Sensitivity analysis for MHD effects and inclination angles on natural convection heat transfer and entropy generation of Al2O3-water nanofluid in square cavity by Response Surface Methodology

The natural convection heat transfer and entropy generation of Al₂O₃-water nanofluid, in a square cavity with inclination angle θ and the presence of a constant axial magnetic field B₀ are examined in this paper. The governing equations are solved numerically by finite volume method. Also an effective parameters analysis was performed by using of the Response Surface Methodology (RSM). The effects of the Rayleigh number (10³, 10⁴, 10⁵ and 10⁶), Hartmann number (0, 10, 30 and 50) and also inclination angles (0°, 30°, 60° and 90°) are investigated. It is observed that the mean Nusselt number and the total entropy generation increase when the Rayleigh number increases. It is also found that, regardless of the Ha parameter, by increasing of the inclination angles, the mean Nusselt number and entropy generation rate increase until inclination angle 30° and then they decrease. Also, for low Ra numbers, by increasing the Ha parameter, the mean Nusselt number increases until Ha = 10 and then decreases. The analysis showed that the sensitivity of the Nusselt number and the entropy generation to Ha parameter was too small, and as a result it was negligible. Also, the sensitivity of the mean Nusselt number and the entropy generation to inclination angle, θ, increases by increasing of this angle. It is also observed that the mean Nusselt number and the entropy generation were more sensitive to the inclination angle θ than the Ha parameter.     

Entropy Generation During Natural Convection in a Porous Cavity: Effect of Thermal Boundary Conditions

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, thermal mixing, and temperature uniformity.     

Entropy Generation of Natural Convection Heat Transfer in a Square Cavity Using Al2O3–Water Nanofluid

Entropy generation of an Al₂O₃–water nanofluid due to heat transfer and fluid friction irreversibility has been investigated in a square cavity subject to different side‐wall temperatures using a nanofluid for natural convection flow. This study has been carried out for the pertinent parameters in the following ranges: Rayleigh number between 10⁴ and 10⁷ and volume fraction between 0 and 0.05. Based on the obtained dimensionless velocity and temperature values, the distributions of local entropy generation, average entropy generation, and average Bejan number are determined. The results are compared for a pure fluid and a nanofluid. It is totally found that the heat transfer, and entropy generation of the nanofluid is more than the pure fluid and minimum entropy generation and Nusselt number occur in the pure fluid at any Rayleigh number. Results depict that the addition of nanoparticles to the pure fluid has more effect on the entropy generation as the Rayleigh number goes up.     

Effect of aspect ratio on entropy generation in a rectangular cavity with differentially heated vertical walls

In the present study, entropy generation in rectangular cavities with the same area but different aspect ratios is numerically investigated. The vertical walls of the cavities are at different constant temperatures while the horizontal walls are adiabatic. Heat transfer between vertical walls occurs by laminar natural convection. Based on the obtained dimensionless velocity and temperature values, the distributions of local entropy generation due to heat transfer and fluid friction, the local Bejan number and local entropy generation number are determined and related maps are plotted. The variation of the total entropy generation and average Bejan number for the whole cavity volume at different aspect ratios for different values of the Rayleigh number and irreversibility distribution ratio are also evaluated. It is found that for a cavity with high value of Rayleigh number (i.e., Ra = 10⁵), the total entropy generation due to fluid friction and total entropy generation number increase with increasing aspect ratio, attain a maximum and then decrease. The present results are compared with reported solutions and excellent agreement is observed. The study is performed for 10² < Ra < 10⁵, 10^− 4 < ? < 10^− 2, and Pr = 0.7.     

Simulation of natural convection and entropy generation of MHD non-Newtonian nanofluid in a cavity using Buongiorno's mathematical model

In this paper, natural convection and entropy generation of non-Newtonian nanofluid, using the Buongiorno's mathematical model in a cavity in the presence of a uniform magnetic field has been analyzed by Finite Difference Lattice Boltzmann method (FDLBM). The cavity is filled with nanofluid which the mixture shows shear-thinning behavior. This study has been performed for the certain pertinent parameters of Rayleigh number (Ra = 10⁴ and 10⁵), Hartmann number (Ha = 0, 15, 30), buoyancy ratio number (N_r = 0.1, 1, and 4), power-law index (n = 0.4–1), Lewis number (Le = 1, 5, and 10), Thermophoresis parameter (N_t = 0.1, 0.5, 1), and Brownian motion parameter (N_b = 0.1, 1, 5). The Prandtl number is fixed at Pr = 1. The Results indicate that the augmentation of Hartmann number causes heat and mass transfer to drop. The increase in Rayleigh number enhances heat and mass transfer for various power-law indexes. The alteration of the power-law index changes heat and mass transfer. In addition, the rise of Hartmann number declines the shear-thinning behavior. The increase in the Lewis number augments mass transfer while it causes heat transfer to drop. The rise of the Thermophoresis and Brownian motion parameters ameliorate mass transfer and declines heat transfer significantly. The augmentation of buoyancy ratio number enhances heat and mass transfer. The augmentation of the power-law index declines various entropy generations in different Rayleigh numbers and Hartmann numbers. The increase in Hartmann number declines total entropy generation in different Rayleigh numbers. In addition, the rise of Rayleigh number and Hartmann number causes Bejan number to drop in various power-law indexes. The enhancement of the Lewis number provokes the total irreversibility to rise. Further, the total entropy generation increases as the buoyancy ratio number augments. It was shown that the increase in the Brownian motion and Thermophoresis parameters enhance the total irreversibility.     

Numerical modeling of natural convection in an open cavity with two vertical thin heat sources subjected to a nanofluid

This paper presents a numerical study of natural convection cooling of two heat sources vertically attached to horizontal walls of a cavity. The right opening boundary is subjected to the copper–water nanofluid at constant low temperature and pressure, while the other boundaries are assumed to be adiabatic. The governing equations have been solved using the finite volume approach, using SIMPLE algorithm on the collocated arrangement. The study has been carried out for the Rayleigh number in the range 10⁴ ≤ Ra ≤ 10⁷, and for solid volume fraction 0 ≤ φ ≤ 0.05. In order to investigate the effect of heat source location, three different placement configurations of heat sources are considered. The effects of both Rayleigh numbers and heat source locations on the streamlines, isotherms, Nusselt number are investigated. The results indicate that the flow field and temperature distributions inside the cavity are strongly dependent on the Rayleigh numbers and the position of the heat sources. The results also indicate that the Nusselt number is an increasing function of the Rayleigh number, the distance between two heat sources, and distance from the wall. In addition it is observed that the average Nusselt number increases linearly with the increase in the solid volume fraction of nanoparticles.     

Numerical simulation and sensitivity analysis of effective parameters on natural convection and entropy generation in a wavy surface cavity filled with a nanofluid using RSM

ABSTRACT

In this work, a 2-D numerical investigation and a sensitivity analysis have been done on the natural convection heat transfer in a wavy surface cavity filled with a nanofluid. For this purpose, the effects of three parameters, the Rayleigh number (10³?≤Ra?≤?10⁵), nanoparticles volume fraction (0.00 ≤??≤?0.04), and the shape of the nanoparticles (spherical, blade, and cylindrical), are studied. Discretization of the governing equations is performed using a finite volume method (FVM) and solved with the SIMPLE algorithm. The effective parameters analysis is processed utilizing the Response Surface Methodology (RSM). Comparison with previously published work is performed and the results are found to be in good agreement. The results showed that increasing the Rayleigh number and ? increases the mean Nusselt number and the total entropy generation. Also, the nanofluids with spherical- and cylindrical-shaped nanoparticles have the highest and lowest Nusselt numbers and entropy generations, respectively. The sensitivity of the mean Nusselt number and entropy generation ratio to Ra and ? is found to be positive, whereas it is predicted to be negative to nanoparticles shape.     

Natural Convection in a Square Enclosure with Two Horizontal Cylinders

This study investigates natural convection in a cooled square enclosure with two inner heated circular cylinders with the same diameter. The centers of two equidiameter cylinders are placed at those of the lower and upper half of the enclosure, respectively. The immersed boundary method (IBM) to model the inner circular cylinders based on the finite volume method is used to study a two-dimensional natural convection for different Rayleigh numbers varying in the range of 10³ ≤ Ra ≤ 10⁵. The effect of the radius of inner circular cylinders in an enclosure on heat transfer and fluid flow at different Rayleigh numbers has been examined. As the Rayleigh number increases, the horizontal symmetry is broken and the asymmetry occurred from the smaller radius. As the radius decreases, the dependence of the convection on the Rayleigh number is considerable. The dependence of the Nusselt number on the radius and the Rayleigh number is presented.     

Unsteady Mixed Convection of a Confined Jet in a Fluid-Superposed High Porosity Medium

Numerical study of a confined jet impingement cooling of a fluid-superposed porous medium heated from below is conducted to investigate the oscillatory mixed convection. The effects of the Rayleigh number (2 × 10⁵ ≤ Ra ≤ 1 × 10⁶) and the Darcy number (1 × 10^?5 ≤ Da ≤ 5 × 10^?4) on the heat transfer are investigated for different Péclet numbers. It is found that, the average Nusselt number increases with the increase in Darcy number or Rayleigh number. The values of average Nusselt number are found to oscillate with time for some combination of Rayleigh numbers (Ra ≥ 4 × 10⁵) and Péclet numbers (200 ≤ Pe ≤ 1000), at which the oscillatory convection occurs. The oscillation of average Nusselt number is investigated for different porous medium height and porous medium-to-fluid heat capacity ratio.     

Entropy generation due to natural convection cooling of a nanofluid

In the present work, entropy generation due to natural convection of a nanofluid that consists of water and Cu in a cavity with a protruded heat source has been studied. To investigate both the First and the Second Law of Thermodynamics for this considered problem the numerical scheme carried out based on finite volume method with the SIMPLE algorithm for pressure-velocity coupling. In this study, the effect of Rayleigh number, solid concentration and heat source location on entropy generation have been revealed. Consequently the optimum case has been selected since the thermal system could have the least entropy generation and the best heat transfer rate. The results have shown the maximum value of Nusselt number and minimum entropy generation are obtained when heat source mountains in the bottom horizontal wall.     

Effect of Undulations on the Natural Convection Heat Transfer and Entropy Generation Inside a Porous Right-Angled Triangular Enclosure

In the present study, natural convection in a two-dimensional porous right-angled triangular enclosure with one wavy wall is studied numerically. Three cases with one, two, and three undulations on the left wall are studied in this analysis. The stream function-vorticity equations are solved using finite-difference technique and a structured nonorthogonal body-fitted mesh is used for computations. The effect of Rayleigh number (Ra = 10³–10⁶), Darcy number (Da = 10^?4–10^?2) and undulations on the heat transfer, fluid flow, and entropy generation is investigated. It is found that average Nusselt number increases with Darcy number and number of undulations present on the left wall at fixed Darcy number.     

A DOMAIN DECOMPOSITION METHOD FOR SOLVING THREE-DIMENSIONAL HEAT TRANSPORT EQUATIONS IN A DOUBLE-LAYERED THIN FILM WITH MICROSCALE THICKNESS

Transient-free convection in a porous enclosure having heat-conducting solid walls of finite thickness under conditions of convective heat exchange with an environment was studied numerically. A heat source of constant temperature was located at the bottom of the cavity. The governing equations in porous volume formulated in dimensionless variables such as the temperature and vector potential functions within the Darcy–Boussinesq approach and the transient three-dimensional heat conduction equation based on the Fourier hypothesis for solid walls with corresponding initial and boundary conditions were solved using an iterative implicit finite-difference method. The main objective was to investigate the influence of the Rayleigh number 10³ ≤ Ra ≤ 10⁶, the Darcy number 10^?5 ≤ Da ≤ 10^?3, the thermal conductivity ratio 1 ≤ k_1,2 ≤ 20, the solid wall thickness ratio 0.1 ≤ l/L ≤ 0.3, and the dimensionless time 0 ≤ τ ≤ 200 on the fluid flow and heat transfer. Comprehensive analysis of the effects of these key parameters on the average Nusselt number at the heat source surface was conducted.     

Natural convection in a triangular cavity filled with air under the effect of external air stream cooling

Natural convection in a triangular cavity filled with air is investigated numerically. In this paper, the cavity is exposed to air stream cooling exerted on its sides and it is heated by a fixed heat flux from the base. The air inside the cavity is assumed to be laminar and obeying Boussinesq approximation. The governing equations are solved numerically using the finite volume technique with SIMPLE algorithm. The results are achieved with a range of Rayleigh number (10⁴ < Ra < 10⁷), free stream Reynolds number (10³ < Re_∞ < 1.5 × 10⁴), four aspect ratios (AR = 0.25, 0.5, 0.866, and 1) and five inclination angles (? = 0°, 30°, 45°, 60°, 90°). The influence of these parameters is displayed on the stream function, isotherms lines, local and average Nusselt numbers. The results reveal that the heat transfer rate increases as Rayleigh number, free stream Reynolds number and AR increase. The highest heat transfer rate is obtained at ? = 0° while the lowest one is obtained at ? = 90°. Furthermore, as the AR augments, the local and average Nusselt numbers are enhanced and the stream function is formed of two symmetric counter‐rotating vortices.     

NATURAL CONVECTION AND ENTROPY GENERATION FROM A CYLINDER WITH HIGH CONDUCTIVITY FINS

The problem of laminar natural convection from a horizontal cylinder with multiple equally spaced high conductivity fins on its outer surface was investigated numerically. The effect of several combinations of number of fins and fin height on the average effective Nusselt number was studied over a wide range of Rayleigh numbers. The results showed that there was an optimal combination of number of fins and fin height for maximum heat transfer from the cylinder for a given value of Rayleigh number. A high number of short fins slightly decreased the heat transfer from the cylinder. The calculated velocity and temperature profiles also were used to study the total entropy generation. The total entropy production was dominated by entropy generation due to thermal effects. The exception was at Ra _D = 10³ and a large cylinder diameter where entropy generation was dominated by entropy generation due to viscous effects. This information can be used to access the changes in the thermodynamic efficiency due to the addition of fins to enhance the natural convection heat transfer from a horizontal cylinder.     

Effects of Wall-Located Heat Barrier on Conjugate Conduction/Natural-Convection Heat Transfer and Fluid Flow in Enclosures

The effects of a heat barrier, located in the ceiling wall of an enclosure, on conjugate conduction/natural convection are investigated numerically. The vertical walls of the enclosure are differentially heated and the horizontal walls are adiabatic. Heatline technique is used to visualize heat transport. The variations of average Nusselt number, dimensionless heat transfer rate through the ceiling wall, and dimensionless overall heat transfer rate are studied. Calculations are performed for different Rayleigh numbers (10³ ≤ Ra ≤ 10⁶), thermal conductivity ratios (1 ≤ K ≤ 100), dimensionless locations of the heat barrier (0 < X _h  < 1),and two dimensionless ceiling wall thicknesses (D = 0.05 and D = 0.20). For high thermal conductivity ratio (K = 100), the heat barrier considerably reduces the dimensionless overall heat transfer rate. The effect of the heat barrier on dimensionless heat transfer rate through the enclosure increases as the Rayleigh number decreases. For low Rayleigh number (i.e., Ra = 10³), a location exists in the ceiling wall for which the dimensionless overall heat transfer rate is minimum.     

Natural convection in a rectangular enclosure containing an oval-shaped heat source and filled with Fe3O4/water nanofluid

This work concerns with the study of natural convection heat transfer in rectangular cavities with an inside oval-shaped heat source filled with Fe₃O₄/water nanofluid. The finite element method is employed to solve the governing equations for this problem. Average Nusselt numbers are presented for a wide range of Rayleigh number (10³ ≤ Ra ≤ 10⁵), volume fraction of nanoparticles (0 ≤ ϕ ≤ 14%), and four different size and shapes of the heat source. Depending on concentration of the nanoparticle, geometry of the heat source, and the value of Rayleigh number different behaviors are monitored for average Nusselt numbers. Configuration of the heat source dictates a significant change on the behavior of the average Nusselt number, while addition of the nanoparticles has a negative effect on the magnitude of Nusselt number for this problem.     

Entropy generation at the onset of natural convection

The entropy generation due to heat transfer and friction has been determined in transient state for laminar natural convection by solving numerically the mass, momentum and energy balance equations, using a control volume finite-element method. The variations of the total entropy generation as function of time for Rayleigh number and irreversibility distribution ratio set at 10³?Ra?10⁵ and 10⁻⁴???10⁻¹ were investigated. The evolution of the maximum of entropy generation with the Rayleigh number is studied. The effect of the irreversibility distribution ratio on the maximum entropy generation and the entropy generation in steady state are analyzed. The irreversibility maps for Rayleigh number set at 10³?Ra?10⁵ and irreversibility distribution ratio ?=10⁻⁴ are plotted.     

Effects of the inclination angle on natural convection heat transfer and entropy generation in a square porous enclosure

ABSTRACT

In this paper, we analyze numerically the effects of the inclination angle on natural convection heat transfer and entropy generation characteristics in a two-dimensional square enclosure saturated with a porous medium. There is a significant alteration in Nusselt number with the orientation of the enclosure at higher values of Rayleigh number. It reveals that the variation of entropy generation rate with the inclination angle is significant for higher values of Darcy number. The dominant source of irreversibility is due to heat transfer at low values of Darcy number, whereas entropy generation due to fluid flow dominates over that due to heat transfer for larger values of Darcy number.     

A Parametric Study of Prandtl Number Effects on Laminar Natural Convection Heat Transfer From a Horizontal Circular Cylinder to Its Coaxial Triangular Enclosure

A parametric study of Prandtl number effects on laminar natural convection heat transfer in a horizontal equilateral triangular cylinder with a coaxial circular cylinder is conducted. The Prandtl number is varied over a wide range from 10^?2 to 10⁵, which corresponds to a variety of working fluids. The governing equations with the Boussinesq approximation for buoyancy are iteratively solved using the finite volume approach. It is shown that the flow patterns and temperature distributions are unique for low-Prandtl-number fluids (Pr ≤ 0.1), and are nearly independent of Prandtl number when Pr ≥ 0.7. In addition, the inclination angle of the triangular enclosure is found to noticeably affect the variations of the local Nusselt number, and to have insignificant influence on the average Nusselt numbers for low Rayleigh numbers when Pr ≥ 0.7.     

Investigation of heat transfer during melting of a PCM by a U‐shaped heat source

An experimental study was conducted to investigate the melting process of a phase change material (PCM) and the associated convection heat transfer due to a U‐shaped heat source embedded in the PCM. The experiments were conducted at four input heat fluxes that varied from 3450 to 5840 W/m². The results showed that the heat transfer behavior, interface movement, and the heat transfer coefficients differed both axially and vertically inside the chamber. The local convective heat transfer coefficient in the inner region, enclosed by the U‐tube, was found to be about 35% higher than that in the outer region over the input heat flux range, resulting in faster melting in the inner region than in the outer region. As melted domain grew vertically from 15% to 100%, it was observed that the overall h in the inner region increased by 40–55% from the lowest to highest heat flux. The melting rate was also found comparatively high up until 65–70% of the total PCM volume melted because of the higher contribution from the inner region. It was also observed that the Rayleigh number increased by approximately 23% in the inner region and 18% in the whole domain as the heat flux increased from 3450 to 5840 W/m². A new Nusselt–Rayleigh number correlation is proposed for the heat transfer during the melting process due to a U‐shaped heat source. Copyright © 2017 John Wiley & Sons, Ltd.