Total Entropy Generation Rate Research Articles

Entropy Generation Rate for Stationary Ballistic-Diffusive Heat Conduction in a Rectangular Flake

Thermodynamic irreversibility in low dimensional flake is considered and entropy generation rate in two-dimensional thin film is examined, Equation of phonon radiative transfer is solved for two-dimensional and rectangular diamond flake. Volumetric and total entropy generation rate are evaluated incorporating the formulation of thermal radiation heat transfer. The influence of flake aspect ratio (width to height) on the entropy generation rate is explored while keeping the Diamond flake area constant for all aspect ratios considered. The findings reveal that the entropy generation rate increases with increasing aspect ratio for fixed boundary conditions.

Numerical investigation of the effect of corrugation profile on the hydrothermal characteristics and entropy generation behavior of laminar forced convection of non-Newtonian water/CMC-CuO nanofluid flow inside a wavy channel

The force convection flow of non-Newtonian water/Carboxy-Methyl Cellulose (CMC)-CuO Nanofluid (NF) in three wavy channels and a straight channel was numerically investigated. The two dimensional governing equations were solved in the computational domain using the FLUENT software. The influence of Re and nanoparticle concentration (φ) on the pressure drop (ΔP), Nu, and global thermal and frictional entropy generation rates (Ṡg,th and Ṡg,f) were studied for different Re and φ values. The results showed that the influence of Re on the Nu is much higher than that of φ. The increasing of the Re and decreasing of φ, results in increasing the Nu for four channels of the study. Besides, the sinusoidal channel has the highest Nu as compared to the other channels. Also, the highest pressure drop and total global entropy generation rate were obtained for the trapezoidal channel.

Multi-objective performance optimization of ammonia decomposition thermal storage reactor

Heat storage technology plays an essential role in the stable operation of solar thermal power generation. In this paper, a one-dimensional model of a tubular filled bed heat absorption reactor for ammonia decomposition is established by applying finite time thermodynamics. Taking the inlet temperature, the outside diameter and the length of the reactor as optimization variables, the multi-objective particle swarm optimization is used to perform multi-objective optimization considering the maximum heat absorption rate and the minimum total entropy generation rate, and the Pareto Fronts are determined under different reactor outer wall temperatures. Finally, three optimized reactors’ design parameters and performance indicators are obtained by LINMAP, TOPSIS and Shannon Entropy decision methods, and the cross-sectional comparisonof the optimal reactors at different outer wall temperatures. Compared to the reference reactor, the three optimized reactors improve heat absorption rate by 58%-143%, while the total entropy generate rate is reduced by 26.4%-38.8%. The obtained results have some guidance for optimal designs of ammonia decomposition reactor in real engineering.

Nonlinear dissipative slip flow of Jeffrey nanomaterial towards a curved surface with entropy generation and activation energy

In this research work, mathematical modeling for steady magnetized two-dimensional (2D) incompressible flow of Jeffrey nanofluid is developed over a stretched curved surface with combined characteristics of activation energy, Brownian motion, viscous dissipation, nonlinear mixed convection, magnetohydrodynamics (MHD), Joule heating and thermophoresis diffusion. Velocity slip condition is further imposed on the curved stretched boundary. Total entropy generation rate which depends on the velocity, temperature and concentration fields is obtained via second law of thermodynamics. The dimensional differential equations are altered into dimensionless ordinary differential system by using appropriate similarity variables. The obtain system of dimensionless differential equations are solved numerically through Built-in-Shooting method. The influence of sundry flow variables associated with this problem like curvature parameter, velocity slip parameter, Deborah number, thermophoresis diffusion, Prandtl number, Brownian motion, chemical reaction, Brinkman number and activation energy are sketched for entropy generation rate, concentration, temperature and velocity field. Furthermore, Nusselt number and skin friction coefficient are calculated numerically in the presence of Deborah number, slip parameter, thermophoresis parameter, Eckert number and Brownian diffusion parameter. It is noted that velocity field is an increasing function of curvature parameter, while contrast impact is observed for Deborah number and velocity slip parameter. It is also seen that the magnitude of skin friction upsurges versus Deborah number while decays against relaxation time. Nusselt number is increased via larger Eckert number and declines against thermophoretic parameter.

Fully developed entropy-optimized MHD nanofluid flow by a variably thickened rotating surface

Entropy generation analysis for three-dimensional (3D) magnetohydrodynamic (MHD) flow of viscous fluid through a rotating disk is addressed in this article. Entropy generation is explored as a function of temperature and velocity. The modeling of the considered problem is performed through Buongiorno model. Conservation of energy comprises dissipation, convective heat transport and Joule heating. Flow under consideration is because of nonlinear stretching velocity of disk. Transformations used lead to the reduction of partial differential equations into ordinary differential equations. Total entropy generation rate is scrutinized. Non-linear computations have been carried out. Domain of convergence for the obtained solutions is identified. Radial, axial and tangential velocities are interpreted. Entropy equation is studied in the presence of dissipation, Brownian diffusion and thermophoresis effects. Velocity and temperature gradients are discussed graphically. Meaningful results are summed up in the concluding section.

Analytical Analysis of Heat Transfer and Entropy Generation in a Tube Filled with Double-Layer Porous Media.

The heat transfer and entropy generation in a tube filled with double-layer porous media are analytically investigated. The wall of the tube is subjected to a constant heat flux. The Darcy-Brinkman model is utilized to describe the fluid flow, and the local thermal non-equilibrium model is employed to establish the energy equations. The solutions of the temperature and velocity distributions are analytically derived and validated in limiting case. The analytical solutions of the local and total entropy generation, as well as the Nusselt number, are further derived to analyze the performance of heat transfer and irreversibility of the tube. The influences of the Darcy number, the Biot number, the dimensionless interfacial radius, and the thermal conductivity ratio, on flow and heat transfer are discussed. The results indicate, for the first time, that the Nusselt number for the tube filled with double-layer porous media can be larger than that for the tube filled with single layer porous medium, while the total entropy generation rate for the tube filled with double-layer porous media can be less than that for the tube filled with single layer porous medium. And the dimensionless interfacial radius corresponding to the maximum value of the Nusselt number is different from that corresponding to the minimum value of the total entropy generation rate.

Thermal-hydraulic and thermodynamic performance of parabolic trough solar receiver partially filled with gradient metal foam

With the aim to improve overall thermal-hydraulic and thermodynamic performance of parabolic trough solar receiver (PTR), a new configuration with partial insertion of gradient metal foam (GMF) is proposed. The effects of GMF with pore density gradient or porosity gradient on turbulent forced convection heat transfer, flow resistance, entropy generation rate and exergetic efficiency of PTR tube are numerically analyzed. The distribution of non-uniform heat flux on receiver tube wall is calculated by Monte Carlo Ray-Trace Method, and the local thermal non-equilibrium model is used, which considers the temperature difference between metal skeleton and fluid. The numerical method is validated by experimental data. The results show that GMF enhances the heat transfer of PTR tube, with Nusselt number being increased by 43.7%–812.6%; brings the increase of flow resistance, with friction factor being 4.2 to 16.7 times of empty tube; improves the overall thermal-hydraulic performance with performance evaluation criteria ranging from 1.5–3.6. The GMF causes maximum reduction of total entropy generation rate and maximum enhancement of exergetic efficiency to be 92.6% and 24.4%, respectively. The PTR tube partially filled with GMF can obtain higher thermal-hydraulic and thermodynamic performance than that with uniform metal foam.

Entropy Generation and Exergy Analysis of Premixed Fuel-Air Combustion in Micro Porous Media Burner.

The performance of porous media micro-burners plays an important role in determining thermal efficiency and improving our daily life. Nowadays, a lot of scholars are actively involved in this research area and ongoing studies are still being carried out due to the burners’ excellent performance. The exergy efficiency and entropy generation of a porous media burner are strongly dependent on the characteristics of the flame and its thermal behavior. In this study, a single-layer and double-layer porous media form were constructed to investigate the effects of various types of porous foam arrangement in a cylindrical burner. The burner was operated using premixed butane-air combustion with an inner diameter of 23 mm and a length of 100 mm. The experiments were carried out in rich fuel conditions with an equivalence ratio, φ ranging from 1.3 to 2.0. The results showed significant improvement in the thermal and exergy efficiency with an increase in the equivalence ratio in a double-layer compared with a single-layer. The peak temperature recorded was 945.21 °C at φ = 1.3 for a porcelain single-layer, and the highest exergy efficiency was 83.47% at φ = 2.0 for an alumina-porcelain double-layer burner. It was also found that the average temperature of the burner wall decreased with an increase in the equivalence ratios for PMB2 and PMB4, whereas the average wall temperature for PMB3 was largely unaffected by the equivalence ratios. The total entropy generation rate reached the highest value at φ = 2.0 for all PMB configurations, and the highest percentage increase for total entropy generation rate was 46.09% for PMB1. The exergy efficiency for all burners was approximately similar with the highest exergy efficiency achieved by PMB4 (17.65%). In addition, the length and location of the flame with thermal distribution was significantly affected by the equivalence ratio between the single-layer and double-layer porous material. Overall, a double-layer porous media burner showed the best performance calculated based on the second law of thermodynamics when compared with other configurations, and it is ideal for domestic application.

Minimum Entropy Generation Rate and Maximum Yield Optimization of Sulfuric Acid Decomposition Process Using NSGA-II.

Based on the theory of finite-time thermodynamics (FTT), the effects of three design parameters, that is, inlet temperature, inlet pressure, and inlet total mole flow rate, of a tubular plug-flow sulfuric acid decomposition reactor on the total entropy generation rate (EGR) and SO2 yield are analyzed firstly. One can find that when the three design parameters are taken as optimization variables, the minimum total EGR and the maximum SO2 yield of the reference reactor restrict each other, i.e., the two different performance objectives cannot achieve the corresponding extremum values at the same time. Then, the second-generation non-dominated solution sequencing genetic algorithm (NSGA-II) is further used to pursue the minimum total EGR and the maximum SO2 yield of the reference reactor by taking the three parameters as optimization design variables. After the multi-objective optimization, the reference reactor can be Pareto improved, and the total EGR can be reduced by 9% and the SO2 yield can be increased by 14% compared to those of the reference reactor. The obtained results could provide certain theoretical guidance for the optimal design of actual sulfuric acid decomposition reactors.

Feature of Entropy Generation in Cu-Al2O3/Ethylene Glycol Hybrid Nanofluid Flow Through a Rotating Channel

This paper aims to delineate the heat transfer enhancement and entropy generation of a magnetohydrodynamic (MHD) flow of a viscous incompressible electrically conducting non-Newtonian Casson hybrid nanofluid between two infinite parallel non-conducting plates channel in a rotating frame. Copper and aluminium oxide nanoparticles are dispersed in ethylene glycol (EG) as a base fluid. Casson model is deployed here to describe the constitutive behaviour of non-Newtonian fluids. The thermal radiation, viscous dissipation and Joule heating (Ohmic dissipation) effects are included in this model. Closed-form solutions are obtained for constitutive equations. Graphs and tables are presented and illustrated to disclose the impact of significant flow parameters on the flow system. The shear stresses and the rate of heat transfer are discussed numerically, and their numerical values for pertinent physical parameters are tabulated. The total entropy generation rate and Bejan number are also discussed and their interpretations with the physical parameters are conferred via graphs. The results obtained from the parametric analysis manifest that the temperature field is boosted up due to the high intensity of magnetic field as well as Coriolis force. The intensification of magnetic parameter contributes to an increase in the rate of heat transfer at the channel walls. The entropy generation can be minimized by improving Casson parameter. Moreover, a comparison between the flows of Casson hybrid nanofluid (Cu-Al2O3/EG) and Casson nanofluid (Cu-EG) is reported. Minimization in entropy generation is achieved for Casson hybrid nanofluid in comparison with Casson nanofluid.

Variational entropy generation minimization of a channel flow: Convective heat transfer in a gas flow

Variational methods are used to optimize convective heat transfer in a channel gas flow. The minimization of a functional objective combining the rate of total entropy generation in the channel on the one hand and the total viscous dissipation on the other hand results in velocity and temperature fields. A weighting factor allows varying the relative importance of these two terms and a virtual body force field is applied to vary the velocity field pattern via the momentum equation source term. The result is velocity configurations that minimize the objective functional. This study shows that the velocity fields determined by the optimization process effectively lead to a reduction in the entropy generation rate in the flow as well as a reduction in the temperatures of the heated plate. In addition, the value of the weighting factor triggers the transition from slightly to highly perturbed velocity and temperature fields when compared to a non-optimized flow. The heat transfer enhancement is assessed and the increase of the Nusselt number is put in perspective with the reduction of the entropy generation rate and the increase of viscous friction. The results could be used to design passive technologies for enhancing wall-to-fluid heat transfer.

Analysis of Radial Force and Vibration Energy in a Centrifugal Pump

Vibration is one of the main issues taken into consideration in the design and manufacture of the pump. The radial force and vibration of the impeller induced by fluid in a centrifugal pump were investigated at different flow rates by numerical simulation. The vibrations on the volute were measured by the experiment. The variation trend of the radial displacements of the impeller is consistent with that of the radial forces, and the variation in the radial displacement lags that of the radial force. The vibration energies on the impeller and the volute were analyzed based on root-mean-square (RMS) values in the frequency domain. The distributions of energy loss in the pumps were calculated to determine the total entropy generation (TEG) and entropy generation rate (EGR). The TEG values as calculated are in close accordance with hydraulic loss. The vibration is a result of the poor flow patterns and consequently results in increased energy losses in the pump.

Evaluation of radiative entropy generation in a high temperature system including H2O, CO2 and soot with non-gray wall

In this paper, radiative entropy generation in a high temperature parallel plate system containing H2O, CO2 and soot with non-gray wall was investigated. Based on Discrete Ordinates method and Narrow Band k-distribution model, the spectral radiative entropy generation rate and radiative entropy generation rate due to different physical processes were given. The effects of CO2, H2O, soot, spectral emissivity of wall, as well as medium temperature on radiative entropy generation were evaluated. Some conclusions were obtained as below. The irreversibility of emission and reflection process on wall has main contribution on radiative entropy generation rate of system. The radiative entropy generation rate increases with the mole fraction of gas and volume fraction of soot. CO2 has less effect on total radiative entropy generation rate, but H2O and soot particle have more effect on total radiative entropy generation rate. The radiative entropy generation rate increases with the increase of total hemispherical absorptance of wall. The radiative entropy generation rate and dimensionless radiative entropy generation increase with the increase of non-uniformity of medium temperature distribution and difference of gas temperature and soot temperature.

Time Evolution Features of Entropy Generation Rate in Turbulent Rayleigh-Bénard Convection with Mixed Insulating and Conducting Boundary Conditions.

Time evolution features of kinetic and thermal entropy generation rates in turbulent Rayleigh-Bénard (RB) convection with mixed insulating and conducting boundary conditions at Ra = 109 are numerically investigated using the lattice Boltzmann method. The state of flow gradually develops from laminar flow to full turbulent thermal convection motion, and further evolves from full turbulent thermal convection to dissipation flow in the process of turbulent energy transfer. It was seen that the viscous, thermal, and total entropy generation rates gradually increase in wide range of t/τ < 32 with temporal evolution. However, the viscous, thermal, and total entropy generation rates evidently decrease at time t/τ = 64 compared to that of early time. The probability density function distributions, spatial-temporal features of the viscous, thermal, and total entropy generation rates in the closed system provide significant physical insight into the process of the energy injection, the kinetic energy, the kinetic energy transfer, the thermal energy transfer, the viscous dissipated flow and thermal dissipation.

Flow and thermal analysis on Darcy-Forchheimer flow of copper-water nanofluid due to a rotating disk: A static and dynamic approach

BackgroundCharacterised with augmented heat transport and thermal efficiency, nanofluids are implementable in diversified applications include pharmaceutical industries, hybrid-powered machines, cooling of different appliances, refrigerator, microelectronic, heat exchanger etc. Taking such advantages into mind, physical aspects of entropy optimization and non-linear thermal radiation in Darchy–Forchheimer flow of copper–water nanofluid due to a rotating disk are examined. A new thermal conductivity model of nanofluids involving static and dynamic approach is considered. This model signifies hydrodynamic interaction among the Brownian motion induced fluid particles. The Cattaneo–Christov heat flux theory is taken into account. The second law of thermodynamics is the instrumental for the determination of total entropy generation rate. MethodsThe system of nonlinear PDEs is converted into system of nonlinear ODEs through favorable transformations. Shooting technique has been applied prospectively to accomplish the desired numerical solution of the transformed equations. ResultsThe behavior of velocity (axial, transverse and tangential) and thermal fields influenced by varied physical parameters is impressed through graphs and numerical tables. Velocity field peters out due to rising porosity parameter as well as volume fraction while thermal field upgrades for higher Biot number and radiation parameter. Significant heat transfer rate is obtained for smaller estimation of radiation parameter. Entropy generation rate and Bejan number exhibit similar trend for radiation parameter and opposite fashion for Reynolds number. ConclusionsThe diminishing velocity distribution for larger access of porous matrix while elevated temperature distribution for higher temperature parameter (due to nonlinear thermal radiation). Entropy minimization is accomplished for grater estimation of Brinkman and Reynolds numbers.

Neural network modeling of thermo-hydraulic attributes and entropy generation of an ecofriendly nanofluid flow inside tubes equipped with novel rotary coaxial double-twisted tape

The current paper numerically predicts the convective heat transfer coefficient, pumping power, and total entropy generation of an ecofriendly-functionalized graphene nanoplatelets nanofluid inside the tubes enhanced with a novel rotary coaxial double-twisted tape, which rotates at various rotational speeds. The impacts of the nanoparticle concentration and twisted ratio are considered. The mathematical models of the heat transfer coefficient, pumping power, and total entropy generation rate are obtained as a function of the weight fraction, angular velocity, and twisted ratio based on the numerical outcomes using Artificial Neural Network (ANN). Several configurations of the neural network are examined, and finally, the best model is found having one hidden layer with 7 neurons in this layer, which can provide excellent precision for measuring the outputs. Moreover, the relevant correlations are presented for all three outputs based on the weights and biases of the ANN.

Electromagnetohydrodynamic Electroosmotic Flow and Entropy Generation of Third-Grade Fluids in a Parallel Microchannel.

The present paper discusses the electromagnetohydrodynamic (EMHD) electroosmotic flow (EOF) and entropy generation of incompressible third-grade fluids in a parallel microchannel. Numerical solutions of the non-homogeneous partial differential equations of velocity and temperature are obtained by the Chebyshev spectral collocation method. The effects of non-Newtonian parameter Λ, Hartman number Ha and Brinkman number Br on the velocity, temperature, Nusselt number and entropy generation are analyzed in detail and shown graphically. The main results show that both temperature and Nusselt number decrease with the non-Newtonian physical parameter, while the local and total entropy generation rates exhibit an adverse trend, which means that non-Newtonian parameter can provoke the local entropy generation rate. In addition, we also find that the increase of non-Newtonian parameter can lead to the increase of the critical Hartman number Hac.

Application of CNT-based micropolar hybrid nanofluid flow in the presence of Newtonian heating

This research addresses the effects of Hall and ion slip in micropolar hybrid nanofluid in the presence of Newtonian heating. Furthermore, the influence of thermal radiation, Darcy–Forchheimer, viscous dissipation, and variable viscosity is discussed. Total entropy generation rate is calculated. Two distinct nanoparticles such as (SWCNT, MWCNT) used as a hybrid nanofluid. Built-in function bvp4c integrates the solution of simulated hydrodynamic boundary value problems. The effects on axial velocity, angular velocity, temperature field, concentration field, Bejan number, and entropy optimization of different flow field variables are displayed graphically. The nanoparticle fraction boosts the temperature field, Bejan number, and entropy generation, while the axial velocity and microrotation field reduces. Furthermore, the entropy generation enhances with higher the Brinkman number and variable viscosity parameter.

Investigation on the thermohydraulic performance of high temperature superconducting (HTS) cables with heat loads using Entropy Generation Minimization (EGM) approach

High temperature superconducting (HTS) cables have revolutionized the way of power transmission in terms of carrying larger currents with lower volume of the conductor. However, such cables experience AC losses which are dissipated as heat. Hence, it is inevitable that these cables be cooled below the critical temperature of the superconductor constituting the HTS cable. In general, LN2 is circulated through the former (corrugated pipe) to retain the superconductivity of HTS tapes. The work consumed for pumping LN2 through long length HTS cables is significantly larger. Hence, it is necessary that the optimization of the pumping power with enhanced heat transfer is achieved. During the process of forced cooling of HTS cables, velocity and thermal gradients which are responsible for entropy generation is unavoidable. Hence, in the present work, an investigation on thermohydraulic performance in HTS cables with various heat loads is performed. Further, the volumetric rate of entropy generation is calculated and an optimum mass flow rate is identified at which minimum entropy generation rate is observed. The thermohydraulic performance and total entropy generation rate for internally cooled HTS cables are computationally investigated using the time averaged Reynolds Averaged Navier-Stokes (RANS) equations implemented in commercial software ANSYS®. This implementation involves Finite Volume Method (FVM) of discretization with κ−ε turbulence equations as closure to the RANS governing equations. Temperature dependent thermophysical properties are considered for predicting the thermohydraulic behavior of LN2 in HTS cable. The analysis is carried out at heat loads ranging from 1-3 W/m with flow rates of 11-20 L/min at an operating temperature of 77 K and pressure of 2.7 bar. The dimensionless numbers such as Bejan number, entropy generation number and performance evaluation are studied to evaluate the optimum flow rate corresponding to lower pumping power and higher cooling capacity at various heat loads. Further, the results obtained from computational simulations are validated with the experimental results available in the literature. Furthermore, the results of volumetric entropy generation rate (EGR) are calculated to optimize the thermohydraulic performance in HTS cables using entropy generation minimization (EGM) approach.

Entropy generation rate minimization for steam methane reforming reactor heated by molten salt

Traditional steam methane reforming facilities for producing hydrogen not only consume a large amount of natural gas, but also emit a lot of greenhouse gas. Considering the utilization of clean energy, the reduction of carbon dioxide emission, and the production of chemicals, this paper establishes a model of steam methane reforming reactor heated by molten salt by utilizing finite-time thermodynamics. In order to reduce the irreversibility of this reactor, the entropy generation rate minimization and some operating parameters are taken as the optimization objective and variables, respectively. The hybrid particle swarm optimization algorithm is proposed for solving this model. Afterwards, the influences of the porosity of the catalyst bed and catalyst activity on the optimal performance are analyzed. The results indicate that the total entropy generation rate of the reactor is reduced by 22.08% after optimizing the inlet parameters of the molten salt and reaction mixture. Within the scope of this study, the total entropy generation rate of the optimal reactor decreases with the increasing porosity of catalyst bed. When the catalyst activity decreases, the hydrogen production rate can remain constant by adjusting the operating parameters. The obtained results are favorable to guide the optimal design of the practical reactors.