Numerical Investigation Of Entropy Generation Research Articles

Numerical investigation of entropy generation for flow boiling of R600A in the corrugated U-bend tube heat exchangers

The development of compact and efficient corrugated heat exchangers for refrigeration and air conditioning systems is reliant upon thermal-hydraulic performance, which is quantifiable in terms of entropy generation. Hence, this study presents the generation of entropy analysis for flow boiling evaporation with an environment-friendly refrigerant (R600a) in the novel design of corrugated (outward circular ribs corrugated, inward circular ribs corrugated, outward triangular ribs corrugated, and inward triangular ribs corrugated) U-bend tube exchangers. The performance of the corrugated tube heat exchangers has been reported in comparison with the smooth U-bend tube heat exchanger. The numerical calculations were executed using CFD code for various masses ranging from 100 to 400 kg/m2s at the saturation temperature and vapor quality of 20 °C and 0.2 respectively while 15 kW/m2 heat flux was applied on the external surface of the straight tubes. The results revealed that the entropy generation increases as the mass flux increases with the inward circular and triangular ribs corrugated tube having the highest generated entropy followed by the outward circular and triangular ribs corrugated and then the smooth tube with the least entropy generation. In reference to smooth tube for the mass flux of 100 kg/m2s, the entropy generation for inward circular and triangular ribs corrugated increased by 46.88% and 130.93% respectively while the outward circular and triangular ribs corrugated increased by 18.35% and 39.26% respectively. Lower dimensionless Bejan numbers were obtained in the corrugated tubes with respect to mass fluxes compared to the smooth tube. The fluid flow irreversibility contribution to the overall entropy generated was higher in the corrugated tubes due to the corrugation surface which causes swirl mixing. The results of the numerical calculations were confirmed and corresponded with those established in the literature.

Numerical Investigation of Entropy Generation of Joule Heating in Non-Axisymmetric Flow of Hybrid Nanofluid Towards Stretching Surface

Abstract The industrial sector has shown a growing interest in hybrid nanofluids affected by magnetohydrodynamics (MHD) owing to their wide range of applications, including photovoltaic water heaters and scraped surface heat exchangers. The main purpose of this study is to look at how entropy is created in a hybrid nanofluid of $A{l}_2{O}_3 - Cu$ mixed with ${H}_2O$ at a non-axisymmetric stagnation point flow with joule heating and viscous dissipation. By using appropriate non-similarity transformations, the PDEs governing the boundary layer region of this issue are transformed into a set of nonlinear PDEs. The BVP4c MATLAB program, which uses local non-similarity and additional truncation, may fix the problem. The velocity profiles in both directions grow when the values of ${\phi }_2,\ M,\lambda $ and A parameters increase. The temperature profile rises as the values of A and $Ec$ grow and lowers as ${\phi }_2$ and M increase. The obtained numerical findings demonstrate significant impacts on both the heat transfer rate and fluid flow parameters of the hybrid nanofluid. When the concentration of nanoparticles and the magnetic parameter are heightened, there is an enhancement seen in the skin friction coefficient and decline in heat transfer rate. In addition, the entropy production profile shows an increasing tendency as a function of the parameters ${\phi }_2,\ M,$ and $Br,$ while demonstrating a decreasing tendency of function of the parameter $\alpha $. The Bejan number profile has a positive correlation with the parameter $\alpha $ but shows a negative correlation with the variables ${\phi }_2,\ M,$ and $Br$.

Numerical investigation of entropy generation of turbulent flow in twisted tri-lobed tubes

Twisted tri-lobed tubes have garnered attention due to their exceptional heat transfer efficiency and straightforward fabrication. Existing literature lacks comprehensive assessments of the overall heat transfer performance of twisted tri-lobed tubes from the perspective of energy loss and irreversibility. This research aims to investigate entropy generation during turbulent water flow within twisted tri-lobed tubes, examining the influence of geometric parameters on local and average entropy production. Findings indicate that larger small circle radius (r) and straight lengths (l), coupled with smaller transition circle radius (R) and twist pitch lengths (p), result in diminished local and average heat transfer entropy production while enhancing local and average frictional entropy production, with heat transfer entropy generation dominating the overall entropy production. Additionally, with increasing Reynolds numbers, all twisted tubes demonstrate an increasing trend in average frictional entropy production, except for some cases (Case 1-Case 4) that exhibit an initial rise followed by a decline in average heat transfer entropy generation. Among the examined Reynolds range, Case 4 displays lower overall irreversibility compared to a plain tube. Following the second law of thermodynamics, Case 4 is preferred. The findings and methodology contribute to enhancing the thermodynamic evaluation of convective heat transfer in twisted tri-lobed tubes.

Numerical simulation of entropy transport in the oscillating fluid flow with transpiration and internal fluid heating by GGDQM

The numerical investigation of entropy generation and its depreciation in oscillating fluid flow with internal fluid heating and transpiration is presented. The current examination includes a flow and heat transfer investigation. The flow is driven by an infinite porous plate that is stretched and oscillated periodically in its plane. Boundary layer approximations (BLAs) are used to simplify the momentum and energy equations. A dimensionless nonlinear system of partial differential equations is solved for the velocity field, temperature profile, entropy generation distribution, and Bejan number using the Gear generalized differential quadrature method (GGDQM). The numerical values of skin friction coefficient and dimensionless heat transfer coefficient are tabulated against various flow governing parameters. The applied numerical scheme reliability is established by comparing numerical estimation of the skin friction coefficient and Nusselt number obtained by the GQGM and Gear Gauss-Lobato spectral method (GGLSM). A comparison of numerical data shows an excellent agreement and validates the reliability of the numerical simulation. Tables and graphs demonstrate the effects of various control parameters on the physical quantities of interest. With the rising Eckert number, the thermal and entropy profiles amplify, whereas a decrease in the Bejan number is observed. Furthermore, ininjection and suction instances, entropy and Bejan number profile arguments at and near the oscillating surface.

Numerical investigation of entropy generation in a solar parabolic trough collector using supercritical carbon dioxide as heat transfer fluid

• A Three-dimensional numerical thermal model is developed for solar Parabolic trough collector with s-CO2 as a heat transfer fluid. • Non-uniform solar heat flux calculated using Monte Carlos Ray Tracing based Optical Tool. • Entropy generation is calculated using the local temperature and velocity fields. • Optimal inlet boundary conditions were obtained for the s-CO2 as heat transfer fluid in the solar parabolic trough collector. Parabolic trough collector (PTC) is a widely used and efficient Concentrating Solar Power (CSP) technology for generating solar thermal power. Supercritical CO 2 (s-CO 2 ) is a heat transfer fluid (HTF) that shows good promising for use in solar PTC for further improvement in its efficiency and operations. A numerical thermal model is developed to understand the performance of s-CO 2 as an HTF in a solar PTC. The local temperature and velocity fields were used to calculate the entropy generated within HTF due to finite temperature differences and fluid flow friction. A commercially available LS-3 parabolic trough collector is used for the analysis with a modified receiver. An optical analysis tool based on Monte Carlo Ray tracing is used to calculate non-uniform heat flux distribution around the circumference of the PTC receiver. Entropy generated at various operating pressures, inlet temperatures, and inlet Reynolds number using s-CO 2 as HTF is calculated and analyzed. Results showed that entropy generated in the PTC receiver is reduced to a minimum at optimal Reynolds number for each of the operating pressures and inlet temperatures of the HTF. The Bejan number estimates the contribution of entropy generated due to heat transfer irreversibilities to the entropy generated due to heat transfer and fluid flow irreversibilities which is between 0.2 and 0.4 at high flow rates and close to 1 at low flow rates. Exergy efficiency analysis supported the optimized inlet boundary conditions.

Numerical investigation of entropy generation on MHD flow of micropolar fluid over a stretching sheet in the presence of a porous medium

Various industrial operations involve frequent heating and cooling of electrical systems. In such circumstances, the development of relevant thermal devices is of extreme importance. During the development of thermal devices, entropy generation should be reduced significantly for realizing efficient performance of the devices. Hence, in the current study, the investigation of micropolar fluid with entropy generation over a stretching sheet is taken into account. The impacts of different physical parameters on the velocity profile, microrotation profile, and temperature profile are studied graphically. The effects of thermal radiation, porous medium, magnetic field, and viscous dissipation are also analyzed. The influences of various involved parameters on physical quantities like skin friction coefficient, couple stress coefficient, and Nusselt number are also illustrated numerically. Moreover, entropy generation and Bejan number are studied graphically. The governing equations are solved by implementing the built-in Newton’s shooting method and code in the Mathematica (Version-9) operating system.

Inclined magneto: convection, internal heat, and entropy generation of nanofluid in an I-shaped cavity saturated with porous media

A numerical investigation of entropy generation due to MHD-free convective of Cu–water nanofluid in a porous I-shaped cavity is reported. The cavity is under Darcy law with inclined uniform magnetic field. The cavity is cooled from the top and a part of bottom wall subjected to uniform heat flux, while the other parts of walls of the cavity are adiabatic. Mathematical pattern formulated employing the single-phase nanofluid approach in governing equations the problem has been solved by finite difference technique. Prime efforts have been concentrated on the impacts of the pertinent parameters on the fluid flow and heat transfer inside the cavity. Numerical data have been plotted in the form of streamlines, isotherms, and average Nusselt numbers. The results show that the Nu number decreases via increasing the Ha number. It increases when the Ra number is increased. The maximum and minimum values of Nusselt occur at B = 0.2 and B = 0.8, respectively. Exerting an angle for magnetic flux leads to the improvement in thermal performance for all amount of B. The effects of Ha, nanofluid volume fraction, heat source size, location and angle of magnetic field on heat transfer, entropy generation, and thermal performance are completely studied and discussed.

Numerical simulation of MHD double diffusive natural convection and entropy generation in a wavy enclosure filled with nanofluid with discrete heating

A numerical investigation of entropy generation, heat and mass transfer is performed on steady double diffusive natural convection of water-based Al2O3 nanofluid within a wavy-walled cavity with a center heater under the influence of an uniform vertical magnetic field. The top horizontal wavy wall, left and right vertical walls of the enclosure are kept at low temperature and concentration of Tc and cc whereas central part of the bottom horizontal wall is maintained at high temperature and concentration of Th and ch and the remaining part is kept adiabatic where temperature and concentration gradient are taken as zero. The Bi-CGStab method and Tri-diagonal algorithm are used to solve the governing equations. The study has been performed for several relevant parameters such as Rayleigh number (103≤Ra≤105), Hartmann number (0≤Ha≤60), buoyancy ratio number (−2≤N≤2), volume fraction of nanoparticles (0.0≤ϕ≤0.2) and different undulation number of the upper wavy wall (n). The Prandtl number and Lewis number are kept fixed at Pr=6.2 and Le=2. The effect of these parameters are revealed in terms of streamlines, isotherms, isoconcentrations, entropy generation, average Nusselt number and Sherwood number. Results indicate that heat and mass transfer rate augment as Rayleigh number and volume fraction of nanoparticles increase and are found to drop with the increase in Hartmann number and buoyancy ratio.

Numerical investigation of entropy generation in microporous channel with thermal radiation and buoyancy force

Microporous channels found to have extensive applications in many fields of engineering, particularly in thermal and petrochemical engineering. In particular, the microelectromechanical systems are useful to develop a large number of microscopic devices and systems such as micromixture, microheat exchangers, microchannel heat sinks, microfuel cells. The present work aims to scrutinize the combined effects of thermal radiation and buoyancy force on entropy generation in magneto-hydrodynamic Jeffrey fluid flow through a vertical microporous channel. The model equations of linear momentum and energy balance are developed and tackled numerically using fourth-order Runge–Kutta method. The results are exhibited pictorially and discussed quantitatively for active parameters which emerged in the mathematical formulation. Validation with previously published work is included, and the current results are in good agreement. It is found that the effects of viscous dissipation and suction/injection on entropy generation in microchannel are important and should not be ignored. Further, it is noticed that the fluid temperature retards with an increasing value of suction and the effect is reversed in the case of injection.

Numerical investigation of entropy generation of turbulent flow in a novel outward corrugated tube

The present study numerically investigates the second law analysis of turbulent flow in novel outward helical corrugated tubes by using a Reynolds Stress Model (RSM). A case of a transverse corrugated tube and five cases of helical corrugated tubes with different height-to-diameter ratios and pitch-to-diameter ratios are examined with Reynolds number ranging from 3800 to 43,800 at a constant wall temperature condition. The results indicate that the secondary flow significantly increases the thermal and viscous dissipation irreversibilities. However, the spiral flow inhibits the secondary flow and the production of local entropy. The heat transfer effective zone (Belocal > 0.5) is mainly located at the sub-layer and buffer-layer, and the ineffective zone (Belocal < 0.2) is located at the turbulent severe pulsation zone. A comprehensive consideration of the total entropy generation number (Ns-tot) and average Bejan number (Beave) indicates that the optimal Re is less than 31,000 for all the cases although Re does not exceed 18,800 in the case of Hl/D = 0.15, pl/D = 1.0 and Hl/D = 0.10, pl/D = 0.5. Additionally, the helical corrugated tube exhibits an overall advantage when compared with a transverse corrugated tube with the same geometrical parameters.

Numerical Investigation of Entropy Generation in Stratified Thermal Stores

This paper investigates the nature of entropy generation in stratified sensible thermal energy stores (SSTES) during charging using a dimensionless axisymmetric numerical model of an SSTES. Time-varying dimensionless entropy generation rates and the cumulative entropy generation in SSTES were determined from finite volume computations. The aspect ratios (AR), Peclet numbers (PeD), and Richardson numbers (Ri), for the stores considered were within the ranges 1≤AR≤4, 5×103≤PeD≤100×103, and 10≤Ri≤104, respectively. Using the Bejan number (Be), the total entropy generation was shown to be almost entirely due to thermal effects in the SSTES. The Be is practically unity for most of the SSTES' charging duration. The contributions of radial thermal gradients to the thermal entropy generation were further shown to be largely negligible in comparison to the contributions of axial thermal gradients, except at low Ri. Entropy generation numbers, Ns, in the SSTES were also computed and found to increase with decreasing AR and PeD and with increasing Ri. PeD was found to have the most significant influence on Ns. Based on this axisymmetric analyses of time-varying entropy generation in SSTES, estimates have been obtained of (1) the relative significance of radial effects on entropy generation within SSTES and (2) the relative significance of viscous shear entropy generation mechanisms within SSTES.

Numerical investigation of entropy generation and heat transfer of pulsating flow in a horizontal channel with an open cavity

In this study, the entropy generation and the heat transfer of pulsating air flow in a horizontal channel with an open cavity heated from below with uniform temperature distribution are numerically investigated. A numerical method based on finite volume method is used to discretize the governing equations. At the inlet of the channel, pulsating velocity is imposed for a range of Strouhal numbers Stp from 0 to 1 and amplitude Ap from 0 to 0.5. The effects of the governing parameters, such as frequency and amplitude of the pulsation, Richardson number, Ri, and aspect ratio of the cavity, L/H on the flow field, temperature distribution, average Nusselt number and average entropy generation, are numerically analyzed. The results indicate that the heat transfer and entropy generation are strongly affected by the frequency and amplitude of the pulsation and this depends on the Richardson number and aspect ratio of the cavity. The pulsation is more effective with the aspect ratio of the cavity L/H = 1.5 in terms of heat transfer enhancement and entropy generation minimization.

Numerical investigation of entropy generation to predict irreversibilities in nanofluid flow within a microchannel: Effects of Brownian diffusion, shear rate and viscosity gradient

In the present contribution, irreversibilities caused by heat transfer and friction for the water-TiO2 nanofluid flow in a circular microchannel are investigated by evaluating entropy generation rates. The effects of viscosity gradient, non-uniform shear rate and Brownian diffusion on particle migration are taken into account in order to examine the effect of nanoparticle arrangement on entropy generation rates. The results show that nanoparticle migration alters concentration distribution and consequently, changes entropy generation rates. Nanoparticle migration increases concentration of the particles in central regions, and this migration is more noticeable for higher mean concentrations and larger particles. Thermal entropy generation rate intensifies with increasing wall heat flux and particle size while decreases with increasing concentration. Frictional entropy generation rate increases by concentration increment and decreases by particles enlargement, while it changes trivially by increasing wall heat flux. Frictional entropy generation rate is larger than thermal entropy generation rate in the microchannel under study and therefore, total entropy generation mostly stems from friction. Thus, total entropy generation rate decreases by particles enlargement, which is a positive result according to second law of thermodynamics. Eventually, a model for entropy generation rates is developed using the numerical data by means of Artificial Neural Network (ANN).

Entropy generation of supercritical water in a vertical tube with concentrated incident solar heat flux on one side

This paper presents the results of a numerical investigation of entropy generation of supercritical water in a vertical tube with concentrated incident solar heat flux on one side. The characteristics of heat transfer and pressure drop in the tube are analyzed first. The decrease in shear stresses near the pseudo-critical region results in the decrease in turbulence production and the increase in friction factor. It is the common cause of heat transfer deterioration and an abrupt increase in pressure drop near the pseudo-critical region. Entropy generation mainly depends on the temperature gradient along the vertical tube’s radial direction which is due to the thickness of the thermal boundary layer and the intensity of secondary flow. The results further show that entropy generation of supercritical water in a vertical tube with concentrated incident solar heat flux on one side decreases with increasing mass flux and decreasing incident heat flux. In addition, to balance the minimum irreversible losses and hydraulic resistance in the tube in a central receiver, the relationship between incident flux and mass flux is determined.

Numerical investigation of entropy generation in microchannels heat sink with different shapes

Entropy generation of 3D cross sections circular, square, and hexagon shapes microchannel heat sinks (MCHS) were numerically performed. The governing equations (continuity, momentum and energy) along with the boundary conditions and the study state conjugate heat transfer problem were solved using the finite volume method (FVM). The Reynolds number in the range of 100 to 1600 and heat flux of 125, 150, 175 and 200 kW/m2 were covered in this study. The overall entropy generation rate and entropy generation number are obtained by integrating the volumetric rate components over the entire heat sink. The results indicated that entropy generation decreases with increases of the Reynolds number. Decreasing the heat flux led to decreasing entropy generation. The square microchannel heat sink has the lowest entropy generation and entropy generation number

Entropy generation analysis of a confined slot impinging jet in a converging channel for a shear thinning nanofluid

In this article, numerical investigation of entropy generation due to heat transfer and fluid fiction is performed on a confined slot impinging jet. The non-Newtonian nanofluid is an aqueous solution of 0.5wt% carboxymethyl cellulose (CMC) with 10nm diameter TiO2 nanoparticles. Two-dimensional laminar flow is considered and a constant temperature is applied on the impingement surface. The nanofluid, as well as the base fluid, exhibits pseudoplastic behavior. The thermal and rheological properties of the base fluid and nanofluid are temperature-dependent. In this paper, correlations for the power law and consistency indices, as well as thermal conductivity, as a function of temperature of the fluid based on some existing experimental data in the literature are developed. In order to consider the effect of converging angle and groove amplitude on entropy generation in the channel, the numerical simulation is performed for different converging angles between 0° and 5° and groove amplitudes in the range of 0–0.007m. The results showed that a large portion of entropy generation is concentrated in the impingement surface. The total entropy generation increases with increasing volume fraction and converging angle. The minimum value of exergy loss tends to occur at higher converging angles by increasing the Reynolds number and jet-impingement surface to distance ratio. Also, the exergy loss decreases with the concave groove amplitudes.

Second law analysis in double diffusive convection through an inclined porous cavity

A numerical investigation of entropy generation in steady–unsteady double diffusive convection through an inclined porous enclosure is carried on. Expressions of different irreversibilities are firstly derived. Then, effects of the enclosure inclination angle, α, and the enclosure aspect ratio, A, on entropy generation, heat and mass transfer, and fluid flow are analysed. It was found that entropy generation exhibits an oscillatory behaviour for lower (Da=10−4) and higher (Da=10−2) medium permeability values, when α≠0°. Minimum entropy generation is found at the aspect ratio A=0.5 and 1, for Da=10−2 and 10−4, respectively. More details about the influence of the above mentioned operating parameters on entropy generation, heat and mass transfer and fluid flow are discussed and graphically presented.

Numerical investigation of entropy generation in laminar forced convection flow over inclined backward and forward facing steps in a duct under bleeding condition

A numerical investigation of entropy generation in laminar forced convection of gas flow over a recess including two inclined backward and forward facing steps in a horizontal duct under bleeding condition is presented. For calculation of entropy generation from the second law of thermodynamics in a forced convection flow, the velocity and temperature distributions are primary needed. For this purpose, the two-dimensional Cartesian coordinate system is used to solve the governing equations which are conservations of mass, momentum and energy. These equations are solved numerically using the computational fluid dynamic techniques to obtain the temperature and velocity fields, while the blocked region method is employed to simulate the inclined surface. Discretized forms of these equations are obtained by the finite volume method and solved using the SIMPLE algorithm. The numerical results are presented graphically and the effects of bleeding coefficient and recess length as the main parameters on the distributions of entropy generation number and Bejan number are investigated. Also, the effect of Reynolds number and bleeding coefficient on total entropy generation which shows the amount of flow irreversibilities is presented for two recess length. The use of present results in the design process of such thermal system would help the system attain the high performance during exploitation. Comparison of numerical results with the available data published in open literature shows a good consistency.

Numerical investigation of entropy generation in a parabolic trough receiver at different concentration ratios

This paper presents results of a numerical analysis of entropy generation in a parabolic trough receiver at different concentration ratios, inlet temperatures and flow rates. Using temperature dependent thermal properties of the heat transfer fluid, the entropy generation due to heat transfer across a finite temperature difference and entropy generation due to fluid friction in the receiver has been determined. Results show a reduction in the entropy generation rate as the inlet temperature increases and an increase in the entropy generation rate as the concentration ratio increases. Results further show that, there is an optimal flow rate at which the entropy generated is a minimum, for every combination of concentration ratio and inlet temperature. The optimal flow rates at which the entropy generated is minimum are presented for different flow rate and concentration ratio, and the results are the same irrespective of the inlet temperature considered. For the range of inlet temperatures, flow rates and concentration ratios considered, the Bejan number, which measures the contribution of entropy generation due to heat transfer irreversibility to the total entropy generation rate is about 1 at low flow rates and is between 0 and 0.24 at the highest flow rate.

Numerical Investigation of Entropy Generation in Unsteady MHD Generalized Couette Flow with Variable Electrical Conductivity

The thermodynamic second law analysis is utilized to investigate the inherent irreversibility in an unsteady hydromagnetic generalized Couette flow with variable electrical conductivity in the presence of induced electric field. Based on some simplified assumption, the model nonlinear governing equations are obtained and solved numerically using semidiscretization finite difference techniques. Effects of various thermophysical parameters on the fluid velocity, temperature, current density, skin friction, the Nusselt number, entropy generation number, and the Bejan number are presented graphically and discussed quantitatively.