Effect of Inclination on Heat Transfer and Fluid Flow in a Finned Enclosure Filled with a Dielectric Liquid

The problem of two-dimensional natural convection flow of a dielectric fluid in a square inclined enclosure with a fin placed on the hot wall is investigated numerically. The fin thickness and length are 1/10 and 1/2 of the enclosure side, respectively. The Rayleigh number is varied from 10³ to 5 × 10⁵ and the solid to fluid thermal conductivity ratio is fixed at 10³. The enclosure tilt or inclination angle is varied from 0° to 90°. The streamlines and isotherms within the enclosure are produced and the heat transfer is calculated. It is found that for 2.5 × 10⁴ ≤ Ra ≤ 2.5 × 10⁵, the average Nusselt number is maximum when γ = 0° and minimum when γ = 90°. For Ra = 5 × 10⁵, the values of enclosure tilt angle for which the average Nusselt number is maximum or minimum are completely different due to the transition to unsteady state. In this case, the maximum heat transfer is obtained for γ = 60°, while the minimum heat transfer is predicted for γ = 0°. Monomial correlations relating the average Nusselt number with the different values of the Rayleigh number from 10⁴ to 10⁵ are determined for two different angles, γ = 0° and γ = 90°.     

Entropy Generation Due to Natural Convection in a Partially Open Cavity with a Thin Heat Source Subjected to a Nanofluid

This article presents a numerical study of natural convection cooling of a heat source mounted inside the cavity, with special attention being paid to entropy generation. The right vertical wall is partially open and is subjected to copper–water nanofluid at a 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 a Rayleigh number in the range 10³ < Ra < 10⁶, and for solid volume fraction 0 <? <0.05. In order to investigate the effect of the heat source and open boundary location, six different configurations are considered. The effects of Rayleigh numbers, heat source and open boundary locations on the streamlines, isotherms, local entropy generation, Nusselt number, and total entropy generation are investigated. The results indicate that when open boundary is located up, the fluid flow augments and hence the heat transfer and Nusselt number increase and total entropy generation decreases.     

Role of Entropy Generation On Thermal Management During Natural Convection in a Tilted Square Cavity with Isothermal and Non-Isothermal Hot Walls

Entropy generation during natural convection within tilted square cavity inclined with different angles (? = 30°and 75°) for various thermal boundary conditions (case 1: isothermal heating and case 2: non-isothermal heating) has been studied. Simulations are carried out over a range of parameters: Rayleigh number (10³ ≤ Ra ≤ 10⁵) and Prandtl numbers (Pr = 0.025 and 998.24). The numerical results are presented in terms of isotherms (θ), streamlines (ψ), entropy generation due to heat transfer (S _θ ) and fluid friction (S _ψ ). Heating strategy is energy efficient for case 2 (non-isothermal heating) due to its less total entropy generation with reasonable heat transfer rate, irrespective of Pr.     

Lattice Boltzmann Simulation of Natural Convection in an Inclined Square Cavity with Spatial Temperature Variation

In this paper, natural convection heat transfer in an inclined square cavity filled with pure air (Pr = 0.71) was numerically analyzed with the lattice Boltzmann method. The heat source element is symmetrically embedded over the center of the bottom wall, and its temperature varies sinusoidally along the length. The top and the rest part of the bottom wall are adiabatic while the sidewalls are fixed at a low temperature. The influences of heat source length, inclination angle, and Rayleigh number (Ra) on flow and heat transfer were investigated. The Nusselt number (Nu) distributions on the heat source surface, the streamlines, and the isotherms were presented. The results show that the inclination angle and heat source length have a significant impact on the flow and temperature fields and the heat transfer performance at high Rayleigh numbers. In addition, the average Nu firstly increases with γ and reaches a local maximum at around γ = 45°, then decreases with increasing γ and reaches minimum at γ = 180° in the cavity with ? = 0.4. Similar behaviors are observed for ? = 0.2 at Ra = 10⁴. Moreover, nonuniform heating produces a significant different type of average Nu and two local minimum average Nu values are observed at around γ = 45° and γ = 180° for Ra = 10⁵ in the cavity with ? = 0.2.     

Laminar Natural Convection of Bingham Fluids in a Square Enclosure with Vertical Walls Subjected to Constant Heat Flux

In this study, two-dimensional steady-state simulations of laminar natural convection in square enclosures with vertical sidewalls subjected to constant heat flux have been carried out, where the enclosures are considered to be completely filled with a yield-stress fluid obeying the Bingham model. Yield stress effects on heat and momentum transport are investigated for nominal values of Rayleigh number (Ra) in the range 10³–10⁶ and a Prandtl number (Pr) range of 0.1–100. It is found that the mean Nusselt number Nu increases with increasing values of Rayleigh number for both Newtonian and Bingham fluids. However, Nu values obtained for Bingham fluids are smaller than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra due to weakening of convective transport. The mean Nusselt number Nu in the case of Bingham fluids is found to decrease with increasing Bingham number, and for large values of Bingham number Bn, the value settles to unity (Nu = 1.0) as heat transfer takes place principally due to thermal conduction. The Nu values for the vertical walls subjected to constant heat flux are smaller than the corresponding values in the same configuration with constant vertical wall temperatures (for identical values of nominal Rayleigh, Prandtl, and Bingham numbers). However, the value of Bingham number at which Nu approaches to unity remains the same for both constant wall temperature and constant wall heat flux configurations. It is demonstrated that for small values of Bingham number Nu increases with increasing Prandtl number, but the opposite behavior occurs for large values of Bingham number. New correlations are proposed for the mean Nusselt number Nu for both Newtonian and Bingham fluids for square enclosures with vertical walls subjected to constant heat flux, which are shown to satisfactorily capture the correct qualitative and quantitative behavior of Nu in response to changes in Ra, Pr, and Bn.     

Analysis of exergy loss vs heat transfer rate for Rayleigh–Bénard convection of various fluids in enclosures with curved walls

The investigation of entropy generation is highly desirable for the optimization of the thermal systems to avoid larger energy wastage and ensure higher heat transfer rate. The numerical investigation of natural convection within enclosures with the concave and convex horizontal walls involving the Rayleigh–Bénard heating is performed via entropy generation approach. The spatial distributions of the temperature (θ), fluid flow (ψ), entropy generation due to heat transfer and fluid friction (S_θ and S_ψ) are discussed extensively for various Rayleigh numbers and Prandtl numbers involving various wall curvatures. A number of complex patterns of spatial distributions of fluid flow and temperature for cavities with concave or convex isothermal walls (top and bottom) have been obtained. The zones of high entropy generation for temperature and fluid flow are detected within cavities with concave and convex horizontal walls. The optimal situation involves the high heat transfer rate with moderate or low entropy generation. Overall, case 3 (highly concave) is found to be optimal over cases 1 and 2 (concave) and cases 1–3 (convex) for all Pr and Ra.     

Natural Convection Coupled with Radiation Heat Transfer in Slanted Square and Shallow Enclosures Containing an Isotropic Scattering Medium

A finite-volume method (FVM) is used to address combined heat transfer, natural convection, and volumetric radiation with an isotropic scattering medium, in a tilted shallow enclosure. Numerical simulations are performed in the in-house fluid flow software GTEA. All the results obtained by the present FVM agree very well with the numerical solutions in the references. The effects of various influencing parameters such as the Planck number (0.0001 ≤ Pl ≤ 10), the scattering albedo (0 ≤ ω ≤ 1), the inclination angle (?60° ≤ α ≤ 90°), and aspect ratio (1 ≤ AR ≤ 5) on flow and heat transfer have been numerically studied. For a constant Pl number, flow is slightly intensified at the midplane as the Ra number increases from 10⁶ to 5 × 10⁶. As the scattering albedo increases, the effect of radiation heat transfer decreases on both slanted and horizontal enclosures. In positive tilt angles, the influence of α on heat transfer is quite remarkable. The highest Nu_rad appears at α = 30° (ω = 1)and 0° (ω = 0, 0.5), whereas Nu_rad is maximum at α = ? 15° (ω = 1) and ?45° (ω = 0, 0.5). At α = ?15°, the maximum and minimum values of Nu_rad are presented for ω = 0, AR = 1 and ω = 1, AR = 5.     

Coupled Natural Convection and Radiation in a Horizontal Rectangular Enclosure Discretely Heated from Below

A numerical study is carried out to investigate the interaction between natural convection and thermal radiation in a horizontal enclosure filled with air and heated discretely from below. The results are presented for a cavity having an aspect ratio A _r  = L′/H′ = 10, while the Rayleigh number and the emissivity of the walls are varied in the ranges 10³ ≤ Ra ≤ 10⁶ and 0 ≤ ε ≤ 1, respectively. The results of the study, presented in terms of flow and temperature patterns, average convective, radiative and total Nusselt numbers, evaluated on the cold wall, show that the problem has multiple solutions. Each of these solutions is characterized by a specific flow structure, and its appearance and range of existence depend strongly on the parameters Ra and ε. The amount of heat evacuated through the cold surface is dependent on the type of solution.     

Lattice Boltzmann Simulation of Turbulent Natural Convection in Tall Enclosures Using Cu/Water Nanofluid

In this article, Lattice Boltzmann simulation of turbulent natural convection with large-eddy simulations (LES) in a square cavity, which is filled by water/copper nanofluid, has been investigated. The present results are validated by the consequences of an experimental research at Pr = 0.71 and Ra = 1.58 × 10⁹. Calculations are performed for high Rayleigh numbers (Ra = 10⁷–10⁹), low volume fractions of nanoparticles (0 ≤ ? ≤ 0.06), and three aspect ratios (A = 0.5, 1, and 2). In this investigation, we present that large-eddy turbulent nanofluid flow is modeled by the Lattice Boltzmann method (LBM) with a clear and simple statement. Effects of nanopartcles are displayed on streamlines, isotherm counters, local Nusselt number, and average Nusselt number. The average Nusselt number enhances with the augmentation of the nanoparticles volume fractions in the base fluid for multifarious aspect ratios and the Rayleigh numbers. Heat transfer declines with the increase in the aspect ratios in the base fluid, but the effects of nanopaticles are dissimilar for various aspect ratios at different Rayleigh numbers.     

Analysis of entropy generation during natural convection in porous enclosures with curved surfaces

The natural convection is analyzed via the entropy generation approach in the differentially heated, porous enclosures with curved (concave or convex) vertical walls. The numerical simulations have been carried out for various fluids (Prandtl number: Pr_m?=?0.015, 0.7, and 7.2) at various permeabilities (Darcy numbers: 10^?5?≤?Da_m?≤?10^?2) for a high value of Rayleigh number (Ra_m?=?10⁶). The finite element method is employed to solve the governing equations and that is further used to calculate the entropy generation and average Nusselt number. The detailed spatial distributions of S_θ and S_ψ are analyzed for all the wall curvatures. Overall, the case with the highly concave surfaces (case 3) is the optimal case at low Da_m, whereas the cases with the less convex surfaces (cases 1 and 2) are the most efficient cases at high Da_m.     

Turbulent natural convection in a composite annulus using a novel numerical scheme and the thermal nonequilibrium hypothesis

Composite cavities formed by a clear space, a layer of porous material, and a solid plate can be engineered for controlling the overall heat transfer across the enclosure. Using different layer dimensions, as well as distinct porous and solid materials, the value of the cavity Nusselt number can be modified with regard to traditional Nu?∝?Raⁿ behavior, which is encountered either in completely empty cavities or in cavities fully fitted with porous materials. Motivated by such novel application, this work presents a study about turbulent natural convection in a composite concentric annulus. The annulus is assumed to be two-dimensional and positioned horizontally, being isothermally heated at the inner cylinder and cooled from the outer surface. Laminar flow is considered in addition to the turbulent regime, which is handled via the standard k–ε model. The wall treatment applied is the High Reynolds approach. The Two-Energy Equation Model (2EEM) is utilized in the porous section. The transport equations are discretized using the control-volume method. The system of algebraic equations is relaxed via the Semi Implicit Pressure-Linked Equations (SIMPLE) algorithm. A new numerical methodology is applied to resolve all three layers in a single computational domain by establishing two temperature sets, defined according to the location inside the composite structure. Nusselt number behavior shows that for Rayleigh number up to 10⁴ there is no significant variation between the laminar and turbulence models, although the differences increase when the flow gets more intense and/or the porous material becomes more permeable. When comparing the effects of Rayleigh number, Darcy number, porosity, and thermal conductivity ratio between the solid and the fluid on Nu, the results indicate that the solid-phase properties have a greater influence in enhancing the overall heat transferred through the cavity.     

Numerical simulation and optimization of turbulent fluids in a three-dimensional angled ribbed channel

ABSTRACT

In this study, numerical simulations of turbulent steam forced convection in a three-dimensional angled ribbed channel with constant heat flux are investigated. The elliptical, coupled, steady-state, and three-dimensional governing partial differential equations for turbulent forced convection are solved numerically using the finite volume approach. The standard k?? turbulence model is applied to solve the turbulent governing equations. Numerical results are first validated using reference’s data reported in the literature and the maximum discrepancy between them is 3%. The effects of Reynolds number, angled rib height ratio, angled rib pitch ratio, and rib angle on the friction factor ratio and averaged Nusselt number are investigated. Numerical results show that the increase in heat transfer is accompanied by an increase in the friction factor ratio of the steam, the minimum friction factor ratio occurs at θ = 30^○ and the maximum friction factor ratio is found at θ = 60^○. In addition, after the validation of the numerical results, the numerical optimization of this problem is also presented by using the response surface methodology coupled with computational fluid dynamic method.     

Convective Heat Transfer from a Thick Hemispherical Plate during Free Liquid Jet Impingement

Convective heat transfer during free liquid jet impingement on a hemispherical solid plate of finite thickness has been examined. The model included the entire fluid region (impinging jet and flow spreading out over the hemispherical surface) and solid plate as a conjugate problem. Solution was done for both isothermal and constant heat flux boundary conditions at the inner surface of the hemispherical plate. Computations were done for jet Reynolds number (Re _j ) ranging from 500 to 2,000, dimensionless nozzle-to-target spacing ratio (β) from 0.75 to 3, and for various dimensionless plate thicknesse-to-nozzle diameter ratios (b/d _n ) from 0.08 to 1.5. Results are presented for local Nusselt number using water (H₂O), flouroinert (FC-77), and oil (MIL-7808) as working fluids, and aluminum, Constantan, copper, silicon, and silver as solid materials. It was observed that plate materials with higher thermal conductivity maintained a more uniform temperature distribution at the solid–fluid interface. A higher Reynolds number increased the Nusselt number over the entire solid–fluid interface.     

Natural Convection: Analysis of Partially Open Enclosures With an Internal Heated Source

A numerical study of the thermal and fluid dynamic behavior of air in partially open two-dimensional enclosures is presented. An analysis is made based on two aspects of the radius, H/W = 1 and 2. The left and right walls are maintained at different constant temperatures, while the upper and bottom walls are thermally insulated. The enclosure has an opening on the right wall and a small heating source located on the bottom or left vertical wall, occupying three different positions. Numerical simulations were performed for several values of Rayleigh number (Ra _e ) in the range between 10³ and 10⁶>, while the intensity of the two effects—the difference in temperature of the vertical walls and the internal heating source (Ra _i )—was evaluated based on the relation R = Ra _i /Ra _e , in the range between 0 and 2,500. Representative results illustrating the effects of relation R on the streamlines and isotherms within the enclosures are reported. In addition, simulation results for the local and average Nusselt numbers on the heated and colded walls of the enclosures are presented and discussed for different values of the parameters R, Ra _e , W _H , and H/W. It is founded that the parameter modifications have significant effects on the average and local Nusselt numbers of the enclosures.     

Numerical Simulation of Unsteady Heat Transfer in a Half-Moon Shape Enclosure with Variable Thermal Boundary Condition for Different Nanofluids

A half-moon shape enclosure which has a very wide range of practical applications in heat transfer is introduced for the first time in this article. The heat transfer is analyzed introducing different commercially available nanofluids such as water–Al₂O₃, water–Cu, water–TiO₂ in this half-moon enclosure. A variable thermal boundary condition is assigned to the model, and the finite-element method is used for the numerical solution of the problem. The effect of solid volume fraction φ, along with a wide range of Rayleigh numbers (Ra = 10⁵–10⁷), are evaluated in various dimensionless times τ. The performance of the shape is described by using streamfunctions, isotherms, charts, and related graphs. It is found that heat transfer in the cavity can be enhanced up to 30% by to the presence of nanoparticles.     

A numerical simulation of heat transfer in an enclosure with a nonlinear heat source

Two-dimensional simulations of natural convection driven by the absorption of nonuniform concentrated solar radiation in a molten binary salt-filled enclosure inclined at 0?≤???≤?60 are presented. The enclosure is volumetrically heated from the top boundary and accommodates a black rigid, heat-conducting plate of finite thickness at the lower boundary, which aids in the generation of natural convective mixing at the lower boundary. The governing equations that account for the depth-dependent absorption of radiation are solved using the finite-element method. Numerical results reveal that increasing the inclination angles decreases the natural convection and higher Rayleigh promotes natural convection.