor of four than that for a circular duct. Further, the unused engine oil gives up to about ten times lower non‐dimensional entropy generation values than that of water but needs about ten times more pumping power to heat transfer ratio. Copyright © 2004 John Wiley & Sons, Ltd.     

A numerical study on entropy generation induced by turbulent forced convection in curved rectangular ducts with various aspect ratios

The present paper analyzes the entropy generation induced by turbulent forced convection in a curved rectangular duct with external heating by numerical methods. The problem is assumed as steady, three-dimensional and turbulent. The flow features, including the secondary flow motions, the distribution of local entropy generation as well as the overall entropy generation in the whole flow fields, are analyzed. For a baseline case with Re = 20,000, external heat flux q? = 0.112 and aspect ratio γ = 1, the results show the entropy generation induced by the frictional irreversibility concentrates within the regions adjacent to the duct walls, whereas the entropy generation resulted from the heat transfer irreversibility only significantly occurs near the outer wall of the duct where the external heat flux imposed. Except the baseline case, two additional cases with aspect ratio equal to 0.25 and 4 are calculated. Through the comparison of the three aspect-ratio cases, it is seen that the resultant entropy generations in the flow fields for the three cases are all dominated by the frictional irreversibilities. Among the three aspect-ratio cases, the resultant entropy generation is minimal in the γ = 1 case. Accordingly, the case with γ = 1 is concluded to be the optimal aspect ratio under the current flow condition based on the minimal entropy generation principle.     

Entropy generation minimization of a MHD (magnetohydrodynamic) flow in a microchannel

The dissipative processes that arise in a microchannel flow subjected to electromagnetic interactions, as occurs in a MHD (magnetohydrodynamic) micropump, are analyzed. The entropy generation rate is used as a tool for the assessment of the intrinsic irreversibilities present in the microchannel owing to viscous friction, heat flow and electric conduction. The flow in a parallel plate microchannel produced by a Lorentz force created by a transverse magnetic field and an injected electric current is considered assuming a thermally fully developed flow and conducting walls of finite thickness. The conjugate heat transfer problem in the fluid and solid walls is solved analytically using thermal boundary conditions of the third kind at the outer surfaces of the walls and continuity of temperature and heat flux across the fluid-wall interfaces. Velocity, temperature and current density fields in the fluid and walls are used to calculate the global entropy generation rate. Conditions under which this quantity is minimized are determined for specific values of the geometrical and physical parameters of the system. The Nusselt number is also calculated and explored for different conditions. Results can be used to determine optimized conditions that lead to a minimum dissipation consistent with the physical constraints demanded by the microdevice.     

Analysis of Entropy Generation of Combined Heat and Mass Transfer in Internal and External Flows with the Assumption of Local Thermodynamic Equilibrium

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Application of EoEP principle with variable heat transfer coefficient in minimizing entropy production in heat exchangers

A more realistic application of the entropy minimization principle EoEP is presented. This principle dictates uniform local entropy generations along the heat exchanger in order to minimize the total entropy generation rate due only to heat transfer. For a certain heat duty and area of an existing exchanger, this is done by changing the temperatures of one fluid while the temperatures of the other fluid are held constant. Since the heat duty is fixed, the change in the temperatures of the fluid after the change, however, may sometimes cause a drastic change in its flow rate. This may cause considerable changes in the overall heat transfer coefficient (U) and, consequently, in the entropy generation rate. Depending on the choice of the fluid for changing, the new entropy generation rates may be higher or lower than those based on constant U as is the case in papers recently published. So, the classical application of the EoEP principle needs to be modified to achieve more realistic entropy generation rates. In this study, the principle of EoEP with variable U is applied to some cases of heat exchange, and a simple method is presented as a criterion for the proper choice of the fluid to be changed.     

Exergy transfer characteristics of forced convective heat transfer through a duct with constant wall temperature

The exergy transfer characteristics of fluid flow and heat transfer inside a circular duct under fully developed laminar and turbulent forced convection are presented. Temperature is kept constant at the duct wall. The exergy transfer Nusselt number is put forward and the analytical expressions for exergy transfer Nusselt number are obtained as functions of heat transfer Nusselt number, Reynolds number, Prandtl number, etc. The variations of the local and mean convective exergy transfer coefficient, non-dimensional exergy flux, exergy transfer rate, etc. with operating parameters are presented graphically. By reference to a smooth duct and taking air as working fluid, a numerical analysis of the influence of the Reynolds number and non-dimensional cross-sectional position on exergy transfer characteristics has been conducted. The results show that the process parameters and configuration in the fluid flow and heat transfer inside a duct should be properly selected so that the forced convection process could have the best exergy utilization. In addition, the results corresponding to the exergy transfer and energy transfer are compared.     

Entropy generation minimization of free convection film condensation on an elliptical cylinder

This paper aims to perform thermodynamic analysis of saturated vapor flowing slowly onto and condensing on an elliptical cylinder. This analysis provides us how the geometric parameter-ellipticity affects entropy generation during film-wise condensation heat transfer process. The results observe that local condensate film thickness decreases with an increase in ellipticity of a cylinder. From the first law point of view, the local heat transfer coefficient enhances as ellipticity increases. Meanwhile, from the second law point of view, entropy generation increases with increasing the value of ellipticity. We derive an expression for entropy generation, which accounts for the combined action of the specified irreversibilities. The result demonstrates that thermal irreversibility dominates over film flow friction irreversibility. Finally, an expression of minimizing entropy generation in laminar film condensation heat transfer is obtained.     

Second Law Efficiency Analysis of Heat Exchangers

Analytical analysis of unbalanced heat exchangers is carried out to study the second law thermodynamic performance parameter through second law efficiency by varying length‐to‐diameter ratio for counter flow and parallel flow configurations. In a single closed form expression, three important irreversibilities occurring in the heat exchangers—namely, due to heat transfer, pressure drop, and imbalance between the mass flow streams—are considered, which is not possible in first law thermodynamic analysis. The study is carried out by giving special influence to geometric characteristics like tube length‐to‐diameter dimensions; working conditions like changing heat capacity ratio, changing the value of maximum heat capacity rate on the hot stream and cold stream separately and fluid flow type, i.e., laminar and turbulent flows for a fully developed condition. Further, second law efficiency analysis is carried out for condenser and evaporator heat exchangers by varying the effectiveness and number of heat transfer units for different values of inlet temperature to reference the temperature ratio by considering heat transfer irreversibility. Optimum heat exchanger geometrical dimensions, namely length‐to‐diameter ratio can be obtained from the second law analysis corresponding to lower total entropy generation and higher second law efficiency. Second law analysis incorporates all the heat exchanger irreversibilities. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21109     

Generation of entropy during forced convection of heat in nanofluid stagnation-point flows over a cylinder embedded in porous media

Thermodynamics and heat transfer of an impinging nanofluid flow upon a cylinder with constant surface temperature and embedded in porous media are investigated. Numerical solutions reveal the flow velocity and temperature fields as well as the Nusselt number. These are then used to calculate the rate of entropy generation within the system by viscous and heat transfer irreversibilities. It is demonstrated that changes in the concentration of nanoparticles modify the thermal and hydrodynamic boundary layers and hence can alter the Nusselt number and entropy generation considerably. However, the shear stress on the surface of the cylinder is observed to be less affected by the variations in the concentration of nanoparticles. Further, the Reynolds number and non-uniform transpiration are shown to affect the Nusselt number and entropy generation. It is argued that the influences of Reynolds number on the boundary layer thickness can majorly modify the irreversibility and Bejan number.     

Entropy generation of viscous dissipative nanofluid flow in microchannels

An analytical study on the viscous dissipation effect on entropy generation in laminar fully developed forced convection of water–alumina nanofluid in circular microchannels is reported. In the first-law analysis, closed form solutions of the temperature distributions in the radial direction for the models with and without viscous dissipation term in the energy equation are obtained. The results show that the heat transfer coefficient decreases with nanoparticle volume fraction largely in the laminar regime of nanofluid flow in microchannel when the viscous dissipation effect is taken into account. In the second-law analysis, the two models are compared by analyzing their relative deviations in entropy generation for different Reynolds number and nanoparticle volume fraction. When the viscous dissipation is taken into account, the temperature distribution is prominently affected and consequently the entropy generation ascribable to the heat transfer irreversibility is significantly increased. The increase of entropy generation induced by the increase of nanoparticle volume fraction is attributed to the increase of both the thermal conductivity and viscosity of nanofluid which causes augmentation in the heat transfer and fluid friction irreversibilities, respectively. By incorporating the viscous dissipation effect, both thermal performance and exergetic effectiveness for forced convection of nanofluid in microchannels dwindle with nanoparticle volume fraction, contrary to the widespread conjecture that nanofluids possess advantage over pure fluid associated with higher overall effectiveness from the aspects of first-law and second-law of thermodynamics.     

S型流道冷板的流体域熵产分析及流道优化

粘性流体在流动和传热过程中,由于粘性耗散和热传导的存在造成能量损失。为分析流体流动和传热过程的能量损失并得到冷板的最优流道形式,本文以某电子器件用S型流道液冷冷板为分析对象,通过数值模拟,得到S型流道液冷冷板的流体域熵产率随工质流量的变化规律,对流体域充分发展的直段和弯段内熵产率大小进行了比较,并在固定流量下,分析了熵产率大小沿工质流动方向上的变化情况。提出冷板流道优化方案,并从换热表现、压头损失和总能量损失三方面对不同流道形式的冷板进行了综合评价和比较,得到了冷板流道的最优形式,为工程实际提供参考。     

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.     

Heat transfer and entropy generation optimization of forced convection in porous-saturated ducts of rectangular cross-section

We investigate analytically the first and the second law characteristics of fully developed forced convection inside a porous-saturated duct of rectangular cross-section. The Darcy–Brinkman flow model is employed. Three different types of thermal boundary conditions are examined. Expressions for the Nusselt number, the Bejan number, and the dimensionless entropy generation rate are presented in terms of the system parameters. The conclusions of this analytical study will make it possible to compare, evaluate, and optimize alternative rectangular duct design options in terms of heat transfer, pressure drop, and entropy generation.     

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.