Entropy

Editorial

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12 pages, 2427 KiB

Open AccessEditorial

How to Teach Heat Transfer More Systematically by Involving Entropy

by Heinz Herwig

Entropy 2018, 20(10), 791; https://doi.org/10.3390/e20100791 - 15 Oct 2018

Cited by 6 | Viewed by 3719

Abstract

In order to teach heat transfer systematically and with a clear physical background, it is recommended that entropy should not be ignored as a fundamental quantity. Heat transfer processes are characterized by introducing the so-called “entropic potential” of the transferred energy, and an [...] Read more.

In order to teach heat transfer systematically and with a clear physical background, it is recommended that entropy should not be ignored as a fundamental quantity. Heat transfer processes are characterized by introducing the so-called “entropic potential” of the transferred energy, and an assessment number is based on this new quantity. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

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Research

Jump to: Editorial

21 pages, 8927 KiB

Open AccessArticle

Entropy Generation in MHD Conjugate Flow with Wall Shear Stress over an Infinite Plate: Exact Analysis

by Arshad Khan, Faizan ul Karim, Ilyas Khan, Tawfeeq Abdullah Alkanhal, Farhad Ali, Dolat Khan and Kottakkaran Sooppy Nisar

Entropy 2019, 21(4), 359; https://doi.org/10.3390/e21040359 - 3 Apr 2019

Cited by 18 | Viewed by 3143

Abstract

The current work will describe the entropy generation in an unsteady magnetohydrodynamic (MHD) flow with a combined influence of mass and heat transfer through a porous medium. It will consider the flow in the XY plane and the plate with isothermal and ramped [...] Read more.

The current work will describe the entropy generation in an unsteady magnetohydrodynamic (MHD) flow with a combined influence of mass and heat transfer through a porous medium. It will consider the flow in the XY plane and the plate with isothermal and ramped wall temperature. The wall shear stress is also considered. The influences of different pertinent parameters on velocity, the Bejan number and on the total entropy generation number are reported graphically. Entropy generation in the fluid is controlled and reduced on the boundary by using wall shear stress. It is observed in this paper that by taking suitable values of pertinent parameters, the energy losses in the system can be minimized. These parameters are the Schmitt number, mass diffusion parameter, Prandtl number, Grashof number, magnetic parameter and modified Grashof number. These results will play an important role in the heat flow of uncertainty and must, therefore, be controlled and managed effectively. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

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10 pages, 260 KiB

Open AccessArticle

On Entropic Framework Based on Standard and Fractional Phonon Boltzmann Transport Equations

by Shu-Nan Li and Bing-Yang Cao

Entropy 2019, 21(2), 204; https://doi.org/10.3390/e21020204 - 21 Feb 2019

Cited by 9 | Viewed by 2760

Abstract

Generalized expressions of the entropy and related concepts in non-Fourier heat conduction have attracted increasing attention in recent years. Based on standard and fractional phonon Boltzmann transport equations (BTEs), we study entropic functionals including entropy density, entropy flux and entropy production rate. Using [...] Read more.

Generalized expressions of the entropy and related concepts in non-Fourier heat conduction have attracted increasing attention in recent years. Based on standard and fractional phonon Boltzmann transport equations (BTEs), we study entropic functionals including entropy density, entropy flux and entropy production rate. Using the relaxation time approximation and power series expansion, macroscopic approximations are derived for these entropic concepts. For the standard BTE, our results can recover the entropic frameworks of classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT) as if there exists a well-defined effective thermal conductivity. For the fractional BTEs corresponding to the generalized Cattaneo equation (GCE) class, the entropy flux and entropy production rate will deviate from the forms in CIT and EIT. In these cases, the entropy flux and entropy production rate will contain fractional-order operators, which reflect memory effects. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

21 pages, 12169 KiB

Open AccessEditor’s ChoiceArticle

Entropy Generation Analysis and Thermodynamic Optimization of Jet Impingement Cooling Using Large Eddy Simulation

by Florian Ries, Yongxiang Li, Kaushal Nishad, Johannes Janicka and Amsini Sadiki

Entropy 2019, 21(2), 129; https://doi.org/10.3390/e21020129 - 30 Jan 2019

Cited by 31 | Viewed by 6036

Abstract

In this work, entropy generation analysis is applied to characterize and optimize a turbulent impinging jet on a heated solid surface. In particular, the influence of plate inclinations and Reynolds numbers on the turbulent heat and fluid flow properties and its impact on [...] Read more.

In this work, entropy generation analysis is applied to characterize and optimize a turbulent impinging jet on a heated solid surface. In particular, the influence of plate inclinations and Reynolds numbers on the turbulent heat and fluid flow properties and its impact on the thermodynamic performance of such flow arrangements are numerically investigated. For this purpose, novel model equations are derived in the frame of Large Eddy Simulation (LES) that allows calculation of local entropy generation rates in a post-processing phase including the effect of unresolved subgrid-scale irreversibilities. From this LES-based study, distinctive features of heat and flow dynamics of the impinging fluid are detected and optimal operating designs for jet impingement cooling are identified. It turned out that (1) the location of the stagnation point and that of the maximal Nusselt number differ in the case of plate inclination; (2) predominantly the impinged wall acts as a strong source of irreversibility; and (3) a flow arrangement with a jet impinging normally on the heated surface allows the most efficient use of energy which is associated with lowest exergy lost. Furthermore, it is found that increasing the Reynolds number intensifies the heat transfer and upgrades the second law efficiency of such thermal systems. Thereby, the thermal efficiency enhancement can overwhelm the frictional exergy loss. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

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16 pages, 2535 KiB

Open AccessArticle

How to Construct a Combined S-CO₂ Cycle for Coal Fired Power Plant?

by Enhui Sun, Han Hu, Hangning Li, Chao Liu and Jinliang Xu

Entropy 2019, 21(1), 19; https://doi.org/10.3390/e21010019 - 27 Dec 2018

Cited by 17 | Viewed by 4703

Abstract

It is difficult to recover the residual heat from flue gas when supercritical carbon dioxide (S-CO₂) cycle is used for a coal fired power plant, due to the higher CO₂ temperature in tail flue and the limited air temperature in [...] Read more.

It is difficult to recover the residual heat from flue gas when supercritical carbon dioxide (S-CO₂) cycle is used for a coal fired power plant, due to the higher CO₂ temperature in tail flue and the limited air temperature in air preheater. The combined cycle is helpful for residual heat recovery. Thus, it is important to build an efficient bottom cycle. In this paper, we proposed a novel exergy destruction control strategy during residual heat recovery to equal and minimize the exergy destruction for different bottom cycles. Five bottom cycles are analyzed to identify their differences in thermal efficiencies (η_th,b), and the CO₂ temperature entering the bottom cycle heater (T_4b) etc. We show that the exergy destruction can be minimized by a suitable pinch temperature between flue gas and CO₂ in the heater via adjusting T_4b. Among the five bottom cycles, either the recompression cycle (RC) or the partial cooling cycle (PACC) exhibits good performance. The power generation efficiency is 47.04% when the vapor parameters of CO₂ are 620/30 MPa, with the double-reheating-recompression cycle as the top cycle, and RC as the bottom cycle. Such efficiency is higher than that of the supercritical water cycle power plant. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

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16 pages, 465 KiB

Open AccessArticle

A Simple Thermodynamic Model of the Internal Convective Zone of the Earth

by Karen Arango-Reyes, Marco Antonio Barranco-Jiménez, Gonzalo Ares de Parga-Álvarez and Fernando Angulo-Brown

Entropy 2018, 20(12), 985; https://doi.org/10.3390/e20120985 - 18 Dec 2018

Cited by 1 | Viewed by 3739

Abstract

As it is well known both atmospheric and mantle convection are very complex phenomena. The dynamical description of these processes is a very difficult task involving complicated 2-D or 3-D mathematical models. However, a first approximation to these phenomena can be by means [...] Read more.

As it is well known both atmospheric and mantle convection are very complex phenomena. The dynamical description of these processes is a very difficult task involving complicated 2-D or 3-D mathematical models. However, a first approximation to these phenomena can be by means of simplified thermodynamic models where the restriction imposed by the laws of thermodynamics play an important role. An example of this approach is the model proposed by Gordon and Zarmi in 1989 to emulate the convective cells of the atmospheric air by using finite-time thermodynamics (FTT). In the present article we use the FTT Gordon-Zarmi model to coarsely describe the convection in the Earth’s mantle. Our results permit the existence of two layers of convective cells along the mantle. Besides the model reasonably reproduce the temperatures of the main discontinuities in the mantle, such as the 410 km-discontinuity, the Repetti transition zone and the so-called D-Layer. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

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15 pages, 3867 KiB

Open AccessArticle

Irreversibility Analysis of Dissipative Fluid Flow Over A Curved Surface Stimulated by Variable Thermal Conductivity and Uniform Magnetic Field: Utilization of Generalized Differential Quadrature Method

by Muhammad Idrees Afridi, Abderrahim Wakif, Muhammad Qasim and Abid Hussanan

Entropy 2018, 20(12), 943; https://doi.org/10.3390/e20120943 - 7 Dec 2018

Cited by 33 | Viewed by 3491

Abstract

The effects of variable thermal conductivity on heat transfer and entropy generation in a flow over a curved surface are investigated in the present study. In addition, the effects of energy dissipation and Ohmic heating are also incorporated in the modelling of the [...] Read more.

The effects of variable thermal conductivity on heat transfer and entropy generation in a flow over a curved surface are investigated in the present study. In addition, the effects of energy dissipation and Ohmic heating are also incorporated in the modelling of the energy equation. Appropriate transformations are used to develop the self-similar equations from the governing equations of momentum and energy. The resulting self-similar equations are then solved by the Generalized Differential Quadrature Method (GDQM). For the validation and precision of the developed numerical solution, the resulting equations are also solved numerically using the Runge-Kutta-Fehlberg method (RKFM). An excellent agreement is found between the numerical results of the two methods. To examine the impacts of emerging physical parameters on velocity, temperature distribution and entropy generation, the numerical results are plotted against the various values of physical flow parameters and discussed physically in detail. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

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21 pages, 6386 KiB

Open AccessArticle

Entropy Analysis of 3D Non-Newtonian MHD Nanofluid Flow with Nonlinear Thermal Radiation Past over Exponential Stretched Surface

by Muhammad Suleman, Muhammad Ramzan, Madiha Zulfiqar, Muhammad Bilal, Ahmad Shafee, Jae Dong Chung, Dianchen Lu and Umer Farooq

Entropy 2018, 20(12), 930; https://doi.org/10.3390/e20120930 - 5 Dec 2018

Cited by 27 | Viewed by 3289

Abstract

The present study characterizes the flow of three-dimensional viscoelastic magnetohydrodynamic (MHD) nanofluids flow with entropy generation analysis past an exponentially permeable stretched surface with simultaneous impacts of chemical reaction and heat generation/absorption. The analysis was conducted with additional effects nonlinear thermal radiation and [...] Read more.

The present study characterizes the flow of three-dimensional viscoelastic magnetohydrodynamic (MHD) nanofluids flow with entropy generation analysis past an exponentially permeable stretched surface with simultaneous impacts of chemical reaction and heat generation/absorption. The analysis was conducted with additional effects nonlinear thermal radiation and convective heat and mass boundary conditions. Apposite transformations were considered to transform the presented mathematical model to a system of differential equations. Analytical solutions of the proposed model were developed via a well-known homotopy analysis scheme. The numerically calculated values of the dimensionless drag coefficient, local Nusselt number, and mass transfer Nusselt number are presented, with physical insights. The graphs depicting the consequences of numerous parameters on involved distributions with requisite deliberations were also a part of this model. It is seen that the Bejan number is an increasing function of the thermal radiation parameter. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

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18 pages, 2182 KiB

Open AccessArticle

Entropy Density Acceleration and Minimum Dissipation Principle: Correlation with Heat and Matter Transfer in Glucose Catabolism

by Roberto Zivieri and Nicola Pacini

Entropy 2018, 20(12), 929; https://doi.org/10.3390/e20120929 - 5 Dec 2018

Cited by 8 | Viewed by 3425

Abstract

The heat and matter transfer during glucose catabolism in living systems and their relation with entropy production are a challenging subject of the classical thermodynamics applied to biology. In this respect, an analogy between mechanics and thermodynamics has been performed via the definition [...] Read more.

The heat and matter transfer during glucose catabolism in living systems and their relation with entropy production are a challenging subject of the classical thermodynamics applied to biology. In this respect, an analogy between mechanics and thermodynamics has been performed via the definition of the entropy density acceleration expressed by the time derivative of the rate of entropy density and related to heat and matter transfer in minimum living systems. Cells are regarded as open thermodynamic systems that exchange heat and matter resulting from irreversible processes with the intercellular environment. Prigogine’s minimum energy dissipation principle is reformulated using the notion of entropy density acceleration applied to glucose catabolism. It is shown that, for out-of-equilibrium states, the calculated entropy density acceleration for a single cell is finite and negative and approaches as a function of time a zero value at global thermodynamic equilibrium for heat and matter transfer independently of the cell type and the metabolic pathway. These results could be important for a deeper understanding of entropy generation and its correlation with heat transfer in cell biology with special regard to glucose catabolism representing the prototype of irreversible reactions and a crucial metabolic pathway in stem cells and cancer stem cells. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

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12 pages, 2042 KiB

Open AccessArticle

Optimization and Stability of Heat Engines: The Role of Entropy Evolution

by Julian Gonzalez-Ayala, Moises Santillán, Maria Jesus Santos, Antonio Calvo Hernández and José Miguel Mateos Roco

Entropy 2018, 20(11), 865; https://doi.org/10.3390/e20110865 - 9 Nov 2018

Cited by 7 | Viewed by 3439

Abstract

Local stability of maximum power and maximum compromise (Omega) operation regimes dynamic evolution for a low-dissipation heat engine is analyzed. The thermodynamic behavior of trajectories to the stationary state, after perturbing the operation regime, display a trade-off between stability, entropy production, efficiency and [...] Read more.

Local stability of maximum power and maximum compromise (Omega) operation regimes dynamic evolution for a low-dissipation heat engine is analyzed. The thermodynamic behavior of trajectories to the stationary state, after perturbing the operation regime, display a trade-off between stability, entropy production, efficiency and power output. This allows considering stability and optimization as connected pieces of a single phenomenon. Trajectories inside the basin of attraction display the smallest entropy drops. Additionally, it was found that time constraints, related with irreversible and endoreversible behaviors, influence the thermodynamic evolution of relaxation trajectories. The behavior of the evolution in terms of the symmetries of the model and the applied thermal gradients was analyzed. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

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16 pages, 4907 KiB

Open AccessArticle

Entropy and Entransy Dissipation Analysis of a Basic Organic Rankine Cycles (ORCs) to Recover Low-Grade Waste Heat Using Mixture Working Fluids

by Yong-qiang Feng, Qian-hao Luo, Qian Wang, Shuang Wang, Zhi-xia He, Wei Zhang, Xin Wang and Qing-song An

Entropy 2018, 20(11), 818; https://doi.org/10.3390/e20110818 - 24 Oct 2018

Cited by 7 | Viewed by 3611

Abstract

Mixture working fluids can reduce effectively energy loss at heat sources and heat sinks, and therefore enhance the organic Rankine cycle (ORC) performance. The entropy and entransy dissipation analyses of a basic ORC system to recover low-grade waste heat using three mixture working [...] Read more.

Mixture working fluids can reduce effectively energy loss at heat sources and heat sinks, and therefore enhance the organic Rankine cycle (ORC) performance. The entropy and entransy dissipation analyses of a basic ORC system to recover low-grade waste heat using three mixture working fluids (R245fa/R227ea, R245fa/R152a and R245fa/pentane) have been investigated in this study. The basic ORC includes four components: an expander, a condenser, a pump and an evaporator. The heat source temperature is 120 °C while the condenser temperature is 20 °C. The effects of four operating parameters (evaporator outlet temperature, condenser temperature, pinch point temperature difference, degree of superheat), as well as the mass fraction, on entransy dissipation and entropy generation were examined. Results demonstrated that the entransy dissipation is insensitive to the mass fraction of R245fa. The entropy generation distributions at the evaporator for R245/pentane, R245fa/R152a and R245fa/R227ea are in ranges of 66–74%, 68–80% and 66–75%, respectively, with the corresponding entropy generation at the condenser ranges of 13–21%, 4–17% and 11–21%, respectively, while those at the expander for R245/pentane, R245fa/R152a and R245fa/R227ea are approaching 13%, 15% and 14%, respectively. The optimal mass fraction of R245fa for the minimum entropy generation is 0.6 using R245fa/R152a. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

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11 pages, 3103 KiB

Open AccessArticle

Entropy Generation Rates in Two-Dimensional Rayleigh–Taylor Turbulence Mixing

by Xinyu Yang, Haijiang He, Jun Xu, Yikun Wei and Hua Zhang

Entropy 2018, 20(10), 738; https://doi.org/10.3390/e20100738 - 26 Sep 2018

Cited by 7 | Viewed by 2957

Abstract

Entropy generation rates in two-dimensional Rayleigh–Taylor (RT) turbulence mixing are investigated by numerical calculation. We mainly focus on the behavior of thermal entropy generation and viscous entropy generation of global quantities with time evolution in Rayleigh–Taylor turbulence mixing. Our results mainly indicate that, [...] Read more.

Entropy generation rates in two-dimensional Rayleigh–Taylor (RT) turbulence mixing are investigated by numerical calculation. We mainly focus on the behavior of thermal entropy generation and viscous entropy generation of global quantities with time evolution in Rayleigh–Taylor turbulence mixing. Our results mainly indicate that, with time evolution, the intense viscous entropy generation rate

s_{u}

and the intense thermal entropy generation rate

S_{θ}

occur in the large gradient of velocity and interfaces between hot and cold fluids in the RT mixing process. Furthermore, it is also noted that the mixed changing gradient of two quantities from the center of the region to both sides decrease as time evolves, and that the viscous entropy generation rate

{⟨ S_{u} ⟩}_{V}

and thermal entropy generation rate

{⟨ S_{θ} ⟩}_{V}

constantly increase with time evolution; the thermal entropy generation rate

{⟨ S_{θ} ⟩}_{V}

with time evolution always dominates in the entropy generation of the RT mixing region. It is further found that a “smooth” function

{⟨ S_{u} ⟩}_{V} \sim t^{1 / 2}

and a linear function

{⟨ S_{θ} ⟩}_{V} \sim t

are achieved in the spatial averaging entropy generation of RT mixing process, respectively. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

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14 pages, 7130 KiB

Open AccessArticle

Transpiration and Viscous Dissipation Effects on Entropy Generation in Hybrid Nanofluid Flow over a Nonlinear Radially Stretching Disk

by Umer Farooq, Muhammad Idrees Afridi, Muhammad Qasim and D. C. Lu

Entropy 2018, 20(9), 668; https://doi.org/10.3390/e20090668 - 4 Sep 2018

Cited by 74 | Viewed by 5208

Abstract

The present research work explores the effects of suction/injection and viscous dissipation on entropy generation in the boundary layer flow of a hybrid nanofluid (Cu–Al₂O₃–H₂O) over a nonlinear radially stretching porous disk. The energy dissipation function is [...] Read more.

The present research work explores the effects of suction/injection and viscous dissipation on entropy generation in the boundary layer flow of a hybrid nanofluid (Cu–Al₂O₃–H₂O) over a nonlinear radially stretching porous disk. The energy dissipation function is added in the energy equation in order to incorporate the effects of viscous dissipation. The Tiwari and Das model is used in this work. The flow, heat transfer, and entropy generation analysis have been performed using a modified form of the Maxwell Garnett (MG) and Brinkman nanofluid model for effective thermal conductivity and dynamic viscosity, respectively. Suitable transformations are utilized to obtain a set of self-similar ordinary differential equations. Numerical solutions are obtained using shooting and bvp4c Matlab solver. The comparison of solutions shows excellent agreement. To examine the effects of principal flow parameters like suction/injection, the Eckert number, and solid volume fraction, different graphs are plotted and discussed. It is concluded that entropy generation inside the boundary layer of a hybrid nanofluid is high compared to a convectional nanofluid. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

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19 pages, 7393 KiB

Open AccessArticle

Second Law Analysis of Dissipative Flow over a Riga Plate with Non-Linear Rosseland Thermal Radiation and Variable Transport Properties

by Muhammad Idrees Afridi, Muhammad Qasim and Abid Hussanan

Entropy 2018, 20(8), 615; https://doi.org/10.3390/e20080615 - 18 Aug 2018

Cited by 22 | Viewed by 4446

Abstract

In this article, we investigated entropy generation and heat transfer analysis in a viscous flow induced by a horizontally moving Riga plate in the presence of strong suction. The viscosity and thermal conductivity of the fluid are taken to be temperature dependent. The [...] Read more.

In this article, we investigated entropy generation and heat transfer analysis in a viscous flow induced by a horizontally moving Riga plate in the presence of strong suction. The viscosity and thermal conductivity of the fluid are taken to be temperature dependent. The frictional heating function and non-linear radiation terms are also incorporated in the entropy generation and energy equation. The partial differential equations which model the flow are converted into dimensionless form by using proper transformations. Further, the dimensionless equations are reduced by imposing the conditions of strong suction. Numerical solutions are obtained using MATLAB boundary value solver bvp4c and used to evaluate the entropy generation number. The influences of physical flow parameters arise in the mathematical modeling are demonstrated through various graphs. The analysis reveals that velocity decays whereas entropy generation increases with rising values of variable viscosity parameter. Furthermore, entropy generation decays with increasing variable thermal conductivity parameter. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

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19 pages, 7878 KiB

Open AccessArticle

Thermo-Fluid Characteristics of High Temperature Molten Salt Flowing in Single-Leaf Type Hollow Paddles

by Taha Rajeh, Ping Tu, Hua Lin and Houlei Zhang

Entropy 2018, 20(8), 581; https://doi.org/10.3390/e20080581 - 7 Aug 2018

Cited by 4 | Viewed by 3754

Abstract

A single-leaf type paddle heat exchanger with molten salt as the working fluid is a proper option in high temperature heating processes of materials. In this paper, based on computational fluid dynamics (CFD) simulations, we present the thermo-fluid characteristics of high temperature molten [...] Read more.

A single-leaf type paddle heat exchanger with molten salt as the working fluid is a proper option in high temperature heating processes of materials. In this paper, based on computational fluid dynamics (CFD) simulations, we present the thermo-fluid characteristics of high temperature molten salt flowing in single-leaf type hollow paddles in the view of both the first law and the second law of thermodynamics. The results show that the heat transfer rate of the hollow paddles is significantly greater than that of solid paddles. The penalty of the heat transfer enhancement is additional pressure drop and larger total irreversibility (i.e., total entropy generation rate). Increasing the volume of the fluid space helps to enhance the heat transfer, but there exists an upper limit. Hollow paddles are more favorable in heat transfer enhancement for designs with a larger height of the paddles, flow rate of molten salt and material-side heat transfer coefficient. The diameter of the flow holes influences the pressure drop strongly, but their position is not important for heat transfer in the studied range. Other measures of modifying the fluid flow and heat transfer like internal baffles, more flow holes or multiple channels for small fluid volume are further discussed. For few baffles, their effects are limited. More flow holes reduce the pressure drop obviously. For the hollow paddles with small fluid volume, it is possible to increase the heat transfer rate with more fluid channels. The trade-off among fluid flow, heat transfer and mechanical strength is necessary. The thermo-fluid characteristics revealed in this paper will provide guidance for practical designs. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

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21 pages, 5648 KiB

Open AccessArticle

Entropy Generation Due to the Heat Transfer for Evolving Spherical Objects

by Ho-Young Kwak

Entropy 2018, 20(8), 562; https://doi.org/10.3390/e20080562 - 28 Jul 2018

Cited by 2 | Viewed by 3630

Abstract

Heat transfer accompanying entropy generation for the evolving mini and microbubbles in solution is discussed based on the explicit solutions for the hydrodynamic equations related to the bubble motion. Even though the pressure difference between the gas inside the bubble and liquid outside [...] Read more.

Heat transfer accompanying entropy generation for the evolving mini and microbubbles in solution is discussed based on the explicit solutions for the hydrodynamic equations related to the bubble motion. Even though the pressure difference between the gas inside the bubble and liquid outside the bubble is a major driving force for bubble evolution, the heat transfer by conduction at the bubble-liquid interface affects the delicate evolution of the bubble, especially for sonoluminescing the gas bubble in sulfuric acid solution. On the other hand, our explicit solutions for the continuity, Euler equation, and Newtonian gravitational equation reveal that supernovae evolve by the gravitational force radiating heat in space during the expanding or collapsing phase. In this article, how the entropy generation due to heat transfer affects the bubble motion delicately and how heat transfer is generated by gravitational energy and evolving speed for the supernovae will be discussed. The heat transfer experienced by the bubble and supernovae during their evolution produces a positive entropy generation rate. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

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9 pages, 1678 KiB

Open AccessArticle

Thermal Characteristics of Staggered Double-Layer Microchannel Heat Sink

by Dalei Jing and Lei He

Entropy 2018, 20(7), 537; https://doi.org/10.3390/e20070537 - 19 Jul 2018

Cited by 14 | Viewed by 3959

Abstract

The present work numerically studies the thermal characteristics of a staggered double-layer microchannel heat sink (DLMCHS) with an offset between the upper layer of microchannels and lower layer of microchannels in the width direction, and investigates effects of inlet velocity and geometric parameters [...] Read more.

The present work numerically studies the thermal characteristics of a staggered double-layer microchannel heat sink (DLMCHS) with an offset between the upper layer of microchannels and lower layer of microchannels in the width direction, and investigates effects of inlet velocity and geometric parameters including the offset of the two layers of microchannels, vertical rib thickness and microchannel aspect ratio on the thermal resistance of the staggered DLMCHS. The present work found that the thermal resistance of the staggered DLMCHS increases with the increasing offset value when the vertical rib thickness is small, but decreases firstly and then increases as the offset value increases when the vertical rib thickness is large enough. Furthermore, the thermal resistance of the staggered DLMCHS decreases with the increasing offset when the aspect ratio is small, but increases with the increasing offset when the aspect ratio is large enough. Thus, for the DLMCHS with a small microchannel aspect ratio and large vertical rib thickness, the offset between the upper layer of microchannels and the lower layer of microchannels in the width direction is a potential method to reduce thermal resistance and improve the thermal performance of the DLMCHS. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

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12 pages, 10295 KiB

Open AccessArticle

Refrigeration Performance and Entropy Generation Analysis for Reciprocating Magnetic Refrigerator with Gd Plates

by Yonghua You, Zhongda Wu, Yong Yang, Jie Yu, Dong Zhang and Zhuang Zhang

Entropy 2018, 20(6), 427; https://doi.org/10.3390/e20060427 - 1 Jun 2018

Cited by 5 | Viewed by 5112

Abstract

In the current work, a novel 2D numerical model of stationary grids was developed for reciprocating magnetic refrigerators, with Gd plates, in which the magneto-caloric properties, derived from the Weiss molecular field theory, were adopted for the built-in energy source of the magneto-caloric [...] Read more.

In the current work, a novel 2D numerical model of stationary grids was developed for reciprocating magnetic refrigerators, with Gd plates, in which the magneto-caloric properties, derived from the Weiss molecular field theory, were adopted for the built-in energy source of the magneto-caloric effect. The numerical simulation was conducted under the conditions of different structural and operational parameters, and the effects of the relative fluid displacement (φ) on the specific refrigeration capacity (qref) and the Coefficient of Performance (COP) were obtained. Besides the variations of entropy, the generation rate and number were studied and the contours of the local entropy generation rate are presented for discussion. From the current work, it is found that with an increase in φ, both the qref and COP followed the convex variation trend, while the entropy generation number (Ns) varied concavely. As for the current cases, the maximal qref and COP were equal to 151.2 kW/m³ and 9.11, respectively, while the lowest Ns was the value of 2.4 × 10⁻⁴ K⁻¹. However, the optimal φ for the largest qref and COP, and for the lowest Ns, were inconsistent, thus, some compromises need be made in the optimization of magnetic refrigerators. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

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25 pages, 1155 KiB

Open AccessArticle

Entropy Generation on Nanofluid Thin Film Flow of Eyring–Powell Fluid with Thermal Radiation and MHD Effect on an Unsteady Porous Stretching Sheet

by Mohammad Ishaq, Gohar Ali, Zahir Shah, Saeed Islam and Sher Muhammad

Entropy 2018, 20(6), 412; https://doi.org/10.3390/e20060412 - 28 May 2018

Cited by 57 | Viewed by 5632

Abstract

This research paper investigates entropy generation analysis on two-dimensional nanofluid film flow of Eyring–Powell fluid with heat amd mass transmission over an unsteady porous stretching sheet in the existence of uniform magnetic field (MHD). The flow of liquid films are taken under the [...] Read more.

This research paper investigates entropy generation analysis on two-dimensional nanofluid film flow of Eyring–Powell fluid with heat amd mass transmission over an unsteady porous stretching sheet in the existence of uniform magnetic field (MHD). The flow of liquid films are taken under the impact of thermal radiation. The basic time dependent equations of heat transfer, momentum and mass transfer are modeled and converted to a system of differential equations by employing appropriate similarity transformation with unsteady dimensionless parameters. Entropy analysis is the main focus in this work and the impact of physical parameters on the entropy profile are discussed in detail. The influence of thermophoresis and Brownian motion has been taken in the nanofluids model. An optima approach has been applied to acquire the solution of modeled problem. The convergence of the HAM (Homotopy Analysis Method) has been presented numerically. The disparity of the Nusslet number, Skin friction, Sherwood number and their influence on the velocity, heat and concentration fields has been scrutinized. Moreover, for comprehension, the physical presentation of the embedded parameters are explored analytically for entropy generation and discussed. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

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10 pages, 1517 KiB

Open AccessArticle

Effective Boundary Slip Induced by Surface Roughness and Their Coupled Effect on Convective Heat Transfer of Liquid Flow

by Yunlu Pan, Dalei Jing, He Zhang and Xuezeng Zhao

Entropy 2018, 20(5), 334; https://doi.org/10.3390/e20050334 - 2 May 2018

Cited by 9 | Viewed by 4833

Abstract

As a significant interfacial property for micro/nano fluidic system, the effective boundary slip can be induced by the surface roughness. However, the effect of surface roughness on the effective slip is still not clear, both increased and decreased effective boundary slip were found [...] Read more.

As a significant interfacial property for micro/nano fluidic system, the effective boundary slip can be induced by the surface roughness. However, the effect of surface roughness on the effective slip is still not clear, both increased and decreased effective boundary slip were found with increased roughness. The present work develops a simplified model to study the effect of surface roughness on the effective boundary slip. In the created rough models, the reference position of the rough surfaces to determinate effective boundary slip was set based on ISO/ASME standard and the surface roughness parameters including Ra (arithmetical mean deviation of the assessed profile), Rsm (mean width of the assessed profile elements) and shape of the texture varied to form different surface roughness. Then, the effective boundary slip of fluid flow through the rough surface was analyzed by using COMSOL 5.3. The results show that the effective boundary slip induced by surface roughness of fully wetted rough surface keeps negative and further decreases with increasing Ra or decreasing Rsm. Different shape of roughness texture also results in different effective slip. A simplified corrected method for the measured effective boundary slip was developed and proved to be efficient when the Rsm is no larger than 200 nm. Another important finding in the present work is that the convective heat transfer firstly increases followed by an unobvious change with increasing Ra, while the effective boundary slip keeps decreasing. It is believed that the increasing Ra enlarges the area of solid-liquid interface for convective heat transfer, however, when Ra is large enough, the decreasing roughness-induced effective boundary slip counteracts the enhancement effect of roughness itself on the convective heat transfer. Full article

(This article belongs to the Special Issue Entropy Generation and Heat Transfer)

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