Entropy Generation During Natural Convection in a Porous Cavity: Effect of Thermal Boundary Conditions
02 Aug 2012-Numerical Heat Transfer Part A-applications (Taylor & Francis Group)-Vol. 62, Iss: 4, pp 336-364
TL;DR: In this article, the authors investigated the effect of different boundary conditions on entropy generation, and showed that the entropy generation rates are reduced in sinusoidal heating (case 2) when compared to that for uniform heating with a penalty on thermal mixing, and that there exists an intermediate Da for optimal values of entropy generation.
Abstract: Entropy generation plays a significant role in the overall efficiency of a given system, and a judicious choice of optimal boundary conditions can be made based on a knowledge of entropy generation. Five different boundary conditions are considered and their effect of the permeability of the porous medium, heat transfer regime (conduction and convection) on entropy generation due to heat transfer, and fluid friction irreversibilities are investigated in detail for molten metals (Pr = 0.026) and aqueous solutions (Pr = 10), with Darcy numbers (Da) between 10−5–10−3 and at a representative high Rayleigh number, Ra = 5 × 105. It is observed that the entropy generation rates are reduced in sinusoidal heating (case 2) when compared to that for uniform heating (case 1), with a penalty on thermal mixing. Finally, the analysis of total entropy generation due to variation in Da and thermal mixing and temperature uniformity indicates that, there exists an intermediate Da for optimal values of entropy generation, th...
Citations
More filters
01 Jan 1997
TL;DR: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems and discusses the main points in the application to electromagnetic design, including formulation and implementation.
Abstract: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.
1,820 citations
TL;DR: In this paper, the authors investigated the entropy generation due to conjugate natural convection-conduction heat transfer in a square domain under steady-state condition, and the results showed that both the average Nusselt number and entropy generation are increasing functions of K ro while they are maxima at some critical values of D.
Abstract: Entropy generation due to conjugate natural convection–conduction heat transfer in a square domain is numerically investigated under steady-state condition. The domain composed of porous cavity heated by a triangular solid wall and saturated with a CuO–water nanofluid. Equations governing the heat transfer in the triangular solid together with the heat and nanofluid flow in the nanofluid-saturated porous medium are solved numerically using the over-successive relaxation finite-difference method. A temperature dependent thermal conductivity and modified expression for the thermal expansion of nanofluid are adopted. A new criterion for assessment of the thermal performance is proposed. The investigated parameters are the nanoparticles volume fraction φ (0–0.05), modified Rayleigh number Ra (10–1000), solid wall to base-fluid saturated porous medium thermal conductivity ratio K ro (0.44, 1, 23.8), and the triangular solid thickness D (0.1–1). The results show that both the average Nusselt number and the entropy generation are increasing functions of K ro , while they are maxima at some critical values of D . It is also found that the addition of nanoparticles increases the entropy generation. According to the new proposed criterion, the results show that the largest solid thickness ( D = 1.0) and the lower wall thermal conductivity ratio manifest better thermal performance.
142 citations
TL;DR: In this article, the entropy generation in natural convection of nanofluid in a wavy cavity using a single-phase model was analyzed using the finite difference method of the second-order accuracy.
Abstract: Purpose
The 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/approach
The 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).
Findings
It 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.
Originality
The 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.
128 citations
TL;DR: It is found that the applied magnetic field can suppress both the natural convection and the entropy generation rate, and the nanoparticles addition can be useful if a compromised magnetic field value represented by a Hartman number of 30 is applied.
Abstract: This paper investigates the entropy generation and natural convection inside a C-shaped cavity filled with CuO-water nanofluid and subjected to a uniform magnetic field. The Brownian motion effect is considered in predicting the nanofluid properties. The governing equations are solved using the finite volume method with the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm. The studied parameters are the Rayleigh number (1000 ≤ Ra ≤ 15,000), Hartman number (0 ≤ Ha ≤ 45), nanofluid volume fraction (0 ≤ φ ≤ 0.06), and the cavity aspect ratio (0.1 ≤ AR ≤ 0.7). The results have shown that the nanoparticles volume fraction enhances the natural convection but undesirably increases the entropy generation rate. It is also found that the applied magnetic field can suppress both the natural convection and the entropy generation rate, where for Ra = 1000 and φ = 0.04, the percentage reductions in total entropy generation decreases from 96.27% to 48.17% for Ha = 45 compared to zero magnetic field when the aspect ratio is increased from 0.1 to 0.7. The results of performance criterion have shown that the nanoparticles addition can be useful if a compromised magnetic field value represented by a Hartman number of 30 is applied.
120 citations
TL;DR: In this paper, a numerical study is made on the mixed convection of copper-water nanofluid inside a differentially heated skew enclosure, where the finite volume based SIMPLEC algorithm is used to solve the transformed equations for fluid flow and heat transfer equations in the computational domain.
Abstract: A numerical study is made on the mixed convection of copper–water nanofluid inside a differentially heated skew enclosure. Co-ordinate transformations are used to transform the physical domain to the computational domain in an orthogonal co-ordinate. The finite volume based SIMPLEC algorithm is used to solve the transformed equations for fluid flow and heat transfer equations in the computational domain. The fluid flow and heat transfer characteristics are studied for a wide range of skew angles ( 30 ° ⩽ λ ⩽ 150 ° ) , nanoparticle volume fraction ( 0.0 ⩽ ϕ ⩽ 0.2 ) and Richardson number ( 0.1 ⩽ Ri ⩽ 5 ) at a fixed value of Reynolds number. The entropy generation and Bejan number are evaluated to demonstrate the thermodynamic optimization of the mixed convection. It is shown that the heat transfer rate increases remarkably by the addition of nanoparticles. The flow field is sensible to the skew angle variation. Our results show that the heat transfer augmentation through nanoparticles with lower rate in entropy generation enhancement can be achieved in a skewed cavity.
76 citations
References
More filters
TL;DR: In this paper, the thermal partial oxidation process of methane was investigated numerically and experimentally using CHEMKIN tools to determine the practical operating conditions and the effects of air preheating temperature, thermal load and air ratio on the reforming process.
Abstract: The thermal partial oxidation process of methane was investigated numerically and experimentally. Thermodynamic calculations and kinetic simulation were performed using CHEMKIN tools to determine the practical operating conditions. Experimentally, a porous material-based reactor was built to perform the partial oxidation process. Temperature profiles along the reactor central axis and concentration profiles of CO, H2, CO2, C2H2 and CH4 were measured. Two different porous structures were installed in the reaction zone: Al2O3 fiber static mixer structures and SiC foams. The effects of air preheating temperature, thermal load and air ratio on the reforming process were investigated for both structures. The numerical calculation showed that an air ratio down to 0.4 is a practical limit to perform the partial oxidation process. Experimentally, it was found that the air preheating temperature has no significant influence on the syngas composition; however, it does affect the soot point (λc). Higher heat recuperation was detected in the case of SiC foam based reformer than in the case of the Al2O3 mixer one. The SiC foam based reactor showed also a better performance than the Al2O3 regarding the soot point. For air preheating temperature of 700 °C, the current soot point for the SiC foam based reformer was 0.42, while it was 0.45 for the Al2O3 mixer one.
104 citations
TL;DR: In this paper, two optimization criteria, minimum weight and minimum entropy generation, are simultaneously applied to deduce the main geometric characteristics of the two finned cross-flow heat exchangers that the environmental control system (ECS) of commercial aircraft normally incorporate.
Abstract: In this work, two optimization criteria, minimum weight and minimum entropy generation are simultaneously applied to deduce the main geometric characteristics of the two finned cross-flow heat exchangers that the environmental control system (ECS) of commercial aircraft normally incorporate. The performance of this system, described and modelled in this paper, is optimized as a whole instead of considering the optimal operation of isolated devices. The ECS is based on Brayton inverse cycle, where two air streams are involved, one to be conditioned or the main stream and a coolant one. The whole evolution of the two streams is analyzed. The main stream is studied starting from ambient conditions, before entering the aircraft engine, following with the bleed process until the turbine exit where the required temperature and pressure conditions are achieved. The coolant ram air stream is also considered from ambient conditions to the nozzle exit from where it is rejected. The heat exchanger surfaces have been selected using a compactness criterion but taking into account that compactness increases pressure losses. Once the parameters and variables are identified, the optimization task would lead to an optimum geometry by means of a trade-off solution. The numerical results found in this case illustrate the adequacy of this kind of optimization to study complex thermal systems.
103 citations
"Entropy Generation During Natural C..." refers methods in this paper
...The EGM approach has been applied to optimize natural convection systems [24, 25], pin-fin heat sinks [26], fuel cells [27], heat exchangers [28, 29], environmental control of aircraft [30, 31], combustion in porous media [32], etc....
[...]
TL;DR: In this article, 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 is analyzed and the results are compared.
Abstract: 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.
99 citations
"Entropy Generation During Natural C..." refers background in this paper
...Recently, Zahmatkesh [36] reported the entropy generation in a porous square cavity; however, only two boundary conditions (uniform and sinusoidal heating conditions) were considered....
[...]
TL;DR: In this paper, the effects of the amplitude of the bottom wall temperature variation and the heat source length on the natural convection in the cavity are investigated for Rayleigh number range 20-500.
Abstract: Numerical study of natural convection in a porous cavity is carried out in the present paper. Natural convection is induced when the bottom wall is heated and the top wall is cooled while the vertical walls are adiabatic. The heated wall is assumed to have spatial sinusoidal temperature variation about a constant mean value which is higher than the cold top wall temperature. The non-dimensional governing equations are derived based on the Darcy model. The effects of the amplitude of the bottom wall temperature variation and the heat source length on the natural convection in the cavity are investigated for Rayleigh number range 20–500. It is found that the average Nusselt number increases when the length of the heat source or the amplitude of the temperature variation increases. It is observed that the heat transfer per unit area of the heat source decreases by increasing the length of the heated segment.
93 citations
TL;DR: In this paper, a numerical analysis of the entropy production due to heat transfer and fluid flow in isosceles triangular enclosures with partially heated from below and symmetrically cooled from sloping walls is performed.
Abstract: A numerical analysis of the entropy production has been performed due to natural convection heat transfer and fluid flow in isosceles triangular enclosures with partially heated from below and symmetrically cooled from sloping walls. Governing equations are solved by finite difference method. Governing parameters on flow and temperature fields are Rayleigh number (10 3 ⩽ Ra ⩽ 8.8 × 10 5 ), dimensionless length of heater (0.25 ⩽ (l′ = l/ L ) ⩽ 1.0), dimensionless location of heater (0.25 ⩽ ( c ′ = c / L ) ⩽ 0.75) and inclination angle of slopping walls (30° ⩽ β ⩽ 60°). Heat transfer results are presented in terms of local and mean Nusselt numbers ( Nu ) while entropy production results are shown with entropy production number ( N s ) and Bejan number ( Be ). Isotherms, streamlines, contours of entropy production due to heat transfer and fluid friction irreversibility are plotted. It is observed that entropy production number increases but Bejan number decreases with increasing of Rayleigh number. However, both entropy production due to heat transfer and fluid friction irreversibility are affected by higher inclination angle of triangle and length of heater.
89 citations