Natural convection flow of Cu–Water nanofluid in horizontal cylindrical annuli with inner triangular cylinder using lattice Boltzmann method

In this paper the lattice Boltzmann method is used to investigate the effect of nanoparticles on natural convection heat transfer in two-dimensional horizontal annulus. The study consists of an annular-shape enclosure, which is created between a heated triangular inner cylinder and a circular outer cylinder. The inner and outer surface temperatures were set as hot (T_h) and cold temperatures (T_c), respectively and assumed to be isotherms. The effect of nanoparticle volume fraction to the enhancement of heat transfer was examined at different Rayleigh numbers. Furthermore, the effect of vertical, horizontal, and diagonal eccentricities at various locations is examined at Ra = 10⁴. The result is presented in the form of streamlines, isotherms, and local and average Nusselt number. Results show that the Nusselt number and the maximum stream functions increase by augmentation of solid volume fraction. Average Nusselt number increases when the inner cylinder moves downward, but it decreases, when the location of inner cylinder changes horizontally.     

Lattice Boltzmann simulation of natural convection heat transfer in an elliptical-triangular annulus

A numerical study for steady-state, laminar natural convection in a horizontal annulus between a heated triangular inner cylinder and cold elliptical outer cylinder was investigated using lattice Boltzmann method. Both inner and outer surfaces are maintained at the constant temperature and air is the working fluid. Study is carried out for Rayleigh numbers ranging from 1.0 × 10³ to 5.0 × 10⁵. The effects of different aspect ratios and elliptical cylinder orientation were studied at different Rayleigh numbers. The local and average Nusselt numbers and percentage of increment heat transfer rate were presented. The average Nusselt number was correlated. The results show that by decreasing the value of aspect ratio and/or increasing the Rayleigh number, the Nusselt number increases. Also the heat transfer rate increases when the ellipse positioned vertically.     

Natural convection in an annulus between coaxial horizontal cylinders with internal heat generation

Natural convection of gas (Pr = 0.7) between two horizontal coaxial cylinders with uniform internal heat generation is numerically investigated. Such a problem plays an important role in the analysis of lasers in which a similar circuit of a heat-conducting path is used. It has been found that the behavior of the system critically depends on three parameters including the inverse relative gap width σ(=diameter of the inner cylinder/gap width), the Rayleigh number Ra and the modified Rayleigh number Ra_T which describes heat generation. In the case Ra_T = 0 our results coincide with the known ones. It has been established that in such a system there exist two types of fluid flow for low Rayleigh numbers with different vortex structure. Optimization of the corresponding coaxial laser system has been analyzed.     

Natural convection effects on heat and mass transfer in a curvilinear triangular cavity

Finite element method is used in this study to analyze the effects of buoyancy ratio and Lewis number on heat and mass transfer in a triangular cavity with zig-zag shaped bottom wall. Buoyancy ratio is defined as the ratio of Grashof number of solutal and thermal. Inclined walls of the cavity have lower temperature and concentration according to zig-zag shaped bottom wall. Enclosed space consists mostly of an absorber plate and two inclined glass covers that form a cavity. Both high temperature and high concentrations are applied to bottom corrugated wall. Computations were done for different values of buoyancy ratio (?10 ? Br ? 10), Lewis number (0.1 ? Le ? 20) and thermal Rayleigh number (10⁴ ? Ra_T ? 10⁶). Streamlines, isotherms, iso-concentration, average Nusselt and Sherwood numbers are obtained. It is found that average Nusselt and Sherwood numbers increase by 89.18% and 101.91% respectively as Br increases from ?10 to 20 at Ra_T = 10⁶. Also, average Nusselt decreases by 16.22% and Sherwood numbers increases by 144.84% as Le increases from 0.1 to 20 at this Rayleigh number.     

Simulation of turbulent natural convection in a porous cylindrical annulus using a macroscopic two-equation model

This work presents numerical computations for laminar and turbulent natural convection within a horizontal cylindrical annulus filled with a fluid saturated porous medium. Computations covered the range 25 < Ra_m < 500 and 3.2 × 10⁻⁴ > Da > 3.2 × 10⁻⁶ and made use of the finite volume method. The inner and outer walls are maintained at constant but different temperatures. The macroscopic k–ε turbulence model with wall function is used to handle turbulent flows in porous media. First, the turbulence model is switched off and the laminar branch of the solution is found when increasing the Rayleigh number, Ra_m. Subsequently, the turbulence model is included and calculations start at high Ra_m, merging to the laminar branch for a reducing Ra_m. This convergence of results as Ra_m decreases can be seen as an estimate of the so-called laminarization phenomenon. Here, a critical Rayleigh number was not identified and results indicated that when the porosity, Prandtl number, conductivity ratio between the fluid and the solid matrix and Ra_m are kept fixed, the lower the Darcy number, the higher is the difference of the average Nusselt number given by the laminar and turbulent models.     

Bénard convection from a circular cylinder in a packed bed

Bénard convection around a circular heated cylinder embedded in a packed bed of spheres is studied numerically. The Forchheimer–Brinkman–extended Darcy momentum model with the Local Thermal Non-Equilibrium energy model is used in the mathematical formulation for the porous layer. The governing parameters considered are the Rayleigh number (10³ ≤ Ra ≤ 5 × 10⁷) and the thermal conductivity ratio (0.1 ≤ k_r ≤ 10,000). The structural properties of the packed bed are kept constant as: cylinder-to-particle diameter ratio D/d = 20 and porosity ε = 0.5, while the Prandtl number is fixed at Pr = 0.71. It is found that the presence of the porous medium suppresses significantly the strong free convection produced in the empty enclosure, and reduces considerably the high intensity of the pair of vortices generated behind the cylinder. Also, the results show that the porous medium can play the role of insulator or enhancer of heat transfer from the heat source, depending mainly on their thermal conductivities regardless of the Rayleigh number.     

Transient natural convective heat transfer of a low-Prandtl-number fluid inside a horizontal circular cylinder with an inner coaxial triangular cylinder

A numerical study of transient natural convection of liquid gallium (Pr = 0.023) from a horizontal triangular cylinder to its coaxial cylindrical enclosure is performed. The aspect ratio is fixed at 2 and two positions of the inner triangular cylinder are considered. The development of the convective flow and heat transfer is shown via the time histories of the average Nusselt number over the outer circular wall for various Grashof numbers. Temporal phases of the flow development are identified as: initializing, developing, transitioning, and steady/quasi-steady state or oscillating. Typical flow patterns and temperature distributions at these phases are presented by means of streamlines and isotherms, respectively. Pitchfork bifurcation is present for both positions of the inner triangular cylinder when Gr ? 5 × 10⁴. The time-averaged Nusselt number over the outer circular cylinder, the flow development time, and the onset time of pitchfork bifurcation are predicted and scaled with the Grashof number. It is found that the time-averaged Nusselt number is apparently increased by horizontally placing the top side of the inner triangular cylinder for Gr ? 1 × 10⁵.     

Heat transfer in a small gap between co-axial rotating cylinders

This paper investigates the local heat transfer of a co-axial rotating cylinder. In the inner flow field of the rotating cylinder, the dimensionless parameters include the rotational Reynolds number (Re_Ω) and buoyancy parameter (Gr). The test rig is designed to make the rotating in the inner cylinder and stationary in the outer cylinder. The local temperature distributions of the inner and outer cylinder on axial direction were measured. Under the experimental condition, whereas the ranges of the rotational Reynolds number are 2400 ≤ Re_Ω ≤ 45,000. Experimental results reveal that the rotational Reynolds number's increase is with the heat transfer coefficient distributions increase types. Finally, the local heat transfer rate on the wall are correlated and compared with that in the existing literature.     

Numerical analysis of natural convection heat transfer in a horizontal annulus partially filled with a fluid-saturated porous substrate

The current study centers around a numerical investigation of natural convection heat transfer within a two-dimensional, horizontal annulus that is partially filled with a fluid-saturated porous medium. In addition, the porous sleeve is considered to be press fitted to the inner surface of the outer cylinder. Both cylinders are maintained at constant and uniform temperatures with the inner cylinder being subjected to a relatively higher temperature than the outer one. Moreover, the Forchheimer and Brinkman effects are taken into consideration when simulating the fluid motion inside the porous sleeve. Furthermore, the local thermal equilibrium condition is assumed to be applicable for the current investigation. The working fluid is air while copper is used to represent the solid phase. The porosity is considered to be uniform and constant with ε = 0.9. The main objective of this study is to examine the effect of the porous sleeve on the buoyancy induced flow motion under steady-state condition. Such an effect is studied using the following dimensionless parameters: Pr = 0.05–50, Ra = 10²–10⁶ and Da = 10^?4–10^?6. Also, the study highlights the effect of the dimensionless porous sleeve thickness (b) and thermal conductivity ratio (k_s/k_f) in the range between 1.1–1.9 and 1–150, respectively.     

Flow over and forced convection heat transfer in Newtonian fluids from a semi-circular cylinder

Momentum and heat transfer characteristics of a semi-circular cylinder immersed in unconfined flowing Newtonian fluids have been investigated numerically. The governing equations, namely, continuity, Navier–Stokes and energy, have been solved in the steady flow regime over wide ranges of the Reynolds number (0.01 ? Re ? 39.5) and Prandtl number (Pr ? 100). Prior to the investigation of drag and heat transfer phenomena, the critical values of the Reynolds number for wake formation (0.55 < Re^c < 0.6) and for the onset of vortex shedding (39.5 < Re_c < 40) have been identified. The corresponding values of the lift coefficient, drag coefficient, and Strouhal number are also presented. After establishing the limit of the steady flow regime, the influence of the Reynolds number (0.01 ? Re ? 39.5) and Prandtl number (Pr = 0.72, 1, 10, 50 and 100) on the global flow and heat transfer characteristics have been elucidated. Detailed kinematics of the flow is investigated in terms of the streamline and vorticity profiles and the variation of pressure coefficient in the vicinity of the cylinder. The functional dependence of the individual and total drag coefficients on the Reynolds number is explored. The Nusselt number shows an additional dependence on the Prandtl number. In addition, the isotherm profiles, local Nusselt number (Nu_L) and average Nusselt number (Nu) are also presented to analyze the heat transfer characteristic of a semi-circular cylinder in Newtonian media.     

Magnetoconvection in an enclosure of water near its density maximum with Soret and Dufour effects

In this paper, unsteady double-diffusive magnetoconvection of water in an enclosure with Soret and Dufour effects around the density maximum has been numerically investigated. The right vertical wall has constant temperature, θ_c, while left vertical wall is θ_h, with θ_h > θ_c. The concentration in right wall is maintained lower than left wall (c_h > c_c). The remaining horizontal walls are adiabatic. The governing equations are solved by control volume method using SIMPLE algorithm with QUICK scheme. Representative results illustrating the effects of the thermal Rayleigh number, Hartmann number, the direction of magnetic field, density inversion parameter, buoyancy ratio, Schmidt number, and Soret and Dufour parameters on the contour maps of the fluid flow, temperature and concentration as well as the profile of velocity at mid-section of the enclosure are reported. In addition, numerical results for the average Nusselt and Sherwood numbers are presented for various parametric conditions and discussed.     

Natural convection in a square cavity filled with a porous medium: Effects of various thermal boundary conditions

Natural convection flows in a square cavity filled with a porous matrix has been studied numerically using penalty finite element method for uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls. Darcy–Forchheimer model is used to simulate the momentum transfer in the porous medium. The numerical procedure is adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁶, Darcy number Da, 10⁻⁵ ⩽ Da ⩽ 10⁻³, and Prandtl number Pr, 0.71 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous thermal boundary conditions. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case for all Rayleigh numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. It has been found that the heat transfer is primarily due to conduction for Da ⩽ 10⁻⁵ irrespective of Ra and Pr. The conductive heat transfer regime as a function of Ra has also been reported for Da ⩾ 10⁻⁴. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes the power law correlations between average Nusselt number and Rayleigh numbers are presented.     

Effect of a magnetic field on natural convection in an open cavity subjugated to water/alumina nanofluid using Lattice Boltzmann method

In this paper, the effect of a magnetic field on natural convection in an open enclosure which subjugated to water/alumina nanofluid using Lattice Boltzmann method has been investigated. The cavity is filled with water and nanoparticles of Al₂O₃ at the presence of a magnetic field. Calculations were performed for Rayleigh numbers (Ra = 10⁴–10⁶), volume fractions of nanoparticles (φ = 0,0.02,0.04 and .0.06) and Hartmann number (0 ≤ Ha ≤ 90) with interval 30 while the magnetic field is considered horizontally. Results show that the heat transfer decreases by the increment of Hartmann number for various Rayleigh numbers and volume fractions. The magnetic field augments the effect of nanoparticles at Rayleigh number of Ra = 10⁶ regularly. Just as the most effect of nanoparticles for Ra = 10⁴ is observed at Ha = 30, so the most influence of nanoparticles occurs at Ha = 60 for Ra = 10⁵.     

Influence of natural convection on the melting of ice block surrounded by water on all sides

The ice block at initial temperature T_is = 0 °C is fixed at the center of a long, prismatic enclosure with isothermal vertical walls and insulated horizontal walls. The enclosure is completely filled with water at initial temperature T_il = 0 °C. Six numerical simulations were performed by varying vertical wall temperatures from T_W = 2 to 12 °C (range of Rayleigh number from 4.22 × 10⁶ to 2.28 × 10⁷). In the case of T_W > 8 °C the ice melts faster from above and for T_W < 8 °C from below. In the case of T_W = 8 °C, two vortices are separated by nearly vertical 4 °C isotherm and the average Nusselt number remains constant during the convection dominated regime.     

Unsteady conjugate natural convection in a square enclosure filled with a porous medium

Mathematical simulation of unsteady natural convection modes in a square cavity filled with a porous medium having finite thickness heat-conducting walls with local heat source in conditions of heterogeneous heat exchange with an environment at one of the external boundaries has been carried out. Numerical analysis was based on Darcy–Forchheimer model in dimensionless variables such as a stream function, a vorticity vector and a temperature. The special attention was given to analysis of Rayleigh number effect Ra = 10⁴, 10⁵, 10⁶, of Darcy number effect Da = 10^?5, 10^?4, 10^?3, ∞, of the transient factor effect 0 < τ < 1000 and of the heat conductivity ratio k_2,1 = 3.7 × 10^?2, 5.7 × 10^?4, 6.8 × 10^?5 on the velocity and temperature fields. The influence scales of the defining parameters on the average Nusselt number have been detected.     

Computational analysis of natural convection in a parallelogrammic cavity with a hot concentric circular cylinder moving at different vertical locations

A finite volume numerical simulation of natural convection in a parallelogrammic air-filled cavity having a heated concentric circular cylinder is performed. The left and right sidewalls of the cavity are maintained at a uniform cold temperature, while both upper and lower walls of it are considered thermally insulated. A wide range of significant parameters such as Rayleigh number, inclination angle and cylinder vertical locations are considered in the present study. Comparison with previously published works is made and found to be an excellent agreement. The results show that the strength of the flow circulation and the thickness of thermal boundary layer around the hot circular cylinder are increased dramatically when the Rayleigh number increases. Also, to increase the flow circulation inside the parallelogrammic cavity, it is recommended to make the inner cylinder moves downward until it reaches to [δ = − 0.2] and the parallelogrammic cavity sidewalls inclined to [Φ = 15°]. Moreover, it is found that for various values of the inclination angle, the average Nusselt numbers at inner cylinder surface and at both cavity sidewalls, decrease when the cylinder moves upward, while they increase when the cylinder moves downward.     

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.     

Mixed convective transport in a lid-driven cavity containing a nanofluid and a rotating circular cylinder at the center

The mixed convective transport of Cu-H₂O nanofluid in a differentially heated and lid-driven square enclosure in the presence of a rotating circular cylinder is investigated numerically. The top wall of the enclosure is sliding from left to right at a uniform speed while all other walls are stationary. A thermally insulated circular cylinder is placed centrally within the enclosure. The cylinder can rotate about its centroidal axis. The top and bottom walls are kept isothermal at different temperatures while the side walls are assumed adiabatic. Simulations are performed for, Richardson number 1 ≤ Ri ≤ 10, dimensionless rotational speed 0 ≤ Ω ≤ 5 and nanoparticle concentration 0 ≤ ϕ ≤ 0.20 keeping the Grashof number fixed as Gr = 10⁴. The flow and thermal fields are analyzed through streamline and isotherm plots for various Ω and Ri. Furthermore, the drag coefficient of the moving lid and Nusselt number of the hot wall are also computed to understand the effects of Ω and Ri on them. It is observed that the heat transfer greatly depends on the rotational speed of the cylinder, mixed convective strength and the nanoparticle concentration.     

Effects of thermal boundary conditions on natural convection flows within a square cavity

A numerical study to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls has been performed. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10³ ⩽ Ra ⩽ 10⁵ and Prandtl number Pr, 0.7 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rates at the center of the bottom wall than the uniform heating case for all Rayleigh numbers; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented.     

Investigation of natural convection induced outer side heat transfer rate of coiled-tube heat exchangers

Natural convection induced heat transfer has been studied over the outer surface of helically coiled-tube heat exchangers. Several different geometrical configurations (curvature ratio δ ε [0.035, 0.082]) and a wide range of flow parameters (60 <= T_tank <= 90, T_in = 19 and 60 <= T_in <= 90, T_tank = 20, 4000 <= Re <= 45000) have been examined to broaden the validity of the results gained from this research. A fluid-to-fluid boundary condition has been applied in the numerical calculations to create the most realistic flow configurations. Validity of the numerical calculations has been tested by experiments available in the open literature. Calculated results of the inner side heat transfer rate have also been compared to existing empirical formulas and experimental results to test the validity of the numerical computation in an independent way from the outer side validation of common helical tube heat exchangers. Water has been chosen to the working fluid inside and outside of the coiled tube (3 < Pr < 7). Outer side heat transfer rate along the helical tube axis has been investigated to get information about the performance of the heat transport process at different location of the helical tube. It was found that the outer side heat transfer rate is slightly dependent on the inner flow rate of any helical tube in case of increasing temperature differences between the tank working fluid temperature and the coil inlet temperature. A stable thermal boundary layer has been found along the axial direction of the tube.In addition to this the qualitative behavior of the peripherally averaged Nusselt number versus the axial location along the helical tube function is strongly dependent on the direction of the heat flow (from the tube to the storage tank and the reversed direction). Inner side heat transfer rate of helical coils have also been investigated in case of fluid-to-fluid boundary conditions and the calculation results have been compared with different prediction formulas published in the last couples of decades.