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Journal ArticleDOI

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
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Book ChapterDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
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

Journal ArticleDOI
05 Feb 2016-Entropy
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

Journal ArticleDOI
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.

76 citations

References
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Journal ArticleDOI
TL;DR: In this paper, a boundary-layer theory is developed for vertical plane flows in saturated porous medium, where diffusion effects can be neglected except in regions where the gradients of fluid properties are very large.
Abstract: When the dimensions of a convective system in a saturated porous medium are sufficiently great, diffusion effects can be neglected except in regions where the gradients of fluid properties are very large. A boundary-layer theory is developed for vertical plane flows in such regions. In special cases, the theory is equivalent to that for laminar incompressible flow in a two-dimensional half-jet, or in a plane jet or round jet, for which similarity solutions are well known.A number of experiments have been performed using a Hele-Shaw cell immersed in water, with a source of potassium permanganate solution located between the plates. At very small values of the source strength, a flow analogous to that of a plane jet from a slit is obtained. The distance advanced by the jet front, or cap, is measured as a function of time, and the velocity is found to be nearly proportional to the velocity of the fluid on the axis of the steady jet behind the cap, as given by the similarity law of Schlichting and Bickley. At large values of the source strength, a two-dimensional ‘broad jet’ of homogeneous solution descending under gravity is produced; the shape of the flow region can be calculated with little error from potential theory, neglecting the effect of the mixing layers.A possible example of a mixing layer observed in a geothermal region is examined. The theoretical form of the temperature distribution is calculated numerically, taking into account the large viscosity variation with temperature and also the possibility of a large permeability variation. These effects are found to have less influence upon the solution than might have been expected. Quantitative values obtained for the physical parameters are consistent with other geophysical observations.

223 citations

Journal ArticleDOI
TL;DR: In this paper, a two-dimensional steady free convection in a square cavity bounded by isothermal vertical walls at different temperatures and adiabatic horizontal walls has been studied numerically by adopting a twotemperature model of heat transfer.

217 citations


"Entropy Generation During Natural C..." refers methods or result in this paper

  • ...Further, the present numerical procedure is validated for a porous medium case where a porous square cavity, with air (Pr¼ 0.71) as fluid, is heated isothermally on the left wall while the right wall is maintained cold isothermal and the horizontal walls are maintained adiabatic, similar to the problem reported by Bejan [49], Manole and Lage [50], Saeid and Pop [51], and Baytas and Pop [52]....

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  • ...74% compared to the one reported by Baytas and Pop [52]....

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  • ...71) as fluid, is heated isothermally on the left wall while the right wall is maintained cold isothermal and the horizontal walls are maintained adiabatic, similar to the problem reported by Bejan [49], Manole and Lage [50], Saeid and Pop [51], and Baytas and Pop [52]....

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  • ...It may be noted that the error between the average Nusselt number obtained by current numerical procedure is only 0.74% compared to the one reported by Baytas and Pop [52]....

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Journal ArticleDOI
TL;DR: In this paper, a new shell-and-tube heat exchanger optimization design approach is developed, wherein the dimensionless entropy generation rate obtained by scaling the entropy generation on the ratio of the heat transfer rate to the inlet temperature of cold fluid is employed as the objective function.

144 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....

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Journal ArticleDOI
TL;DR: In this article, the authors presented a numerical analysis of entropy generation in rectangular cavities that were submitted to the natural convection process, which was caused by temperature differences between the vertical walls of the cavities.

138 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....

    [...]

Journal ArticleDOI
TL;DR: In this paper, it was shown that the ratio κ / Dϵ = 0·633, where D is the molecular diffusivity of the solute when the porous medium is absent, is a property of the porous material alone and can be determined directly by diffusion measurements.
Abstract: If a long vertical tube filled with porous material contains a viscous solution, the density of which increases with height as a result of the presence of the dissolved substance, the equilibrium of the liquid is stable provided that the density gradient does not anywhere exceed the value d ρ /d Z = 3·390 μκ / gkb 2 Here κ , the diffusivity of the solute through the saturated porous medium, is defined to be the quantity of solute diffusing across unit area within the porous medium per unit time under unit density gradient. The above expression for the density gradient at neutral stability has been compared experimentally with Taylor’s value for the corresponding density gradient in a vertical capillary tube. For a porous medium consisting of randomly packed glass spheres of mean diameter about 0·2 mm and porosity ϵ = 0·365, it has been found that the two results are consistent provided that the ratio κ / Dϵ = 0·633, where D is the molecular diffusivity of the solute when the porous medium is absent. As this dimensionless ratio is a property of the porous material alone, it can be determined directly by diffusion measurements. An alternative method of measuring κ / Dϵ , based upon an electrical analogue, has led to a value of 0·641 for the same porous material, which is in good numerical agreement.

114 citations