Total Entropy Generation Rate Research Articles

Entropy Generation Minimization for Reverse Water Gas Shift (RWGS) Reactors.

Thermal design and optimization for reverse water gas shift (RWGS) reactors is particularly important to fuel synthesis in naval or commercial scenarios. The RWGS reactor with irreversibilities of heat transfer, chemical reaction and viscous flow is studied based on finite time thermodynamics or entropy generation minimization theory in this paper. The total entropy generation rate (EGR) in the RWGS reactor with different boundary conditions is minimized subject to specific feed compositions and chemical conversion using optimal control theory, and the optimal configurations obtained are compared with three reference reactors with linear, constant reservoir temperature and constant heat flux operations, which are commonly used in engineering. The results show that a drastic EGR reduction of up to 23% can be achieved by optimizing the reservoir temperature profile, the inlet temperature of feed gas and the reactor length simultaneously, compared to that of the reference reactor with the linear reservoir temperature. These optimization efforts are mainly achieved by reducing the irreversibility of heat transfer. Optimal paths have subsections of relatively constant thermal force, chemical force and local EGR. A conceptual optimal design of sandwich structure for the compact modular reactor is proposed, without elaborate control tools or excessive interstage equipment. The results can provide guidelines for designing industrial RWGS reactors in naval or commercial scenarios.

Entropy generation in radiative motion of tangent hyperbolic nanofluid in presence of activation energy and nonlinear mixed convection

In this communication, an optimization of entropy generation is performed through thermodynamics second law. Tangent hyperbolic nanomaterial model is used which describes the important slip mechanism namely Brownian and thermophoresis diffusions. MHD fluid is considered. The novel binary chemical reaction model is implemented to characterize the impact of activation energy. Nonlinear mixed convection, dissipation and Joule heating are considered. Appropriate similarity transformations are implemented to get the required coupled ODEs system. The obtained system is tackled for series solutions by homotopy method. Graphs are constructed to analyze the impact of different flow parameters on entropy number, nanoparticle volume concentration, temperature and velocity fields. Total entropy generation rate is calculated via various flow variables. It is noticed from obtained results that entropy number depend up thermal irreversibility, viscous dissipation and Joule heating irreversibility and concentration irreversibility. Decreasing behavior of concentration is witnessed for higher estimations of chemical reaction variable. Entropy number is more for higher Hartmann number, Weissenberg number and chemical reaction variable while contrast behavior is noted for Bejan number.

Numerical Study on Entropy Generation in Thermal Convection with Differentially Discrete Heat Boundary Conditions.

Entropy generation in thermal convection with differentially discrete heat boundary conditions at various Rayleigh numbers (Ra) are numerically investigated using the lattice Boltzmann method. We mainly focused on the effects of Ra and discrete heat boundary conditions on entropy generation in thermal convection according to the minimal entropy generation principle. The results showed that the presence of the discrete heat source at the bottom boundary promotes the transition to a substantial convection, and the viscous entropy generation rate (Su) generally increases in magnitude at the central region of the channel with increasing Ra. Total entropy generation rate (S) and thermal entropy generation rate (Sθ) are larger in magnitude in the region with the largest temperature gradient in the channel. Our results also indicated that the thermal entropy generation, viscous entropy generation, and total entropy generation increase exponentially with the increase of Rayleigh number. It is noted that lower percentage of single heat source area in the bottom boundary increases the intensities of viscous entropy generation, thermal entropy generation and total entropy generation. Comparing with the classical homogeneous thermal convection, the thermal entropy generation, viscous entropy generation, and total entropy generation are improved by the presence of discrete heat sources at the bottom boundary.

Al2O3–Water nanofluid heat transfer and entropy generation in a ribbed channel with wavy wall in the presence of magnetic field

In this article, a parametric study is conducted to evaluate heat transfer enhancement in a ribbed channel containing Al2O3–Water nanofluid with wavy wall. The physical domain is under the influence of the magnetic field that creates a negative force against the working fluid to move. Nanofluid with higher temperature enters the cool ribbed duct and heat is exchanged along the walls of channel. The effects of the dominant parameters including number of the blocks, solid volume fractions of nanofluid, Hartmann number, Reynolds number, and different states of amplitude sine waves are numerically tested on the local and average Nusselt number, skin friction, and total entropy generation. Excellent agreement between present study and previous literature is observed. It is found that, an augmentation in magnetic field will result in higher values of both local and average Nusselt number accompanying with bigger values of skin friction and entropy generation. Computations illustrate that, increasing the solid volume fraction of the Al2O3 nanoparticles will raise the Nusselt number and total entropy generation rate but its effect on the skin friction is negligible. Also, numerical results imply that increasing amplitude sine waves of the geometry has incremental effect on the Nusselt number and skin friction but its effect on the total entropy generation rate is not so clear. Moreover, by adding number of the used blocks in the presence of magnetic field, the local Nusselt number experiences more jumps but it does not increase the average Nusselt number, necessarily. In addition, using more blocks increases skin friction but it has a reverse effect on the total entropy generation rate.

Analysis of mixed convection and entropy generation of nanofluid filled triangular enclosure with a flexible sidewall under the influence of a rotating cylinder

In this study, mixed convection and entropy generation in a nanofluid filled triangular cavity under the influence of rotating cylinder and flexible sidewall were numerically analyzed with finite element method. The inclined sidewall was cooled while the left vertical wall is partially heated. Heat transfer rate enhances as the values of Rayleigh number, angular rotational velocity of the cylinder, elastic modulus of the flexible sidewall and solid nanoparticles volume fraction increase. Nusselt number enhances more in the counter-clockwise direction of the cylinder as compared to clockwise directional rotation and 13.55% of average heat transfer enhancement was achieved for $$\varOmega =3000$$ when compared to motionless cylinder. Average Nusselt number increases by about 30.50% when the elastic modulus of the flexible wall is changed from 500 to $$10^5$$ . The changes in the velocity profiles are significant for the lower part of the triangular enclosure with respect to changes in angular rotational velocity and elastic modulus as compared to upper part of the cavity. Adding nanoparticles increases heat transfer especially for the lower part of the cavity and 49.63% of heat transfer enhancement was achieved for the highest volume fraction when compared to base fluid. Normalized total entropy generation rates enhance for higher values of elastic modulus of the flexible wall, angular rotational speed of the circular cylinder and nanoparticle volume fractions.

Thermodynamic analyses and optimizations of extraction process of CO2 from acidic seawater by using hollow fiber membrane contactor

Extraction process of CO2 from acidic seawater by using hollow fiber membrane contactor is studied in this paper by using finite time thermodynamics or entropy generation minimization theory. Analytical formulae of the extraction rate of CO2 and entropy generation rate (EGR) caused by mass transfer (MT) and the flow of the process are obtained when the acidic seawater (liquid phase) flows in the lumen side and the H2 (gaseous phase) flows in the shell side conversely. Relations between the concentration of CO2 and contactor length in both liquid phase and gaseous phase, between the MT flux and contactor length, between the pressure of the two phases and the contactor length, as well as between the local EGR and contactor length are obtained by numerical examples. The influences of the volume flow rates of the acidic seawater and the H2 at the inlet, the number and the length of hollow fibers on the extraction rate of CO2 and EGR per MT rate are also analyzed. The results show that the extraction rate of CO2 can reach up to more than 98%. The EGRs caused by MT and fluid flow account for 85.99% and 14.01% of the total EGR, respectively. Furthermore, the total EGR caused by MT and fluid flow is minimized by using nonlinear programming method with fixed extraction rate of CO2 when the gas mixture of H2 and CO2 flows in the shell side and the concentration of CO2 in the gaseous phase is completely controllable. The EGR of the minimum EGR MT strategy can be decreased by 36.57% than that of the MT strategy that H2 flows in shell side, in which the EGR caused by MT is decreased by 42.52% and the EGR caused by the flow remain basically unchanged. The EGR caused by MT is minimized by using optimal control theory and the analytical solution of the optimal concentration configuration of CO2 in the gaseous phase is obtained.

Analysis of Heat Transfer and Entropy Generation in a Channel Partially Filled With N-Layer Porous Media

Convective heat transfer in a channel partially filled with porous medium has received a lot of attention due to its wide engineering applications. However, most researches focused on a channel partially filled with single layer porous medium. In this paper, we will analyze the heat transfer and entropy generation inside a channel partially filled with N-layer porous media. The flow and the heat transfer in the porous region are described by the Darcy–Brinkman model and the local thermal nonequilibrium model, respectively. At the porous-free fluid interface, the momentum and the heat transfer are described by the stress jump boundary condition and the heat flux jump boundary condition, respectively; while at the interface between two different porous layers, the momentum and the heat transfer are described by the stress continuity boundary condition and the heat flux continuity boundary condition, respectively. The analytical solutions for the velocity and temperature in the channel are derived and used to calculate the overall Nusselt number, the total entropy generation rate, the Bejan number, and the friction factor. Furthermore, the performances of the flow and heat transfer of a channel partially filled with third-layer porous media are studied.

Comparison of the thermo-hydraulic performance and the entropy generation rate for two types of low temperature solar collectors using CFD

In this work, a comparison of the thermo-hydraulic performance and the entropy generation rate for two different types of low temperature solar collectors: flat plate solar collector (FPC) and water-in-glass evacuated tube solar collector (ETC), is addressed. The absorber area for both solar collectors were considered to be equal for a reliable comparison. The operation of the solar collectors was simulated under different volumetric flow rates and solar radiation values for the state of Guanajuato in Mexico. The volumetric flow rate for both collectors ranged from 1 to 9 L/min. The variation of the solar radiation was based on: (1) the solar radiation taken from several experimental tests reported elsewhere, (2) the month with the lowest average solar radiation in one year, (3) the average solar radiation of one year and (4) the month with the highest average solar radiation in one year. The buoyancy effects were considered in the CFD simulations using the Boussinesq approximation (BA) model. The distribution profiles of temperature, pressure, and velocity inside the tubes of the solar collectors, along with the local entropy generation rate distribution due to heat transfer and the fluid viscosity, are shown in detail. The results show a better thermal performance for the solar water-in-glass evacuated tube collector (ETC) than for the flat plate solar collector (FPC) at low flow rates (under 3.0 L/min). The outlet temperature reached is similar in both collectors for volumetric flow rates higher than 3.0 L/min. The analysis of the entropy generation rate shows that the generation due to the transfer of heat is higher for the ETC than for the FPC, and this contribution is up to 10% of the total entropy generation rate; on the other hand, the generation rate due to the fluid viscosity is higher for the FPC than the ETC at high volumetric flow rates (above 3.5 L/min), however, this contribution is negligible. Finally, the total entropy generation rate is higher for the FPC than the ETC at low volumetric flow rates (below 3.0 L/min) and this is increased if the solar radiation increases.

Role of differential vs Rayleigh-Bénard heating at curved walls for efficient processing via entropy generation approach

The present study deals with the finite element based numerical simulations of heat transfer and entropy generation rates during natural convection for fluid saturated porous media in enclosures involving curved walls (case 1: lower curvature and case 2: higher curvature) with various thermal boundary conditions. The differential heating (isothermally hot left wall and cold right wall and adiabatic horizontal walls) and Rayleigh-Bénard heating (isothermally hot bottom wall and cold top wall involving adiabatic left and right walls) are considered. The locations and magnitudes of the entropy generation due to heat transfer (Sθ) and fluid friction (Sψ) are presented and discussed based on the spatial distributions of isotherms and streamlines, respectively. The magnitudes of local entropy generation (Sθ,Sψ), total entropy generation (Stotal) and average heat transfer rates (Nur‾ and Nut‾) are significantly lesser for the Rayleigh-Bénard heating compared to the differential heating for all the cases involving all Dam and Prm. The Rayleigh-Bénard heating is the optimal strategy for all Dam and Prm involving both the concave cases except for 10-3⩽Dam⩽10-2,Prm=10 and case 1 (concave) domain. The Rayleigh-Bénard heating is also the optimal strategy compared to the differential heating involving the convex cases at 10-5⩽Dam⩽10-4 whereas the differential heating is the optimal heating strategy for Dam⩾10-3 involving both Prm for the convex cases.

Entropy generation minimization (EGM) for convection nanomaterial flow with nonlinear radiative heat flux

Here entropy generation and magnetohydrodynamics (MHD) impacts in unsteady viscous nanoliquid flow are elaborated. Flow induced is by impermeable rotating disk. Application of thermodynamic second law is employed for the analysis of entropy generation. Nanofluid characteristics have been addressed through thermophoresis and Brownian movement. Nonlinear versions of mixed convection and thermal radiation are introduced simultaneously. The process of non-dimensionalization is performed via implementation of suitable variables. Nonlinear computations have been carried out. The rate of total entropy generation is evaluated for distinct arising variables. Skin-friction and Nusselt and Sherwood numbers in addition to velocity, temperature and nanoparticles concentration are emphasized. We found increasing trend in temperature and velocity for unsteadiness factor whereas opposite scenario is noticed regarding nanoparticles concentration. Entropy generation rate enhances with increasing of Brinkman number, Eckert number and magnetic parameter while the opposite behavior is recorded for Reynolds number. While Bejan number has direct relation to Eckert number, Reynolds number, and magnetic parameter, While for Brinkman number the situation is opposite. Moreover the surface acts as effective source of irreversibility when entropy generation rate is closed to the surface is higher.

Entropy generation minimization and binary chemical reaction with Arrhenius activation energy in MHD radiative flow of nanomaterial

Our aim here is to investigate the MHD radiative nanomaterial flow of Casson fluid towards a stretched surface. Heat transport mechanism is examined through thermal radiation and heat source/sink. Entropy generation is explored as a function of concentration, temperature and velocity. Total entropy generation rate is inspected for various flow parameters. Impacts of Brownian movement and thermophoresis on entropy generation have been also scrutinized. Nanofluid model with Brownian motion and thermophoresis mechanisms are analyzed. Additionally, activation energy and chemical reaction are also implemented. Governing flow expressions consist of momentum, energy and concentration of nanoparticles. Appropriate similarity transformations are utilized to convert the flow expressions to ordinary ones. The obtaining coupled nonlinear differential equations have been tackled with the help of BPV4c. Attention is particularly given to the entropy generation and Bejan number. The graphical outcomes are discussed for velocity, concentration, temperature, entropy generation and Bejan number. From graphical outcomes, it is examined that velocity and temperature fields show contrast behavior for higher magnetic variable. It is found that radiative variable increases the effective thermal diffusivity and temperature enhances. To our knowledge the flow of nanomaterial with entropy generation minimization and activation energy is just investigated in this paper.

Entropy generation of nanofluid flow in a microchannel heat sink

Abstract Present study aims to investigate the effects of the presence of nano sized TiO2 particles in the base fluid on entropy generation rate in a microchannel heat sink. Pure water was chosen as base fluid, and TiO2 particles were suspended into the pure water in five different particle volume fractions of 0.25%, 0.5%, 1.0%, 1.5% and 2.0%. Under laminar, steady state flow and constant heat flux boundary conditions, thermal, frictional, total entropy generation rates and entropy generation number ratios of nanofluids were experimentally analyzed in microchannel flow for different channel heights of 200 µm, 300 µm, 400 µm and 500 µm. It was observed that frictional and total entropy generation rates increased as thermal entropy generation rate were decreasing with an increase in particle volume fraction. In microchannel flows, thermal entropy generation could be neglected due to its too low rate smaller than 1.10e−07 in total entropy generation. Higher channel heights caused higher thermal entropy generation rates, and increasing channel height yielded an increase from 30% to 52% in thermal entropy generation. When channel height decreased, an increase of 66%–98% in frictional entropy generation was obtained. Adding TiO2 nanoparticles into the base fluid caused thermal entropy generation to decrease about 1.8%–32.4%, frictional entropy generation to increase about 3.3%–21.6%.

Unsteady Conjugate Natural Convective Heat Transfer and Entropy Generation in a Porous Semicircular Cavity

The problem of unsteady conjugate natural convection and entropy generation within a semicircular porous cavity bounded by solid wall of finite thickness and conductivity has been investigated numerically. The governing partial differential equations with the corresponding initial and boundary conditions have been solved by the finite difference method using the dimensionless stream function, vorticity, and temperature formulation. Numerical results for the isolines of the stream function, temperature, and the local entropy generation due to heat transfer and fluid friction as well as the average Nusselt and Bejan numbers, and the average total entropy generation and fluid flow rate have been analyzed for different values of the Rayleigh number, Darcy number, thermal conductivity ratio, and the dimensionless time. It has been found that low values of the temperature difference reflect the entropy generation, mainly in the upper corners of the cavity, while for high Rayleigh numbers, the entropy generation occurs also along the internal solid–porous interface. A growth of the thermal conductivity ratio leads to an increase in the average Bejan number and the average entropy generation due to a reduction of the heat loss inside the heat-conducting solid wall.

Two-dimensional heat and mass transfer and thermodynamic analyses of porous microreactors with Soret and thermal radiation effects—An analytical approach

Transport of heat and mass and the thermodynamics of porous microreactors with thermal diffusion and radiation effects are investigated analytically. The examined configuration includes an axisymmetric, thick-wall microchannel with an iso-flux thermal boundary condition imposed on the external surfaces. The microchannel is filled with porous materials and accommodates a zeroth order homogenous chemical reaction. Internal radiative heat transfer is modelled in addition to heat convection and conduction, while the local thermal non-equilibrium approach is taken within the porous section of the system. The transport of species is coupled with that of heat via the inclusion of thermodiffusion or Soret effect. Two-dimensional heat and mass transfer differential equations are solved analytically. The results are subsequently used to predict the thermodynamic irreversibilities inside the reactor and a thorough analysis of local and total entropy generation rates is performed. Also, the changes in Nusselt number, calculated on the internal walls of the microreactor, versus various parameters are reported. It is shown that the radiation effects can impact the temperature of the solid phase of the porous medium and lead to alteration of Nusselt number. It is further observed that the transfer of mass is the main source of irreversibility in the system. The findings are of particular use for the design and analysis of the microreactors with homogenous chemical reactions and can be also used for the validation of computational models.

Nonlinear radiative heat flux and heat source/sink on entropy generation minimization rate

Entropy generation minimization in nonlinear radiative mixed convective flow towards a variable thicked surface is addressed. Entropy generation for momentum and temperature is carried out. The source for this flow analysis is stretching velocity of sheet. Transformations are used to reduce system of partial differential equations into ordinary ones. Total entropy generation rate is determined. Series solutions for the zeroth and mth order deformation systems are computed. Domain of convergence for obtained solutions is identified. Velocity, temperature and concentration fields are plotted and interpreted. Entropy equation is studied through nonlinear mixed convection and radiative heat flux. Velocity and temperature gradients are discussed through graphs. Meaningful results are concluded in the final remarks.

Entropy generation analysis for convective heat transfer of nanofluids in tree-shaped network flowing channels

In this paper, convective heat transfer processes of nanofluids flowing through tree-shaped network flowing channels with prescribed heat flux on channel wall are investigated. The entropy generation rate equations of nanofluids flowing through the tree-shaped network channels are deduced; the interaction between volume fractions of nanoparticles and entropy generation rate is investigated. For H-shaped tree network flowing channels, the recurrence formulas of total entropy generation rate and the order number of flowing channels are deduced, and the numerical examples are presented. A new dimensionless number is proposed to describe the entropy generation properties of nanofluids. Analytical solutions of entropy generation rate distribution of any order of H-shaped construct of flowing channel using nanofluids are obtained.

Entropy generation minimization (EGM) in nonlinear mixed convective flow of nanomaterial with Joule heating and slip condition

Main emphasis here is to investigate the novel characteristics of entropy generation in nonlinear mixed convective flow of nanofluid between two stretchable rotating disks. Buongiorno nanofluid model of nanomaterial is implemented in mathematical modeling. Nanofluid aspects for thermophoresis and Brownian movement are considered. Heat transport mechanism is examined subject to convective condition and Joule heating. Velocity slip is considered at the lower and upper disks. Total entropy generation rate is discussed. Systems of PDEs is first converted into ODEs and then tackled by for convergent solutions. The impacts of Reynold number, Prandtl number, Hartman number, velocity slip parameter, Biot numbers of heat and mass transfer, thermophoresis, Brownian motion, nonlinear convection parameters for temperature and concentration, mixed convection parameter and Schmidt number on velocities, temperature, Bejan number, concentration and total entropy generation rate are graphically examined. Our investigation reveal that entropy generation rate and Bejan number have inverse behavior for higher estimation of Hartman number. Moreover velocity and temperature gradients are physically interpreted.

Thermal-hydraulic performance of interrupted microchannel heat sinks with different rib geometries in transverse microchambers

The thermal-hydraulic performance of microchannel heat sinks with ribs in the interrupted transverse microchambers is studied using a three-dimensional conjugated heat transfer model and considering entrance effect, viscous heating and temperature-dependent thermophysical properties. Five different configurations of ribs and four lengths along the flow direction for every rib configuration are selected to analyze the effects of rib geometry on the thermal-hydraulic performance. The five rib configurations are rectangular, backward triangular, diamond, forward triangular and ellipsoidal, and the rib geometry parameters include expansion-constriction profile, ratio and length. The effects of rib geometry on thermal-hydraulic performance are firstly examined by the variations of friction factor and Nusselt number with Reynolds number, and corresponding correlations are proposed. Then, the conductive, convective and fluid capacitive thermal resistances are analyzed to obtain some insight into the basic heat transfer mechanism. Next, the entropy generation rates due to heat transfer and fluid friction are investigated for the analysis of the lost available work and irreversibility in the heat transfer process. Finally, the performance evaluation criteria is calculated to comprehensively assess the performance of such interrupted microchannel heat sinks with different rib geometry. For the studied operation parameters and rib geometries, the interrupted microchannel heat sinks with ribs in the transverse microchambers show a 4–31% decrease in the total thermal resistance, a 4–26% decrease in the total entropy generation rates, the maximum value 1.39 in performance evaluation criteria, compared with the straight microchannel heat sink.

Efficiency improvement of thermal power plants through specific entropy generation

Numerous studies have indicated that when neither the rate of heat input nor the power output in a thermal power plant is treated as a fixed parameter, minimizing the entropy generation does not lead to an improved thermal efficiency. This article presents a unified approach to resolve this issue by introducing specific entropy generation defined as the total entropy generation rate per unit flowrate of the fuel. A regenerative gas turbine and a combined cycle power plants are chosen for the purpose of discussion. It is found that the thermal efficiency inversely correlates with specific entropy generation, and minimization of specific entropy generation is identical to maximization of thermal efficiency. An illustrative example is presented to show how specific entropy generation can be applied to improve the efficiency of an integrated cycle. The results reveal that 85% of the inefficiencies of the combined cycle studied takes place in the gas turbine cycle. Recovering the thermal energy of the flue gases for both preheating the air and producing the steam within heat recovery steam generator yields 3.5 percentage points more efficiency than the case in which the heat of flue gases is only recovered for producing steam. With this modification, minimum specific entropy generation is dropped from 1489 to 1391 (J/K·mole fuel).

Entropy generation analysis for the cavitating head-drop characteristic of a centrifugal pump

Cavitation is a challenging flow abnormality that leads to undesirable effects on the hydraulic behaviour of centrifugal pumps. This study analyses the cavitating flow at a normal flow rate using the shear stress transport k-ω turbulence model and the Zwart cavitation model to capture the cavitation development and spatial distribution of vapour structures within the pump. A general description of the pump head-drop phenomenon was analysed through the study of local and global flow fields. The relationship between vapour distribution and entropy generation fields was mainly investigated through the local flow analysis method. Results show that the tendency of total entropy generation rate within the impeller coincides with the pump head-drop curve. The entropy generation rate changes slightly at the early stage of the cavitation development whereas rapidly increases when the cavitation has fully developed. Cavitation development enhances the hydraulic losses and flow unsteadiness in the impeller. These hydraulic losses are located substantially at the interface of the cavity, especially at the rear portion of the cavity region.