Dimensionless Entropy Generation Number Research Articles

Comparison of using air, CO2 and helium for the cooling of square-shaped electronic parts: CFD study with entropy generation analysis

Numerical simulation has been used in the current work to investigate improving the cool-down of electronic parts of cubical form involving dummy parts within a rectangular duct. Three working fluids (air, CO2, and helium) were used to cool 12 electrical chip arrays in the duct. The simulation investigates the effects of cooling fluid type and shifting hot element placements on whole cooling functioning at various Reynolds numbers. Also, the impact of the distance among electronic parts is researched. This is accomplished by moving the heat sources while leaving other components in their original positions as dummies to preserve the flow characteristics. The Reynolds number falls between (500-19000). The dimensionless entropy generation number reduces with the rise of the Reynolds number, while the pumping power ratio increases. It is determined that the dimensionless entropy generation computed for the case of constant viscosity of air yields slightly greater values than those obtained for the case of temperature-dependent viscosity. A high level of agreement in the experimental work is used to verify the standard k-model.

Influence of power-law index and hybrid-nanoparticles concentrations on the behavior of non-Newtonian hybrid nanofluid inside water solar collector

Nowadays, there is great attention given to solar collectors (SCs) for their important applications based on the advantages of nanotechnology and solar radiation. Hybrid nanofluid (HNF) is our first option due to its thermophysical properties that help in improving the overall performance, unlike other nanofluids. This paper gives a detailed novel analysis of SCs with the existence of Newtonian, power-law HNF in unsteady conditions and a three-dimensional model under the consideration of Brownian motion and thermophoresis parameter. In this research, the group transformation method (GTM) and similarity transformation steady state fluid dynamics are used to transform the mathematical model into a simpler system. This coupled system of ordinary differential equations with the related functions, dimensionless entropy generation and Bejan number is achieved at two cases of power-law index. The impact of involved parameters on velocity profile, temperature distribution, concentration field, entropy output of the system and Bejan number is depicted prominently by various graphs. The fluid velocity shows improvement with higher values of power-law index and shape factor, while it diminishes with magnetic parameter and Prandtl number. Enhancing the values of magnetic field and shape factor, results in increase of temperature characteristic which decreases with Prandtl number and power-law index. Increment in the concentration ratio parameter leads to maximize the entropy generation, whereas entropy generation diminishes with higher values of temperature ratio and magnetic parameter. The obtained results and the previously published work are compared qualitatively and quantitatively to each other to validate that the applied method is more efficient. It is predicted that the Nusselt number improves by 28.18% when the Prandtl number is taken range [Formula: see text]. The percentage of increasing in Sherwood number is noted to be 18.61% for range [Formula: see text] of Brownian motion parameter.

Constructal Optimizations of Line-to-Line Vascular Channels with Turbulent Convection Heat Transfer.

The multi-scale line-to-line vascular channels (LVCs) widely exist in nature because of their excellent transmission characteristics. In this paper, models of LVCs with turbulent convection heat transfer are established. Based on constructal theory and the entropy generation minimization principle, the constructal optimizations of LVCs with any order are conducted by taking the angles at bifurcations as the optimization variables. The heat flux on the channel wall per unit length is fixed and uniform. The areas occupied by vasculature and the total volumes of channels are fixed. The analytical expressions of the optimal angles, dimensionless total entropy generation rate and entropy generation number (EGN) of LVCs with any order versus dimensionless mass flow rate are obtained, respectively. The results indicate that the dimensionless total entropy generation rate of LVCs with any order can be significantly decreased by optimizing the angles of LVCs, which is significantly more when the order of LVCs is higher. As the dimensionless mass flow rate increases, the optimal angles of LVCs with any order remain unchanged first, then the optimal angles at the entrance (root) increase, and the other optimal angles decrease continuously and finally tend to the respective stable values. The optimal angles of LVCs continue to increase from the entrance to the outlet (crown), i.e., the LVCs with a certain order gradually spread out from the root to the crown. The dimensionless total entropy generation rate and EGN of LVCs first decrease and then increase with the growth of the dimensionless mass flow rate. There is optimal dimensionless mass flow rate, making the dimensionless total entropy generation rate and the EGN reach their respective minimums. The results obtained herein can provide some new theoretical guidelines of thermal design and management for the practical applications of LVCs.

Natural convection of hybrid nanofluid heat transport and entropy generation in cavity by using Lattice Boltzmann Method

A mesoscopic study of natural convection due to MWCNT-Fe3O4/Water hybrid nanofluid is conducted utilizing the Lattice Boltzmann Method. The test fluid is filled in a differentially heated rectangular enclosure. Effects of aspect ratio in the range of 0.5–2.0, Rayleigh number varying from 103 to 105 and nanocomposite volume fraction on heat and fluid flow characteristics and entropy generation have been illustrated. It is observed that the mean Nusselt number rises with the increase in Rayleigh number, while it falls as the aspect ratio increases. However, the mean Nusselt number enhances with the increase in MWCNT-Fe3O4 volume fraction up to 0.001. On further increasing the volume fraction, the mean Nusselt number shows either no significant rise or deterioration for the case of MWCNT-Fe3O4 nanocomposite. The dimensionless entropy generation number rises with the increase in the Rayleigh number. However, it falls with an increase in aspect ratio and dimensionless temperature difference. Interestingly in the case of increasing nanoparticle loading fraction, entropy generation number augments first, attains a maximum at 0.001 ​vol fraction of nanocomposite, and then it decreases. Nevertheless, at the low Rayleigh number, it keeps on rising with an increase in nanocomposite volume fraction. The best thermal performance is obtained for the cavity of 0.5 aspect ratio. A correlation for the mean Nusselt number is proposed.

Entropic analysis of a double helical tube heat exchanger including circular depressions on both inner and outer tube

In this research, entropic analysis of a double helical tube heat exchanger including circular depressions on both inner tube and outer tube is provided. Experimentally validated 3D numerical simulation is employed to reach the aim of this study. Entropic characteristics of four cases are investigated and reported. In case “a” both inner tube and outer tube are smooth. In case “b”, circular depressions are created on only inner tube while in case “c” both tubes contain circular depression. Case “d” is the same as case “c” while the depression arrangement is different from case “c”. Dimensionless entropy generation and dimensionless Nu number are used to evaluate the proposed designs based on the first and second laws of thermodynamics. Moreover, heat transfer improvement (HTI) factor is adopted to consider the impacts of said two parameters simultaneously. Results demonstrate that, although creating circular depressions on both tubes significantly improves the heat transfer characteristics of the heat exchanger, it increases the entropy generation level of heat exchanger as well. Case “d” in which the location of any circular depression of the outer tube is placed between any two continuous depressions of the inner tube, gives the highest thermal performance and also entropy generation.

Stagnation-Point Flow of Magneto-Williamson Nanofluid over a Stretching Material with Ohmic Heating and Entropy Analysis

This study communicates stagnation-point flow in magneto-Williamson nanofluid along a convectively heated nonlinear stretchable material in a porous medium. The impacts of Joule heating, thermophoresis together with Brownian motion are also checked in this investigation. In addition, thermodynamic second law is applied to develop entropy generation analysis of crucial parameters with identification of parameters capable of minimizing energy loss in the system. The transport equations are simplified into ordinary differential equations and then integrated numerically using Runge-Kutta-Fehlberg with shooting technique. The effects of the emerging parameters on the dimensionless velocity, temperature, concentration and entropy generation number are publicized through tables and graphs with appropriate discussions. In the limiting conditions, the results are found to conform accurately with published studies in the literature. It is found that the viscous drag can be reduced by lowering the magnitude of Weissenberg number, magnetic field and Darcy parameters while heat transfer at the surface improves in the presence of surface convection, temperature ratio and thermal radiation parameters. Besides, the analysis reveals that entropy generation can be minimized by lowering the magnitude of magnetic field, Schmidt number and surface convection parameters. The reduction in these parameters will promote efficient performance of thermal devices. More so, the results obtained in this study can be useful for the construction of appropriate thermal devices for use in energy and electronic devices.

Second law analysis of a mixture of ethylene glycol/water flow in modified heat exchanger tube by passive heat transfer enhancement technique

This experimental study presents the entropy generation analysis of diverging, converging–diverging and converging conically coiled wire inserts in a heat exchanger tube using ethylene glycol and water mixtures as a working fluid. The experiments are performed with three different volumetric ratios of ethylene glycol and water mixtures and two different pitch ratios of diverging, converging–diverging and converging conically coiled wire inserts. The effects of conically coiled wire inserts on the dimensionless entropy generation number and Bejan number are discussed for the Reynolds number ranging from 4627 to 25,099. The results indicated that the converging conically coiled wire inserts generate higher entropy rates than the other insert types. It is pointed out that the entropy generation numbers for the diverging conically coiled wire inserts used tube reach the lowest value for each fluid type. The experimental results revealed that because the friction forces increase with the use of ethylene glycol, the Bejan number is lower for the fluids with 20 and 40% ethylene glycol than pure water. The highest Bejan number of 0.968 is determined for the smooth tube with pure water at the lowest Reynolds number. The lowest Entropy generation number of 0.42 is obtained for a pure water as a working fluid and diverging conically coiled wire insert with pitch ratio of 2 at the Reynolds number 6882, and the highest entropy generation number of 0.94 is observed while the converging conically coiled wire insert with pitch ratio of 3 is used in tube flow at Reynolds number of 22,230 for fluid type with 60% water and 40% ethylene glycol.

Minimization of Entropy Generation in MHD Mixed Convection Flow with Energy Dissipation and Joule Heating: Utilization of Sparrow-Quack-Boerner Local Non-Similarity Method

This article aims to present the non-similar solution of MHD mixed convection flow using the Sparrow-Quack-Boerner local non-similarity method. Entropy analysis is also performed in the presence of energy dissipation and Joule heating. The buoyancy parameter is chosen as the non-similarity variable and the equations are derived up to the second level of truncation. The dependency of dimensionless velocity profile, temperature distribution, Bejan and entropy generation number on physical parameters has been discussed. As far as the knowledge of the authors is concerned, no attempt has been made on the entropy analysis of MHD mixed convection flow by the local non-similarity method.

Experimental investigation of first and second laws in a direct absorption solar collector using hybrid Fe3O4/SiO2 nanofluid

In this study, energy and entropy analysis of a residential-type direct absorption solar collector using hybrid Fe3O4/SiO2 nanofluid is evaluated experimentally. The hybrid nanofluid samples are prepared in the different volume ratios of Fe3O4/SiO2 (25:75, 50:50 and 75:25) and different volume fractions (500 ppm, 1000 ppm and 2000 ppm). The appropriate nanofluid samples for using as the working fluid of the collector are chosen based on the results of stability and optical properties of nanofluid. Then, outdoor thermal performance of collector is investigated using the experimental setup based on EN12975-2. Measurement of nanofluid optical properties using the spectrophotometry method shows that the extinction coefficient of 2000 ppm hybrid Fe3O4/SiO2 nanofluid is on average 10 cm−1 higher than that of the base fluid. Results of energy analysis display that the collector efficiency is increased by mass flow rate and volume fraction of nanofluid asymptotically. The asymptotic value is about 83% for 2000 ppm hybrid Fe3O4/SiO2 nanofluid. The findings indicate that the variation of exergy efficiency of a direct absorption solar collector with the volume fraction and mass flow rate is similar to energy efficiency. The enhancement of exergy efficiency is 66.4% for mass flow rates of 0.0225 kg s−1 by increasing the volume fraction from 0 to 2000 ppm. It is also observed that dimensionless entropy generation number is decreased by nanofluid volume fraction and by mass flow rate. The lowest entropy generation number is obtained in the mass flow rate of 0.0225 kg s−1 and the volume fraction of 2000 ppm. The variation of Bejan number by volume fraction shows that the contribution of pressure drop in entropy generation is insignificant.

Entropy generation in MHD mixed convection stagnation-point flow in the presence of joule and frictional heating

This article looks at the second law analysis of MHD boundary layer stagnation-point flow past over linearly stretched sheet. The thermal boundary condition is supposed to be non-isothermal and the effects of friction and Joule heating have been analysed. By using similarity transformations, the model nonlinear partial differential equations in two independent variables are reduced to ordinary differential equations. The numerical techniques, namely shooting and fourth order Runge-Kutta are used to give a numerical solution. An expression for dimensionless entropy generation and Bejan number are obtained and computed using velocity and temperature profiles. The main objective of this article is to analyse the effects of a magnetic parameter, Prandtl number, Eckert number, stretching parameter, mixed convection parameter and dimensionless temperature parameter on the volumetric rate of entropy production and Bejan number. It is found that entropy generation increases with enhancing values stretching parameter and decrease with the increasing values of dimensionless temperature parameter.

Thermo-hydraulic characteristics and second-law analysis of a single-phase natural circulation loop with end heat exchangers

In this work, a three-dimensional transient numerical simulation of heat transfer characteristics in a single-phase natural circulation loop (SPNCL) with water as the working fluid in the loop and end heat exchangers is performed. A 3-D computational model of a SPNCL with end heat exchangers is developed. The second-law analysis for the SPNCL is presented and total entropy generation is given. Meanwhile, the transient response is obtained based on the finite difference method solving the one-dimensional momentum and energy equations. Firstly, a mesh dependence test and a model verification with the laminar correlation presented by Vijayan are conducted. Then the effects of driving temperature difference and heating or cooling fluid velocity on the thermos-hydraulic performance and dimensionless entropy generation number are investigated by fixing the cooling fluids temperature of 273K. Results show that a stable flow can be reached for all the cases. The formation of the stable natural circulation is the consequence of coupling between heating and cooling fluid. The time of quiescent state is relatively short due to the thermal asymmetry of the SPNCL. The mass flow rate and heat transfer rate at steady state increase with the increase of driving temperature difference and heating or cooling fluid velocity. It is obviously shown the internal heat transfer coefficient is mainly dependent on the driving temperature difference and increases with the increase of driving temperature difference. The thermal effectiveness and dimensionless entropy generation number also increase with the increase of driving temperature difference and heat transfer irreversibility is dominated in total irreversibility. Moreover, the time evolution of dimensionless mass flow rate shows a damped oscillation behavior.

Entropy generation analysis of a microchannel-condenser for use in a vapor compression refrigeration cycle

Dimensionless entropy generation number in the microchannel condenser of a vapor compression refrigeration cycle is investigated. An air cooled, brazed aluminum parallel flow heat exchanger is considered as the condenser with R-134a as the refrigerant. While the effects of the fin pitch, fin height, louver angle and the air mass flow rate are investigated for the air side, the effect of the channel diameter is examined for the refrigerant side. The analysis is performed segment by segment for the superheated, two phase and subcooled regions using well-established empirical correlations. A mapping study is presented for the variation of entropy generation number with the mentioned parameters. The optimum air mass flow rate interval is found to be between 0.055 and 0.1 kgs−1 for a given fin pitch interval of 1–1.6 mm. This range is within the operating limits of air fans in the market for this size. In this operating range, the optimal dimensions giving the minimum entropy generation numbers are presented. The entropy generation number distribution is given based on the pressure drop, heat transfer or the refrigerant state in the heat exchanger considering superheated, two phase, and subcooled regions. The entropy generation number due to pressure drop on the air side becomes dominant after a mass flow rate around 0.08 kgs−1. Hence, an optimum air mass flow rate generating the minimum entropy generation number is sought for different sizes of the condenser. The condenser length is variable in the range of 84.3–80.6 mm for the mentioned optimal air mass flow rate interval. The condenser height changes depending on desired operational conditions, and it is determined to be 112.5 mm for the fixed values given in the study. The study is unique in the literature in pursuing an entropy generation number mapping study for microchannel two-phase flow in air cooled heat exchangers.

Transient Velocity And Steady State Entropy Generation In A Microfluidic Couette Flow Containing Charged Nano Particles

An analysis has been provided to determine the transient velocity and steady state entropy generation in a microfluidic Couette flow influenced by electro-kinetic effect of charged nanoparticles. The equation for calculating the Couette flow velocity profile is derived for transient flow. The solutions for momentum and energy equations are used to get the exact solution for the dimensionless velocity ratio and dimensionless entropy generation number. The effects of the dimensionless entropy generation number, Bejan number, irreversibility ratio, entropy generation due to fluid friction and due to heat transfer on dimensionless time, relative channel height, Brinkman number, dimensionless temperature ratio, nanoparticle volume fraction are analyzed.

Entropy generation of nanofluid in presence of magnetic field using Lattice Boltzmann Method

In this paper magnetohydrodynamic free convection flow of CuO–water nanofluid in a square enclosure with a rectangular heated body is investigated numerically using Lattice Boltzmann Method (LBM) scheme. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo–Kleinstreuer–Li) correlation. The influence of pertinent parameters such as Hartmann number, nanoparticle volume fraction and Rayleigh number on the flow, heat transfer and entropy generation have been examined. The results show that the heat transfer rate and Dimensionless entropy generation number increase with increase of the Rayleigh number and nanoparticle volume fraction but it decreases with increase of the Hartmann number.

Numerical study of entropy generation for forced convection flow and heat transfer of a Jeffrey fluid over a stretching sheet

Entropy generation for the steady two-dimensional laminar forced convection flow and heat transfer of an incompressible Jeffrey non-Newtonian fluid over a linearly stretching, impermeable and isothermal sheet is numerically investigated. The governing differential equations of continuity, momentum and energy are transformed using suitable similarity transformations to two nonlinear coupled ordinary differential equations (ODEs). Then the ODEs are solved by applying the numerical implicit Keller’s box method. The effects of various parameters of the flow and heat transfer including Deborah number, ratio of relaxation to retardation times, Prandtl number, Eckert number, Reynolds number and Brinkman number on dimensionless velocity, temperature and entropy generation number profiles are analyzed. The results reveal that the entropy generation number increases with the increase of Deborah number while the increase of ratio of relaxation to retardation times causes the entropy generation number to reduce. A comparative study of the numerical results with the results from an exact solution for the dimensionless velocity gradient at the sheet surface is also performed. The comparison shows excellent agreement within 0.05% error.

Optimal design of vertical ground heat exchangers by using entropy generation minimization method and genetic algorithms

This paper presents the development and validation of an optimal design methodology for vertical U-tube ground heat exchangers (GHEs) used in HVAC systems. The dimensionless entropy generation number obtained by scaling the entropy generation due to heat transfer and pressure drop, on the ratio of the heat transfer rate to the average fluid temperature of vertical GHEs is employed as the objective function. Five design variables are first selected based on the global sensitivity analysis and then optimized by a genetic algorithm optimization technique. The entropy generation process combines the heat transfer and fluid mechanics with thermodynamic analysis. A case study shows that this optimal design approach can decrease the total system cost (i.e. the upfront cost and 10-year operation cost) by 5.5%, compared with the original design. The entropy generation number (EGN) of the optimal design case is 12.2% less than that of the base design case. From the thermo-economic aspect, decreasing the upfront cost is more important than decreasing the operational cost for the case studied. The results also demonstrate the effectiveness and feasibility of using the entropy generation minimization method for optimal design of vertical GHEs.

Entropy Generation Analysis of Power-Law Non-Newtonian Fluid Flow Caused by Micropatterned Moving Surface

In the present study, the first and second law analyses of power-law non-Newtonian flow over embedded open parallel microchannels within micropatterned permeable continuous moving surface are examined at prescribed surface temperature. A similarity transformation is used to reduce the governing equations to a set of nonlinear ordinary differential equations. The dimensionless entropy generation number is formulated by an integral of the local rate of entropy generation along the width of the surface based on an equal number of microchannels and no-slip gaps interspersed between those microchannels. The velocity, the temperature, the velocity gradient, and the temperature gradient adjacent to the wall are substituted into this equation resulting from the momentum and energy equations obtained numerically by Dormand-Prince pair and shooting method. Finally, the entropy generation numbers, as well as the Bejan number, are evaluated. It is noted that the presence of the shear thinning (pseudoplastic) fluids creates entropy along the surface, with an opposite effect resulting from shear thickening (dilatant) fluids.

Forced convection in micro-channels filled with porous media in local thermal non-equilibrium conditions

An analytic solution on fully developed forced convection, in parallel plates porous micro-channels is accomplished in Local Thermal Non-Equilibrium (LTNE) condition. The analysis is realized in steady state regime for rarefied gaseous slip flows between two parallel plates with assigned heat flux. The Darcy–Brinkman model is considered in the momentum equation and two energy equations are used to evaluate solid and fluid temperatures. The entropy generation analysis is performed and the total entropy generation number is evaluated as a function of the different dimensionless parameters. The effect of tangential momentum and thermal accommodation coefficients are examined. Results are reported in terms of average Nusselt numbers, dimensionless temperature profiles and total entropy generation number as a function of Biot number (Bi), effective thermal conductive ratio (κ), Darcy number (Da), accommodation coefficients (tangential momentum and thermal) and Knudsen number. Results show that heat transfer increases as Bi increases and reaches asymptotic values. Different trends are observed with respect to tangential momentum accommodation coefficient for assigned thermal accommodation. Total entropy generation number as a function of Da−0.5 presents minimum values with respect to Bi, accommodation coefficients and Brinkman number.

Reducing Entropy Generation in MHD Fluid Flow over Open Parallel Microchannels Embedded in a Micropatterned Permeable Surface

The present study examines embedded open parallel microchannels within a micropatterned permeable surface for reducing entropy generation in MHD fluid flow in microscale systems. A local similarity solution for the transformed governing equations is obtained. The governing partial differential equations along with the boundary conditions are first cast into a dimensionless form and then the reduced ordinary differential equations are solved numerically via the Dormand-Prince pair and shooting method. The dimensionless entropy generation number is formulated by an integral of the local rate of entropy generation along the width of the surface based on an equal number of microchannels and no-slip gaps interspersed between those microchannels. Finally, the entropy generation numbers, as well as the Bejan number, are investigated. It is seen that surface-embedded microchannels can successfully reduce entropy generation in the presence of an applied magnetic field.

Second law analysis for Poiseuille flow of immiscible micropolar fluids in a channel

In this paper, the problem of steady Poiseuille flow of two immiscible incompressible micropolar fluids between two horizontal parallel plates of a channel with constant wall temperatures is studied in terms of entropy generation. The flow is assumed to be governed by Eringen’s micropolar fluid flow equations. The flow region is divided into two zones, the flow of the heavier fluid taking place in the lower zone-I. No slip condition is taken on the plates and at the interface continuity of velocity, micro-rotation, temperature, heat flux and shear stresses is imposed. The velocity, micro-rotation and temperature fields are derived analytically. The dimensionless quantities-entropy generation number (Ns), Bejan number (Be) and irreversibility ratio (ϕ) are analytically derived. The effects of material parameters like micropolarity (ci), couplestress (si) on the velocity, micro-rotation and temperature are investigated. The derived equation for the dimensionless entropy generation number is used to interpret the relative importance of frictions to conduction by varying viscous dissipation parameter. The entropy generation near the plates increases more rapidly in fluid I than in fluid II as viscous dissipation effects become more important in zone I. The velocity and temperature profiles are found to be in good agreement with the distributions of the dimensionless entropy generation number (Ns).