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.     

A comparative study of viscous dissipation effect on entropy generation in single-phase liquid flow in microchannels

The influence of viscous dissipation on entropy generation in fully developed forced convection for single-phase liquid flow in a circular microchannel under imposed uniform wall heat flux has been studied. In the first-law analysis, closed form solutions of the radial temperature profiles for the models with and without viscous dissipation term in the energy equation are obtained. In the second-law analysis, for different Brinkman number and dimensionless heat flux, the variations of dimensionless entropy generation and Bejan number as a function of the radial distance are investigated. The two models are compared by analyzing their relative deviations in dimensionless entropy generation and Bejan number. Comparisons are also performed for average dimensionless entropy generation and average Bejan number. Contribution of heat transfer irreversibility and fluid friction irreversibility to the deviations is analyzed and discussed. It is found that, under certain conditions, the effect of viscous dissipation on entropy generation in microchannel is significant and should not be neglected.     

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.     

Entropy generation analysis in a uniformly heated microchannel heat sink

Present investigation analyzes the issue of entropy generation in a uniformly heated microchannel heat sink (MCHS). Analytical approach used to solve forced convection problem across MCHS, is a porous medium model based on extended Darcy equation for fluid flow and two-equation model for heat transfer. Simultaneously, closed form velocity solution in a rectangular channel is employed to capture z-directional viscous effect diffusion and its pronounced effect on entropy generation through fluid flow. Subsequently, governing equations are cast into dimensionless form and solved analytically. Second law analysis of problem is then conducted on the basis of obtained velocity and temperature fields and expressions for local and average entropy generation rate are derived in dimensionless form. Average entropy generation rate is then utilized as a criterion for assessing the system performance. Finally, the effect of influential parameters such as, channel aspect ratio (α_S), group parameter (Br/Ω), thermal conductivity ratio (C) and porosity (ε) on thermal and total entropy generation is investigated. In order to examine the accuracy of the analysis, the results of thermal evaluation are compared to one of the previous investigations conducted for thermal optimization of MCHS.     

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.     

Optimization of Microchannel Heat Sinks Using Genetic Algorithm

In this study, a genetic algorithm is employed to minimize the entropy generation rate in microchannel heat sinks. The entropy generation rate allows the combined effects of thermal performance and pressure drop to be assessed simultaneously as the heat sink interacts with the surrounding flow field. Previously developed models for the heat transfer, pressure drop and entropy generation rate are used in the optimization procedure. The results of optimization are compared with existing results obtained by the Newton–Raphson method. It is observed that the GA gives better overall performance of the microchannel heat sinks.     

Numerical Optimization for Nanofluid Flow in Microchannels Using Entropy Generation Minimization

This study presents the numerical simulation of the three-dimensional incompressible steady and laminar fluid flow of a trapezoidal microchannel heat sink using nanofluids as a cooling fluid. Navier–Stokes equations with a conjugate energy equation are discretized by the finite-volume method. Numerical computations are performed for inlet velocity (W _in = 4 m/s, 6 m/s, and 10 m/s), hydraulic diameter D _h  = 106.66 μm, and heat flux (q″ = 200 kW/m². Numerical optimization is demonstrated as a trapezoidal microchannel heat sink design which uses the combination of a full factorial design and the genetic algorithm method. Three optimal design variables represent the ratio of upper width and lower width of the microchannel (1.2 ≤ α ≤ 3.6), the ratio of the height of the microchannel to the difference between the upper and lower width of the microchannel (0.5 ≤ β ≤ 1.866), and the volume fraction (0 ≤ φ ≤ 4%). The dimensionless entropy generation rate of a trapezoidal microchannel is minimized for fixed heat flux and inlet velocity. Numerical results for the system dimensionless entropy generation rate show that the system dimensionless friction entropy generation rate increases with Reynolds number; on the contrary, the higher the Reynolds number, the lower the system dimensionless thermal entropy generation rate. The results below show that the two-phase model gives higher enhancement than the single-phase model assuming a steadily developing laminar flow.     

Thermal management of methanol reforming reactors for the portable production of hydrogen

Three-dimensional numerical simulations were performed to address the thermal management issues associated with the design of a methanol reforming microchannel reactor for the portable production of hydrogen. The design of the reactor was fundamentally related to the direct coupling of reforming and combustion reactions by performing them on opposite sides of dividing walls in a parallel flow configuration. Effective autothermal operation was achieved through a combination of microchannel reactor technology with heat exchange in a direction perpendicular to the reacting fluid flow. Computational fluid dynamics simulations and thermodynamic analysis were carried out to investigate the effect of various design parameters on the characteristics of the generation, consumption, and exchange of thermal energy within the system. The results indicated that the ability to control temperature and temperature uniformity is of great importance to the performance of the system. The degree of temperature uniformity favorably affects the autothermal operation of the reactor. Temperature uniformity of the reactor can be improved by controlling the rate of heat transfer through a variety of factors such as wall thermal conductivity, fluid velocities, and dimensions. High wall thermal conductivity would be greatly beneficial to the performance of the system and the temperature uniformity of the reactor.     

Heat transfer and entropy analysis for a transparent gas flowing in a tube

Heat transfer by forced convection and radiation in tubes is very important for high‐temperature heat exchangers, which find wide applications in power plants. In addition, the entropy analysis gives insight into the qualitative measure of the heat transfer processes. Consequently, in the present study, forced convection and radiation heat transfer in flow through a tube is considered. The wall and fluid sides temperature rise are predicted for different tube lengths. The entropy analysis is carried out and the influence of tube length and heat transfer coefficient on the volumetric entropy generation are examined. It is found that the wall temperature and the volumetric entropy generation increases as the tube length increases. The point of maximum volumetric entropy generation moves close to the tube inlet as the tube length increases. In addition, the maximum volumetric entropy generation becomes independent of tube length for high heat transfer coefficients. Copyright © 1999 John Wiley & Sons, Ltd.     

Irreversibility analysis of micropolar nanofluid flow using Darcy–Forchheimer rule in an inclined microchannel with multiple slip effects

The present work explores the consequence of the flow of micropolar fluid in an inclined microchannel when exposed to linear radiation in presence of a magnetic field. The microchannel is embedded with a porous medium and the Darcy–Forchheimer model is implemented. The walls of the microchannel facilitate the simultaneous suction and injection of the micropolar fluid. A multiple slip regime and temperature jump conditions were assumed at the boundaries. The equations are modeled and nondimensionalized using nondimensional entities and further solved with the aid of the Runge–Kutta–Fehlberg method. Entropy generated in the medium and ratio of irreversibilities is also computed. Results so obtained deliberate that enhancement in Darcy number has caused an increment in entropy generation rate whereas the opposite nature is attained for the Bejan number. Magnifying the radiation parameter has resulted in diminishing the profile of entropy generation rate and Bejan number.     

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.     

Entropy generation due to flow and heat transfer in nanofluids

Present study provides a theoretical investigation of the entropy generation analysis due to flow and heat transfer in nanofluids. For this purpose, the most common alumina–water nanofluids are considered as the model fluid. Since entropy is sensitive to diameter, three different diameters of tube in their different regimes have been taken. Those are microchannel (0.1 mm), minichannel (1 mm) and conventional channel (10 mm). To consider the effect of conductivity and viscosity, two different models have been used to represent theoretical and experimental values. It has been found that the reduced equation with the help of order of magnitude analysis predicts microchannel and conventional channel entropy generation behaviour of nanofluids very well. The alumina–water with high viscosity nanofluids are better coolant for use in minichannels and conventional channels with laminar flow and microchannels and minichannel with turbulent flow. It is not advisable to use alumina–water nanofluids with high viscosity in microchannels with laminar flow or minichannels and conventional channels with turbulent flow. Also there is need to develop low viscosity alumina–water nanofluids for use in microchannel with laminar flow. It is observed that at lower tube diameter, flow friction irreversibility is more significant and at higher tube diameter thermal irreversibility is more. Finally, for both laminar and turbulent flow, there is an optimum diameter at which the entropy generation rate is the minimum for a given nanofluid.     

Flow and thermal analysis of Oldroyd 8 constant fluid in a porous channel

The present research is based on the thermal and flow properties of the viscoelastic Oldroyd 8 constant fluid in an upright microchannel. The energy and momentum equations were solved with the support of temperature Jump and velocity slip boundary conditions. To measure the irreversibility rate of the flow system, the acquired results of velocity and thermal equations were used. To crack the current mathematical model problem, the numerical Runge–Kutta–Fehlberg method was used. With the aid of graphs, the effect of physical parameters such as thermal radiation, thermal-dependent heat source, Joule heating, fluid parameters, velocity slip, and temperature Jump parameters on the fluid flow, thermal energy, and system entropy generation was discussed. Fluid parameters have different effects on the velocity profile. The Grashof and Hartmann numbers demonstrate opposite effects on the momentum field. The thermal energy of the system reduces with thermal radiation and temperature Jump factor. The thermal radiation, Hartmann number, and temperature Jump parameters reduce the system's irreversibility rate. With the Brinkman number and temperature Jump parameter, the irreversibility ratio increases.     

Analysis of entropy generation using nanofluid flow through the circular microchannel and minichannel heat sink

In this paper, different types of entropy generations in the circular shaped microchannel and minichannel are discussed analytically using different types of nanoparticles and base fluids. In this analysis, Copper (Cu), alumina (Al₂O₃) as the nanoparticle and H₂O, ethylene glycol (EG) as the base fluids were used. The volume fractions of the nanoparticles were varied from 2% to 6%. In this paper, the irreversibility or entropy generation analysis as the function of entropy generation ratio, thermal entropy generation rate and fluid friction entropy generation rate for these types of nanofluids in turbulent flow condition have been analyzed using available correlations. Cu–H₂O nanofluid showed the highest decreasing entropy generation rate ratio (36%) compared to these nanofluids flow through the microchannel at 6 vol.%. The higher thermal conductivity of H₂O causes to generate much lower thermal entropy generation rate compared to the EG base fluid. The fluid friction entropy generation rate decreases fruitfully by the increasing of volume fraction of the nanoparticles. Cu–H₂O and Cu–EG nanofluid gave the maximum decreasing rates of the fluid friction entropy generation rate are 38% and 35% respectively at 6% volume fraction of the nanoparticles. Smaller diameter showed less entropy generation in case of all nanofluids.     

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     

Surface Micro-Profiling for Reduced Energy Dissipation and Exergy Loss in Convective Heat Transfer

This article examines the role of slip conditions within surface-embedded microchannels for reducing entropy production of external flows with convective heat transfer. Viscous dissipation of mechanical energy into internal energy within the boundary layer leads to pressure losses and other irreversible losses of energy availability. These exergy losses entail additional input power needed to deliver a fixed mass flow across the surface, subject to a specified rate of heat transfer to/from the wall. By selectively altering geometrical and surface parameters which minimize the net entropy production, the benefits of drag reduction due to the slip-flow conditions can outweigh the higher irreversibility arising from added microchannel area. Predicted results illustrate the changes of optimal Reynolds number and entropy generation number with varying surface parameters for embedded parallel and diverging microchannels. Based on these results, it is viewed that surface micro-profiling offers a useful new technique of taking advantage of slip-flow microfluidic conditions for reducing drag and simultaneously increasing heat transfer effectiveness in external flows.     

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.     

Natural Convection Heat Transfer and Entropy Generation in a Porous Trapezoidal Enclosure Saturated with Power-Law Non-Newtonian Fluids

Abstract

In the present study, natural convection heat transfer and its associated entropy generation in a porous trapezoidal enclosure saturated with a power-law non-Newtonian fluid has been numerically investigated. Horizontal walls of the enclosure are assumed to be adiabatic while the side walls are considered to be kept at a constant temperature. A continuum-based approach is adapted here to model the fluid flow through porous media and the Darcy’s law is modified to account for non-Newtonian rheological behavior of the fluid. The obtained governing equations are discretized using the finite volume method and a detailed parametric study is undertaken to account for the effects of various relevant parameters of the problem on the heat transfer and entropy generation rates. It was shown that the impact of the power-law index on both entropy generation and heat transfer significantly intensifies in a convection-dominated flow regime inside the enclosure, especially for a shear thinning liquid. Moreover, heat transfer rate and entropy generation increase as the sidewall angle is elevated.     

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.     

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.