Experimental and numerical analysis of buoyancy-induced flow in inclined triangular enclosures

The buoyancy‐induced heat transfer and fluid flow in a triangular enclosure are investigated both numerically and experimentally. The enclosure is heated from one wall and the adjacent wall is insulated. Hypotenuse of the triangle is cooled isothermally. The numerical tests and experiments covered a range of Rayleigh number, Ra, from 1.5 × 10⁴ to 1.5 × 10⁵. The local and average Nusselt numbers are given for different orientation angles. A code was written based on finite difference method in Fortran platform to solve governing equations of natural convection. Experimental and numerical results show good agreement. It is observed that inclination angle can be used as a control parameter for heat transfer.     

Mixed convection heat transfer in a differentially heated square enclosure with a conductive rotating circular cylinder at different vertical locations

In this investigation, a numerical simulation using a finite volume scheme is carried out for a laminar steady mixed convection problem in a two-dimensional square enclosure of width and height (L), with a rotating circular cylinder of radius (R = 0.2 L) enclosed inside it. The solution is performed to analyze mixed convection in this enclosure where the left side wall is subjected to an isothermal temperature higher than the opposite right side wall. The upper and lower enclosure walls are considered adiabatic. The enclosure under study is filled with air with Prandtl number is taken as 0.71. Fluid flow and thermal fields and the average Nusselt number are presented for the Richardson numbers ranging as 0, 1, 5 and 10, while Reynolds number ranging as 50, 100, 200 and 300. The effects of various locations and solid-fluid thermal conductivity ratios on the heat transport process are studied in the present work. The results of the present investigation explain that increase in the Richardson and Reynolds numbers has a significant role on the flow and temperature fields and the rotating cylinder locations have an important effect in enhancing convection heat transfer in the square enclosure. The results explain also, that the average Nusselt number value increases as the Reynolds and Richardson numbers increase and the convection phenomenon is strongly affected by these parameters. The results showed a good agreement with further published works.     

Effect of Prandtl Number on Free Convection from Two Cylinders in a Square Enclosure

This study explores the effect of Prandtl number on the laminar natural convection heat transfer to Newtonian fluids in a square enclosure consisting of one hot circular cylinder and one cold circular cylinder. The walls of the square enclosure are maintained isothermal and at the same temperature as the cold cylinder and the fluid medium. The governing partial differential equations have been solved numerically over the following ranges of conditions: Grashof number, 10 to 10⁵; Prandtl number, 0.7 to 100 (or the range of Rayleigh numbers as 7 to 10⁷); and relative positioning of the cylinders, ?0.25 to 0.25. However, the ratio of the radius of the cylinder to the side of the enclosure is held fixed at 0.2. Extensive results on the streamline and isotherm contours, the local Nusselt number distribution, and the average Nusselt number are discussed to delineate the influence of Grashof and Prandtl numbers on them for a given location with respect to the horizontal center line. The surface-averaged Nusselt number shows a positive dependence on Grashof and Prandtl numbers for a fixed location of the two cylinders. The heat transfer results have been correlated as a function of the Rayleigh number and geometric parameters, thereby enabling its prediction in a new application.     

Laminar Natural Convection of Bingham Fluids in Square Cross-Sectioned Cylindrical Annular Cavity with Differentially Heated Vertical Walls Subjected to Constant Heat Fluxes

Steady-state numerical simulations have been conducted to investigate natural convection of yield stress fluids obeying Bingham model in square cross-sectioned axisymmetric cylindrical annular enclosure with vertical walls subjected to constant heat fluxes for nominal Rayleigh number range of 10³ to 10⁶, nominal Prandtl number of 10 to 10³ for different values of internal cylinder radius. It is found that the mean Nusselt number on the inner periphery increases (decreases) with increasing nominal Rayleigh (Bingham) number due to strengthening (weakening) of thermal advection. However, the values of the mean Nusselt number on the inner periphery obtained for Bingham fluids are smaller than that obtained for Newtonian fluids for the same set of nominal Rayleigh and Prandtl numbers. The mean Nusselt number normalized by the corresponding value obtained for pure conductive transport increases with increasing internal radius before asymptotically approaching the mean Nusselt number for a square enclosure. This suggests that the ratio of the convective to the conductive transport strengthens with increasing cylinder radius in the cylindrical annular cavity. Detailed physical explanations have been provided for the effects of the aforementioned parameters on the mean Nusselt number on the inner periphery and correlations have been proposed for the mean Nusselt number on the inner periphery for both Newtonian and Bingham fluids.     

Three-dimensional natural convection in an enclosure with a sphere at different vertical locations

Numerical calculations are carried out for the three-dimensional natural convection induced by a temperature difference between a cold outer cubic enclosure and a hot inner sphere. The immersed-boundary method (IBM) to model a sphere based on the finite volume method is used to study a three-dimensional natural convection for different Rayleigh numbers varying in the range of 10³–10⁶. This study investigates the effect of the inner sphere location on the heat transfer and fluid flow. The flow and thermal fields eventually reach the steady state for all Rayleigh numbers regardless of the sphere location. For Rayleigh numbers of 10⁵ and 10⁶, the variation of local Nusselt number of the sphere along the circumferential direction is large, showing the strong three dimensionality of the natural convection in the enclosure unlike to the cases of lower Rayleigh numbers of 10³ and 10⁴. For the highest Rayleigh number, the local peaks of the Nusselt number on the top wall of the enclosure shows the sinusoidal distribution along the circumferential direction. The flow and thermal fields, and the local and surface-averaged Nusselt numbers on the sphere and the enclosure are highlighted in detail.     

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.     

Modeling of conjugated heat transfer in a thick walled enclosure filled with nanofluid

The objective of this paper is to investigate the conjugated heat transfer in a thick walled cavity filled with copper-water nanofluid. The analysis uses a two-dimensional rectangular enclosure under conjugated convective-conductive heat transfer conditions and considers a range of Rayleigh numbers. The enclosure was subjected to a constant and uniform heat flux at the left thick wall generating a natural convection flow. The thicknesses of the other boundaries are assumed to be zero. The right wall is kept at a low constant temperature while the horizontal walls are assumed to be adiabatic. A moveable divider is located at the bottom wall of the cavity. The governing equations are derived based on the conceptual model in the Cartesian coordinate system. The study has been carried out for the Rayleigh number in the range of 10⁵ ≤ Ra ≤ 10⁸, and for the solid volume fraction at 0 ≤ ? ≤ 0.05. Results are presented in the form of streamlines, isotherms, average Nusselt number and input heat absorption by the nanofluid. The effects of solid volume fraction of nanofluids, the location of the divider and also the value of the ambient convective heat transfer coefficient on the hydrodynamic and thermal characteristics of flow have been analyzed. An increase in the average Nusselt number was found with the solid concentration for the whole range of Rayleigh number. In addition, results show that the position of the divider and the ambient convective heat transfer coefficient have a considerable effect on the heat transfer enhancement.     

Effect of Fluid Yield Stress on Natural Convection From Horizontal Cylinders in a Square Enclosure

In this study, laminar natural convection heat transfer to Bingham plastic fluids from two differentially heated isothermal cylinders confined in a square enclosure (with isothermal walls) has been investigated numerically. The governing partial differential equations have been solved over the ranges of the dimensionless parameters, namely, Rayleigh number, 10² to 10⁶, Prandtl number, 10 to 100, and Bingham number, 0.01 to 100, for seven locations of inner cylinders as ±0.25, ±0.2, ±0.1 and 0. These values correspond to the range of Grashof number varying from 10 to 10⁵. The detailed flow and temperature fields are visualized in terms of the streamlines and isotherm contours. Further insights are developed by examining the iso-shear rate contours and the yield surfaces delineating the fluid-like and solid-like regions. The corresponding heat transfer results are analyzed in terms of the distribution of the local Nusselt number along the cylinder surface together with its surface averaged value as functions of the Rayleigh number, Prandtl number, Bingham number, and positions of the cylinders. It is found that the average Nusselt number increases with the increasing values of the Rayleigh number and decreases with the increasing Bingham number. For sufficiently large values of the Bingham number, the average Nusselt number reaches its asymptotic value wherein heat transfer takes place solely by conduction. Based on the present numerical results, simple correlations for the prediction of the average Nusselt number and the limiting Bingham number have been developed. Also, a dimensionless criterion denoting the cessation of convection regime is outlined for this configuration.     

Free Convection in Confined Power-Law Fluids From Two Side-by-Side Cylinders in a Square Enclosure

Laminar free convection heat transfer in power-law fluids from two side-by-side cylinders (one hot and one cold) confined in a square duct has been studied numerically in the two-dimensional flow regime. For a fixed value of the ratio of cylinder radius to size of the enclosure, the effect of geometrical placement of the cylinders is studied on the resulting velocity and temperature fields in the laminar free convection regime by considering six asymmetric locations of the two cylinders. In particular, extensive results reported herein span the range of conditions of Grashof number, 10 to 10⁵; Prandtl number, 0.7 to 100, thereby yielding the range of the Rayleigh number as 7 to 10⁷; power-law index, 0.3 to 1.8; and the relative positions (dimensionless) of the cylinders with respect to the centerline, –0.25 to 0.25. The heat transfer characteristics are analyzed in terms of the local Nusselt number along the surfaces of the two cylinders and the enclosure walls. Overall, the average Nusselt number shows a positive dependence on both the Grashof number and the Prandtl number irrespective of the values of power-law index and relative positioning of the cylinders. Also, all else being equal, shear-thinning fluid behavior promotes heat transfer with reference to that in Newtonian fluids. When the two cylinders are situated close to the bottom wall, the rate of heat transfer is augmented with reference to that for the symmetric positioning of the cylinders along the horizontal mid-plane of the enclosure. Conversely, heat transfer deteriorates as the cylinders are located above the centerline of the enclosure. The present numerical results have been consolidated via the use of a modified Rayleigh number, thereby enabling the estimation of the average Nusselt number in a new application.     

A Differential Quadrature Solution of Natural Convection in an Enclosure with a Partial Partition

Natural convection in a partially divided enclosure has been examined numerically using a differential quadrature method. Governing equations for the flow and heat transfer have been constructed by the vorticity-stream function formulation and computational results have been obtained for the Rayleigh numbers, 10⁴, 10⁵, 10⁶, the locations of the partition, 0.2, 0.4, 0.6, 0.8, and the partition ratios, 0.25, 0.50, 0.75, 1.0. The results show that circulation strength, and therefore heat transfer, decreases considerably with increasing partition height especially for the higher values of the Rayleigh number. As the distance of the partition from the hot wall increases, first a decrease and then an increase is observed in the average Nusselt number for the low Rayleigh numbers and first an increase and then a decrease turns out for the high Rayleigh numbers. As for the average Nusselt number on the partition, first it shows a decreasing trend and then an increasing trend as the partition is distanced from the hot wall towards the cold wall. The increase in the partition height brings about significant increase in the average Nusselt number on the partition.     

Transient natural convection in 3D tilted enclosure heated from two opposite sides

In the present work, we investigate numerically the natural convection flow in 3D cubic enclosure tilted at an angle (γ) with respect to the vertical position. The enclosure is heated and cooled from the two opposite walls while the remaining walls are adiabatic. The numerical procedure adopted in this analysis yield consistent performance over a wide range of parameters. Simulations have been carried out for Rayleigh numbers Ra ranging from 10³ to 1.3 × 10⁵, Prandtl number, Pr, (0.71 ≤ Pr ≤ 75) and inclination angle γ (0° ≤ γ ≤ 90°). Particular attention is focused on the three-dimensional steady effects that can arise in such configuration that seem to be unknown in the literature, even for relatively small values of the Rayleigh number. The 3D flow characteristics and thermal fields are analyzed in terms of streamlines, isotherms and Nusselt numbers. A periodic behavior of the 3D flow has been observed at Ra = 8.5 × 10⁴ with a fundamental frequency of 8.27. The Hopf bifurcation is localized. In addition, time-dependent solutions reveal that the flow characteristics depend on the inclination angle γ. The effects of Prandtl number on heat transfer and fluid flow is significant for Pr ≥ 6.     

A numerical study of natural convection in a square enclosure with a circular cylinder at different vertical locations

Numerical calculations are carried out for natural convection induced by a temperature difference between a cold outer square enclosure and a hot inner circular cylinder. A two-dimensional solution for unsteady natural convection is obtained, using the immersed boundary method (IBM) to model an inner circular cylinder based on the finite volume method for different Rayleigh numbers varying over the range of 10³–10⁶. The study goes further to investigate the effect of the inner cylinder location on the heat transfer and fluid flow. The location of the inner circular cylinder is changed vertically along the center-line of square enclosure. The number, size and formation of the cell strongly depend on the Rayleigh number and the position of the inner circular cylinder. The changes in heat transfer quantities have also been presented.     

Lattice Boltzmann simulation of natural convection in tall enclosures using water/SiO2 nanofluid

Natural convection in enclosures using water/SiO₂ nanofluid is simulated with Lattice Boltzmann method (LBM). This investigation compared with other numerical methods and found to be in excellent agreement. This study has been carried out for the pertinent parameters in the following ranges: the Rayleigh number of base fluid, Ra = 10³-10⁵, the volumetric fraction of nanoparticles between 0 and 4% and aspect ratio (A) of the enclosure between 0.5 and 2. The thermal conductivity of nanofluids is obtained on basis of experimental data. The comparisons show that the average Nusselt number increases with volume fraction for the whole range of Rayleigh numbers and aspect ratios. Also the effect of nanoparticles on heat transfer augments as the enclosure aspect ratio increases.     

Investigation of buoyancy-driven flow and heat transfer in a trapezoidal cavity filled with water–Cu nanofluid

A numerical study is conducted to investigate the transport mechanism of free convection in a trapezoidal enclosure filled with water–Cu nanofluid. The horizontal walls of the enclosure are insulated while the inclined walls are kept at constant but different temperatures. The numerical approach is based on the finite element technique with Galerkin's weighted residual simulation. Solutions are obtained for a wide range of the aspect ratio (AR) and Prandtl number (Pr) with Rayleigh number (Ra = 10⁵) and solid volume fraction (? = 0.05). The streamlines, isotherm plots and the variation of the average Nusselt number at the left hot wall are presented and discussed. It is found that both AR and Pr affect the fluid flow and heat transfer in the enclosure. A correlation is also developed graphically for the average Nusselt number as a function of the Prandtl number as well as the cavity aspect ratio.     

Effects of inclination angle on conduction—natural convection in divided enclosures filled with different fluids

Laminar natural convection in inclined enclosures filled with different fluids was studied by a numerical method. The enclosure was divided by a solid impermeable divider. One side of partition of enclosure was filled with air and the other side had water. The enclosure was heated from one vertical wall and cooled from the other while horizontal walls were adiabatic. The governing equations which were written in stream function–vorticity form were solved using a finite difference technique. Results were presented by streamlines, isotherms, mean and local Nusselt numbers for different thermal conductivity ratios of solid impermeable material (plywood or concrete), inclination angle (0° ≤ ? ≤ 360°) and Grashof numbers (10³ ≤ Gr ≤ 10⁶). The code was validated by earlier studies, which are available in the literature on conjugate natural convection heat transfer. Analytical solutions were obtained for low Grashof numbers. Obtained results showed that both heat transfer and flow strength strongly depended on thermal conductivity ratio of the solid material of partition, inclination angle and Grashof numbers. The heat transfer was lower in the air side of the enclosure than that of the water side.     

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.     

Natural convection in an open square cavity with slots

In this paper, we investigate heat transfer by natural convection in an open cavity in which a uniform heat flux is applied to the inside active wall facing the opening with slots. Conservation equations are solved by finite difference–control volume numerical method. The relevant governing parameters are: the Rayleigh numbers from 10³ to 10⁶, the Prandtl number, Pr = 0.7, constant for air, the cavity aspect ratio, A = L/H = 1. Number of slots N is varied from 2 to 8 and the dimensionless opening ratio OR from 0.1 to 0.6. We found that the Nusselt number and the volume flow rate are both increasing functions of the Rayleigh number; they are a decreasing function of the number of slots and increasing function of the opening ratio, though there is an optimum opening ratio at high Rayleigh numbers.     

A numerical study of laminar natural convective heat transfer around a horizontal cylinder inside a concentric air-filled triangular enclosure

A numerical investigation of steady-state laminar natural convective heat transfer around a horizontal cylinder to its concentric triangular enclosure was carried out. The enclosure was filled with air and both the inner and outer cylinders were maintained at uniform temperatures. The buoyancy effect was modeled by applying the Boussinesq approximation of density to the momentum equation and the governing equations were iteratively solved using the control volume approach. The effects of the Rayleigh number and the aspect ratio were examined. Flow and thermal fields were exhibited by means of streamlines and isotherms, respectively. Variations of the maximum value of the dimensionless stream function and the local and average Nusselt numbers were also presented. The average Nusselt number was correlated to the Rayleigh number based on curve-fitting for each aspect ratio. At the highest Rayleigh number studied, the effects of different inclination angles of the enclosure and various cross-section geometries of the inner cylinder were investigated. The computed results indicated that at constant aspect ratio, both the inclination angle and cross-section geometry have insignificant effects on the overall heat transfer rates though the flow patterns are significantly modified.     

Correlations for Natural Convective Heat Transfer From Vertical and Inclined Cylinders

Natural convective heat transfer from the exposed top surface of an inclined isothermal cylinder, with a circular cross section, mounted on a flat adiabatic base plate, has been numerically investigated. The cylinder is mounted normal to the flat adiabatic base plate. The numerical solution has been obtained by solving the dimensionless governing equations, subject to boundary conditions, using the commercial finite-volume method-based code FLUENT. The flow has been assumed to be symmetrical about the vertical center-plane through the cylinder. Results have only been obtained for Prandtl number of 0.7, which is the value existing in the application that originally motivated this study. The simulations consider Rayleigh numbers between 10³ and 10⁷, inclination angles between 0º and 180º, and dimensionless cylinder diameters between 0.25 and 1. The effects of dimensionless diameter, Rayleigh numbers, and inclination angles on the mean Nusselt number for the top exposed surface of the cylinder have been studied. Empirical correlations for the heat transfer rates from the top exposed surface of the cylinder have been derived.