Entropy Generation In Natural Convection Research Articles

Minimization of entropy generation in natural convection using optimum isothermal heaters: CFD analysis

Minimization of entropy generation in natural convection using optimum isothermal heaters: CFD analysis

Non-Newtonian effect on heat transfer and entropy generation of natural convection nanofluid flow inside a vertical wavy porous cavity

A numerical study on heat transfer and entropy generation in natural convection of non-Newtonian nanofluid flow has been explored within a differentially heated two-dimensional wavy porous cavity. In the present study, copper (Cu)–water nanofluid is considered for the investigation where the specific behavior of Cu nanoparticles in water is considered to behave as non-Newtonian based on previously established experimental results. The power-law model and the Brinkman-extended Darcy model has been used to characterize the non-Newtonian porous medium. The governing equations of the flow are solved using the finite volume method with the collocated grid arrangement. Numerical results are presented through streamlines, isotherms, local Nusselt number and entropy generation rate to study the effects of a range of Darcy number (Da), volume fractions (ϕ) of nanofluids, Rayleigh numbers (Ra), and the power-law index (n). Results show that the rate of heat transfer from the wavy wall to the medium becomes enhanced by decreasing the power-law index but increasing the volume fraction of nanoparticles. Increase of porosity level and buoyancy forces of the medium augments flow strength and results in a thinner boundary layer within the cavity. At negligible porosity level of the enclosure, effect of volume fraction of nanoparticles over thermal conductivity of the nanofluids is imperceptible. Interestingly, when the Darcy–Rayleigh number Ra^*gg 10, the power-law effect becomes more significant than the volume fraction effect in the augmentation of the convective heat transfer process. The local entropy generation is highly dominated by heat transfer irreversibility within the porous enclosure for all conditions of the flow medium. The particular wavy shape of the cavity strongly influences the heat transfer flow pattern and local entropy generation. Interestingly, contour graphs of local entropy generation and local Bejan number show a rotationally symmetric pattern of order two about the center of the wavy cavity.

Prenos toplote i stvaranje entropije za prirodnu konvekciju fluida adijabatskim preprekama unutar šupljine zagrejane na levoj strani zida

By using finite difference method, the problem of heat transfer and entropy generation for natural convection of a fluid inside a square cavity with inner adiabatic bodies has been investigated numerically. Calculations have been made for Rayleigh numbers ranging from 102 to 5·104 for two obstacles with different heights. Results are presented as streamlines, isotherm contours and Nusselt number for Prandtl number of 0.71 (assuming the cavity is filled with air). The obtained results demonstrate the effects of pertinent parameters on the fluid flow, thermal fields and heat transfer inside the cavity. The results show that the heat transfer rates generally increase with the shrink of the obstacle size and with the increase of Rayleigh number. The entropy generation is higher at locations with large temperature gradients. Excellent agreement is obtained with previous results in the literature.

Unsteady natural convection with entropy generation in partially open triangular cavities with a local heat source

Purpose The main aim of this work is to perform a numerical analysis on natural convection with entropy generation in a partially open triangular cavity with a local heat source. Design/methodology/approach The unsteady governing dimensionless partial differential equations with corresponding initially and boundary conditions were numerically solved by the finite difference method of the second-order accuracy. The effects of dimensionless time is studied, and other governing parameters are Rayleigh number (Ra = 103 − 105), Prandtl number (Pr = 6.82), heater length (w/L = 0.2, 0.4 and 0.6) and distance of heater ratio (δ/L = 0.3). Findings An increase in the Rayleigh number leads to an increment of the fluid flow and heat transfer rates. Average Bejan number decreases with Ra as opposed to the average Nusselt number and average entropy generation. High values of Ra characterize a formation of long-duration oscillating behavior for the average Nusselt number and entropy generation. Originality/value The originality of this work is to analyze the entropy generation in natural convection in a one side open and partial heater-located cavity. This is a good application for electronical systems or building design.

Natural convection of nanofluid inside a wavy cavity with a non-uniform heating

PurposeThe main purpose of this numerical study is to study on entropy generation in natural convection of nanofluid in a wavy cavity using a single-phase nanofluid model.Design/methodology/approachThe cavity is heated non-uniformly from the wavy wall and cooled from the right side while it is insulated from the horizontal walls. The physical domain of the problem is transformed into a rectangular geometry in the computational domain using an algebraic coordinate transformation by introducing new independent variables ξ and η. The governing dimensionless partial differential equations with corresponding initially and boundary conditions were numerically solved by the finite difference method of the second-order accuracy. The governing parameters are Rayleigh number (Ra = 1000-100000), Prandtl number (Pr = 6.82), solid volume fraction parameter of nanoparticles (φ = 0.0-0.05), aspect ratio parameter (A = 1), undulation number (κ = 1-3), wavy contraction ratio (b = 0.1-0.3) and dimensionless time (τ = 0-0.27).FindingsIt is found that the average Bejan number is an increasing function of nanoparticle volume fraction and a decreasing function of the Rayleigh number, undulation number and wavy contraction ratio. Also, an insertion of nanoparticles leads to an attenuation of convective flow and enhancement of heat transfer.OriginalityThe originality of this work is to analyze the entropy generation in natural convection within a wavy nanofluid cavity using single-phase nanofluid model. The results would benefit scientists and engineers to become familiar with the flow behaviour of such nanofluids, and will be a way to predict the properties of this flow for the possibility of using nanofluids in advanced nuclear systems, in industrial sectors including transportation, power generation, chemical sectors, ventilation, air-conditioning, etc.

Role of various concave/convex walls exposed to solar heating on entropy generation during natural convection within porous right angled triangular enclosures

The solar heating of the inclined wall has the direct application for the processing of various porous materials. Analysis of natural convection is carried out for the built structure where the right wall is exposed to the sun and the left wall is exposed to the cold ambience in the presence of the bottom adiabatic wall. The current work also involves with the study of the entropy generation for natural convection in porous right angled triangular enclosures with the concave/convex right wall. The finite element simulations are performed for a wide range of Darcy number (10-5⩽Dam⩽10) at a representative high Rayleigh number (Ram=106) for various fluids of industrial importance (Prm=7.2: saline water, 0.7: air and 0.01: molten metal). An extensive investigation on the effect of Dam for the entropy generation due to heat transfer (Sθ) and fluid friction (Sψ) is carried out for various cases of wall curvatures. In addition, the total entropy generation rate (Stotal), average Bejan number (Beav) and average Nusselt number (Nul‾) are presented for various Dam and Prm. Overall, the built structure with the concave right wall (case 1) may be recommended for the thermal processing of fluids of all Prm at all Dam via the solar heating on the curved wall.

Analysis of Entropy Generation in Natural Convection of Nanofluid inside a Square Cavity Having Hot Solid Block: Tiwari and Das’ Model

A computational work has been performed in this study to investigate the effects of solid isothermal partition insertion in a nanofluid filled cavity that is cooled via corner isothermal cooler. Mathematical model formulated in dimensionless primitive variables has been solved by finite volume method. The study is performed for different geometrical ratio of solid inserted block and corner isothermal cooler, Rayleigh number and solid volume fraction parameter of nanoparticles. It is observed that an insertion of nanoparticles leads to enhancement of heat transfer and attenuation of convective flow inside the cavity.

Numerical Study of Entropy Generation for Natural Convection in Rectangular Cavity with Circular Corners

This article numerically studies entropy generation due to natural convection in a rectangular cavity with circular corners. In this work, in order to solve the governing equations, an explicit finite-volume procedure and a time-marching method are utilized. Also, instead of the conventional algorithms of SIMPLE, SIMPLEM, and SIMPLEC, an artificial compressibility technique is applied for coupling the continuity to the momentum equations. Entropy generation, as a representation of irreversibility and efficiency loss in engineering heat transfer processes, is analyzed in detail. In this work, effects of the radius of walls corner, Rayleigh number, and distribution ratio on total entropy generation, Nusselt number, and Bejan number are also evaluated. The results show that entropy generation decreases with the increase of the radius of the walls’ corner and increases with the increase of Rayleigh number, aspect ratio, and irreversibility ratio.

Analysis of thermal efficiency via analysis of heat flow and entropy generation during natural convection within porous trapezoidal cavities

Thermal management via distributions of heatlines and entropy generation for natural convection within trapezoidal cavities in presence of hot left wall, cold right wall and adiabatic horizontal walls has been studied in this article. Heat flow visualization has been carried out via heatline concept. Galerkin finite element method has been used to analyze streamlines, isotherms, heatlines, entropy generation due to fluid friction and heat transfer over wide range of parameters (10-5⩽Da⩽10-3,0.015⩽Pr⩽1000 at Ra=106). At low Darcy number (Da=10-5), conduction dominant heat transfer is found based on low magnitudes of streamlines and heatlines. Heatlines indicate that heat transfer occurs from hot left wall to cold right wall and thermal mixing is found inside the cavity. The thermal mixing is enhanced as Da increases from 10-5 to 10-3. The thermal gradients are high near the lower portion of left wall and near upper portion of right wall for Da⩾10-4 irrespective of φ and Pr and thus, thermal boundary layer thickness is small along those zones. The maximum entropy generation due to fluid friction (Sψ,max) occurs along the left wall for φ=30° and 90° irrespective of Pr whereas that occurs along the right wall for φ=60° at Da=10-3. The maximum entropy generation due to heat transfer (Sθ,max) occurs at the left edge of bottom wall irrespective of Pr and Da for φ=30° and 60° whereas that occurs at the left edge of bottom wall and right edge of top wall for φ=90° with Da=10-5 and 10-4. At φ=90° with Da=10-3,Sθ,max occurs along both side walls for Pr=0.015 whereas that occurs along left wall for Pr=1000. It is found that total entropy generation is high for Pr=1000 compared to that of Pr=0.015 at higher Da. It is also found that the trapezoidal cavities with φ=60° and 90° correspond to less entropy generation with significant heat transfer rates at Da=10-3 for Pr=0.015 and Pr=1000 and thus the trapezoidal cavities with φ⩾60° may be the optimal design for thermal processing of Pr=0.015 and Pr=1000 fluids.

Natural convection and entropy generation in a vertically concentric annular space

Natural convection in a vertically concentric annular space is of fundamental interest and practical importance. However, available open literature on entropy generation analysis for it is still sparse. In the present work we investigate systematically the effects of Rayleigh number, curvature of annulus and Prandtl number on flow pattern, temperature distribution and entropy generation for natural convection inside a vertically concentric annuli with the aid of the lattice Boltzmann method. The analyzed range is wide, varying from steady laminar convection to unsteady transitional state. Furthermore, we analysze the non-linear branch of irreversible phenomena from a thermodynamics view point.

Effect of an External Oriented Magnetic Field on Entropy Generation in Natural Convection

The influence of an external oriented magnetic field on entropy generation in natural convection for air and liquid gallium is numerically studied in steady-unsteady states by solving the mass, the momentum and the energy conservation equations. Entropy generation depends on five parameters which are: the Prandtl number, the irreversibility coefficients, the inclination angle of the magnetic field, the thermal Grashof and the Hartmann numbers. Effects of these parameters on total and local irreversibilities as well as on heat transfer and fluid flow are studied. It was found that the magnetic field tends to decrease the convection currents, the heat transfer and entropy generation inside the enclosure. Influence of inclination angle of the magnetic field on local irreversibility is then studied.

Evanescent magnetic field effects on entropy generation at the onset of natural convection

This paper numerically investigates the effect of an externally evanescent magnetic field on total entropy generation in a fluid enclosed in a square cavity by using a control volume finite element method to solve the conservation equations at Prandtl number of 0·71. The values of relaxation time of the magnetic field are chosen, so that the Lorentz force acts only in the transient state of entropy generation in natural convection. The total entropy generation was calculated for, fixed value of irreversibility distribution ratio, different relaxation time varying from 0 to 1/5 and Grashof number varying from 104 to 105. The effects of the Hartman number and the magnetic field inclination angle on the evolution of total entropy generation throughout the transient regime were investigated. Results show that the application of evanescent magnetic field not only suppresses the fluctuation of the total entropy generation in the transient state, but also reduces the gap for magnetic field relaxation time less than 1/10.

Entropy generation for natural convection by heated partitions in a cavity

Entropy generation for natural convection in a partitioned cavity, with adiabatic horizontal and isothermally cooled vertical walls, is studied numerically by both a FORTRAN code and the commercially available CFD-ACE software. Effects of the Rayleigh number, the position of the heated partition, and the dimensionless temperature difference on the local and average entropy generation rate are investigated. Proper scale analysis of the problem showed that, while fluid friction term has nearly no contribution to entropy production, the heat transfer irreversibility increases monotonically with the Nusselt number and the dimensionless temperature difference.

On the importance of thermal boundary conditions in heat transfer and entropy generation for natural convection inside a porous enclosure

The aim of the present paper is to analyze the importance of thermal boundary conditions of the heated/cooled walls in heat transfer and entropy generation characteristics inside a porous enclosure, heated from below. Both the heating and the cooling are carried out uniformly and non-uniformly and the results are compared. The laminar, steady, natural convection heat transfer is calculated by solving numerically the mass, momentum, and energy conservation equations whilst viscous dissipation and the work of pressure forces are included in the energy equation. Moreover, the generation of entropy is calculated taking into account both heat transfer irreversibility and fluid friction irreversibility. As the thermal boundary conditions, sinusoidal temperature distributions are invoked for the non-uniformly heated/cooled walls. Comparison between the results of the present numerical model with the previously published works provides excellent agreement. Results are presented in terms of streamlines, isothermal lines, iso-entropy generation lines, and iso-Bejan lines. Additionally, variations of average Nusselt number, global entropy generation rate, and global Bejan number are analyzed over a wide range of Darcy-modified Rayleigh number ( 10 < Ra < 1000 ). Inspection of the results indicates that thermal boundary conditions are of profound influences on the induced flow as well as heat transfer characteristics and possess prominent consequences on entropy generation rates. It is demonstrated that, the optimum case with respect to heat transfer as well as entropy generation could be achieved by non-uniform heating.

Entropy generation for natural convection in Γ-shaped enclosures

This study deals with the prediction of entropy generation (EG) for natural convection in a Γ-shaped enclosure. Heat removal is achieved from cooler vertical sides while the horizontal walls are insulated perfectly. The results are reported with streamlines, isotherms, mean Nusselt numbers, EG due to heat transfer and fluid friction for Ra number ranging from 10 3 to 10 6, irreversibility distribution ratio ϕ, ranging from 10 − 5 to 10 − 3 , different step height ( h) and step width ( w) values. It is observed that at a fixed Ra number, with an increase in aspect ratio (AR = h/ w) mean Nusselt number values increase. For Ra numbers ranging from 10 3 to 10 4, the total EG is mostly due to heat transfer because of relatively low velocities, but for Ra > 10 4 the contribution to due to fluid friction becomes effective even has comparable values from Ra = 10 5 to Ra = 10 6.

Entropy generation in natural convection in a symmetrically and uniformly heated vertical channel

In this study numerical predictions of local and global entropy generation rates in natural convection in air in a vertical channel symmetrically heated at uniform heat flux are reported. Results of entropy generation analysis are obtained by solving the entropy generation equation based on the velocity and temperature data. The analyzed regime is two-dimensional, laminar and steady state. The numerical procedure expands an existing computer code on natural convection in vertical channels. Results in terms of fields and profiles of local entropy generation, for various Rayleigh number, Ra, and aspect ratio values, L/ b, are given. The distributions of local values show different behaviours for the different Ra values. A correlation between global entropy generation rates, Rayleigh number and aspect ratio is proposed in the ranges 10 3 ⩽ Ra ⩽ 10 6 and 5 ⩽ L/ b ⩽ 20.

Vibrational Effect on Entropy Generation in a Square Porous Cavity

We investigate the nature of entropy generation for natural convection in a two-dimensional square section enclosure vibrating sinusoidally perpendicular to the applied temperature gradient in a zero-gravity field. The enclosure is assumed to fill with porous media. The Darcy momentum equation is used to model the porous media. The full governing differential equations are simplified with the Boussinesq approximation and solved by a finite volume method. Whereas the Prandtl number Pr is fixed to 1.0. Results are presented in terms of average Nusselt number (Nuav), entropy generation number (Nsav), Bejan number (Beav), and kinetic energy (KEav).

Free Convection and Irreversibility Analysis inside a Circular Porous Enclosure

We investigate the nature of heat transfer and entropy generation for natural convection in a two-dimensional circular section enclosure. The enclosure is assumed to fill with porous media. The Darcy momentum equation is used to model the porous media. The full governing differential equations are simplified with the Boussinesq approximation and solved by a finite volume method. Whereas the Prandtl number Pr is fixed to 1.0. Results are presented in terms of Nusselt number, entropy generation number, and Bejan number.

Entropy generation for natural convection in an inclined porous cavity

The issue of entropy generation in a tilted saturated porous cavity for laminar natural convection heat transfer is analysed by solving numerically the mass, momentum and energy balance equations, using Darcy’s law and Boussinesq-incompressible approximation. As boundary conditions of cavity, two opposite walls are kept at constant but different temperatures and the other two are thermally insulated. The parameters considered are the angle of inclination and the Darcy–Rayleigh number. When available, present solutions are compared with known results from the previous researches. Excellent agreement was obtained between results that validate the used computer code. The results show that the calculation of local entropy generation maps are feasible and can supply useful information for the selection of a suitable angle of inclination.

Optimization in an Inclined Enclosure for Minimum Entropy Generation in Natural Convection

Optimization in an Inclined Enclosure for Minimum Entropy Generation in Natural Convection