Numerical investigation of laminar natural convective heat transfer from a horizontal triangular cylinder to its concentric cylindrical enclosure

A numerical simulation was conducted to investigate the steady laminar natural convective heat transfer for air within the horizontal annulus between a heated triangular cylinder and its circular cylindrical enclosure. The Boussinesq approximation was applied to model the buoyancy-driven effect and the governing equations were solved using the finite volume method. Four different Rayleigh numbers and four different radius ratios were considered, and four different inclination angles for the inner triangular cylinder were investigated as well. The computed flow and temperature fields were demonstrated in the form of streamlines and isotherms. Variations of the maximum stream function and the local and average Nusselt numbers were displayed as functions of the above-mentioned parameters. Correlations of the average Nusselt number were proposed based on curve fitting. At constant radius ratio, inclination angles of the inner triangular cylinder are found to have negligible effects on the average Nusselt number.     

Influences of a confined elliptic cylinder at different aspect ratios and inclinations on the laminar natural and mixed convection flows

Numerical investigations were carried out for natural and mixed convection within domains with stationary and rotating complex geometry by using an immersed-boundary method. The method was first validated with flows induced by natural convection in the annulus between concentric circular cylinder and square enclosure, and the grid-function convergence tests were also examined. Natural convection induced by isothermally elliptic cylinder was further investigated for different Rayleigh numbers within the range of 10⁴–10⁶ and the influence of the outer enclosure was also considered. The parameters investigated in the study included Rayleigh number, axis ratio and inclination angle of the elliptic cross-section. Local and average heat transfer characteristics were fully studied around the surfaces of both inner cylinder and outer enclosure. Finally, mixed convection in a square enclosure with an active rotating elliptic cylinder was considered and the heat transfer quantities of the system were obtained for different rotating speeds.     

Natural convection of nanofluids in an enclosure between a circular and a sinusoidal cylinder in the presence of magnetic field

In this study natural convection heat transfer of Cu–water nanofluid in a cold outer circular enclosure containing a hot inner sinusoidal circular cylinder in the presence of horizontal magnetic field is investigated numerically using the Control Volume based Finite Element Method (CVFEM). Both circular enclosure and inner cylinder are maintained at constant temperature. The governing equations of fluid motion and heat transfer in their vorticity stream function form are used to simulate the fluid flow and heat transfer. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. The calculations were performed for different governing parameters such as the Hartmann number, Rayleigh number, values of the number of undulations of the inner cylinder and nanoparticle volume fraction. The results indicate that in the absence of magnetic field, enhancement ratio decreases as Rayleigh number increases while an opposite trend is observed in the presence of magnetic field. Also it is found that the average Nusselt number is an increasing function of nanoparticle volume fraction, the number of undulations and Rayleigh numbers while it is a decreasing function of Hartmann number.     

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.     

Effect of aspect ratio on natural convection in an inclined rectangular enclosure with sinusoidal boundary condition

The aim of the present numerical study is to understand the natural convection flow and heat transfer in an inclined rectangular enclosure with sinusoidal temperature profile on the left wall. The top and bottom walls of the enclosure are kept to be adiabatic. The finite difference method is used to solve the governing equations with a range of inclination angles, aspect ratios and Rayleigh numbers. The results are presented in the form of streamlines, isotherms and Nusselt numbers. The heat transfer increases first then decreases with increasing the inclination of the enclosure for all aspect ratio and Rayleigh number. Increasing the aspect ratio shows a decreasing trend of the heat transfer for all Rayleigh numbers considered. A correlation equation is also introduced for the heat transfer analysis in this study.     

Unsteady natural convection heat transfer from a heated horizontal circular cylinder to its air-filled coaxial triangular enclosure

Unsteady natural convection heat transfer in a horizontal annular region bounded by a heated inner circular cylinder and a coaxial outer triangular cylinder is numerically studied for a wide range of Grashof numbers, aspect ratios, and inclination angles of the triangular enclosure. Different phases are identified during the course of flow development through the evolutions of the average Nusselt number over the inner circular wall. Snapshots of streamlines and isotherms for two typical cases are presented to exhibit identification among these phases. The flow development time and time-averaged Nusselt number over the inner circular wall are predicted and scaled with Grashof number. Additionally, the onset and evolution of pitchfork bifurcation are quantitatively investigated.     

Natural Convection of Water Near its Density Maximum around a Cylinder Inside an Elliptical Enclosure along Slender Orientation

A numerical investigation of natural convection of water near its density maximum around a cylinder inside the concentric elliptical enclosure along slender orientation was carried out. The effects of the aspect ratio, the elliptical ratio, the density inversion parameter, and the Rayleigh number were investigated. The typical flow and thermal fields were exhibited by means of streamlines and isotherms, respectively. Variations of the local and average Nusselt numbers were obtained and discussed with the details of both flow and thermal fields. The mechanism of oscillation was also analyzed when the stable flow transits to the unstable flow. Based on the simulation results, the heat transfer correlation has been proposed.     

Three-dimensional numerical simulation of natural convection in an inclined liquid-filled enclosure with an array of discrete heaters

A three-dimensional (3-D) numerical model is developed to investigate the effects of inclination on the heat transport processes in a liquid-filled rectangular enclosure of finite size. The interactions of flows tangential and normal to the heater surfaces in an inclined enclosure cause a slight oscillation in Nusselt number. Inclination has little effects on the average heat transfer characteristics except configurations close to the conduction case with heaters on top leading to a sharp decrease in Nusselt number. The critical Rayleigh number of 1708 is also observed in the present study regardless of inclinations. Heat transfer from discrete heaters is non-uniform. Maximum Nusselt number occurs at the heater leading edge and decreases towards the trailing edge. Correlations for the row average Nusselt number vs. Rayleigh number at various inclination angles are presented. By taking the average of the discrete heater array, the numerical results compared well with the empirical correlations obtained from a single heater plate in literature.     

Buoyancy-induced flow and heat transfer in a porous annulus between concentric horizontal circular and square cylinders

ABSTRACT

This paper reports on natural convection heat transfer in a porous annulus between concentric horizontal circular and square cylinders. The heated inner circular cylinder is maintained at the uniform hot temperature T_h, whereas the cooled outer square duct is held at the uniform cold temperature T_c. A pressure-based collocated finite-volume method is used to numerically investigate the effects on the total heat transfer of Rayleigh number (Ra), Prandtl number (Pr), Darcy number (Da), porosity (?), and annulus aspect ratio (R/L). Results demonstrate that at low Ra values, conduction is the dominant heat transfer mode. Convection contribution to total heat transfer becomes more important beyond a critical Ra value, which decreases with an increase in Da and/or ?. Furthermore, an increase in the enclosure aspect ratio (R/L) leads to an increase in total heat transfer. A similar behavior is obtained with Prandtl number, where predictions indicate higher heat transfer rates at higher Pr values with its effect increasing as Ra increases. Streamlines and isotherms reveal flow separation for some of the reported cases. Limited computations are also performed for natural convection in a porous annulus between two horizontal concentric circular cylinders having the same inner and outer perimeters as the investigated enclosure. Comparison of the predicted average Nusselt number estimates with similar ones obtained in the original enclosure reveals a large percentage difference in values, demonstrating the strong influence of geometry on natural convection in enclosures.     

Free Convection Heat Transfer from a Confined Horizontal Elliptic Cylinder

The laminar free convection heat transfer from an isothermal horizontal cylinder of elliptical cross-section confined between two adiabatic walls is investigated by the Mach-Zehnder interferometry technique. The ellipse major axis is vertical, and the minor to major axis ratio is kept constant to 0.53. This paper focuses on the effect of wall spacing and Rayleigh number variation on the local and average free convection heat transfer coefficient from the cylinder surface. The local and average Nusselt numbers were determined for the Rayleigh number range of 9 × 10 ² to 3.2 × 10 ³ and wall spacing to cylinder minor axis ratios of 1.9, 2.3, 2.67, 3.17, 3.8, 4.6, 6.12, 8, 13, ∞. Results are indicated with a single correlation that gives the average Nusselt number as a function of the ratio of the wall spacing to cylinder minor axis and the Rayleigh number. There is an optimum distance between the walls in which the Nusselt number is maximum. The experiment was also carried out on a cylinder of circular cross-section with the same periphery and length of the elliptic cylinder to allow a comparison with the results of other research.     

Natural convective flow of a chemically reacting fluid in an annulus

We examine the heat transfer and flow properties induced by natural convection in an annulus between a square enclosure and a circular cylinder filled with a chemically reacting fluid. During the exothermic reaction process in the reacting fluid, there generates heat that induces natural convection in the annulus. The problem is developed defining the vorticity‐stream function. We solve it with the use of the finite difference method. The results show that two counter‐rotating vortices generate in each half about the vertical symmetry line through the center of the inner cylinder. The lower eddies of the inner vortices get closer and closer with the decrease of the aspect ratio and the increase of the Rayleigh number, Frank‐Kamenetskii number, buoyancy force parameter, and Lewis number. Besides this, the eyes of the outer vortices expose similar characteristics for increasing values of the Rayleigh number and buoyancy force parameter, and for decreasing values of the aspect ratio and the Lewis number. It is remarkable that the flow field and the Nusselt number demonstrate completely distinct characteristics for the Lewis number unity, the aspect ratio equal to 0.1, and in the absence of the buoyancy force parameter.     

Numerical investigation of natural convection phenomena in a uniformly heated circular cylinder immersed in square enclosure filled with air at different vertical locations

In this model, a numerical study of two dimensional steady natural convection is performed for a uniform heat source applied on the inner circular cylinder in a square air (Pr = 0.7) filled enclosure in which all boundaries are assumed to be isothermal (at a constant low temperature). The developed mathematical model is governed by the coupled equations of continuity, momentum and energy and is solved by finite volume method. The effects of vertical cylinder locations and Rayleigh numbers on fluid flow and heat transfer performance are investigated. Rayleigh number is varied from 10³ to 10⁶ and the location of the inner cylinder is changed vertically along the centerline of the enclosure from − 0.25 L to 0.25 L upward and downward, respectively. It is found that at small Rayleigh numbers does not have much influence on the flow field while at high Rayleigh numbers have considerable effect on the flow pattern. In addition, the numerical solutions yield a two cellular flow field between the inner cylinder and the enclosure. Also, the total average Nusselt number behaves nonlinearly as a function of locations. Results are presented in terms of the streamlines, isotherms, local and average Nusselt numbers. Detailed results of the numerical has been compared with literature ones, and it gives a reliable agreement.     

Natural convection between a circular enclosure and an elliptic cylinder using Control Volume based Finite Element Method

In this study natural convection heat transfer in a cold outer circular enclosure containing a hot inner elliptic cylinder is investigated numerically using the Control Volume based Finite Element Method (CVFEM). Both of the circular enclosure and the inner cylinder are maintained at constant temperatures with air filled inside the enclosure. The governing equations are used in their vorticity stream function form to simulate the fluid flow and heat transfer. The numerical calculations are performed for various Rayleigh numbers, the inclination angle of the enclosure and different sizes of inner cylinder. The results show that streamlines, isotherms, and the number, size and formation of the cells inside the enclosure are strongly depend on these parameters which considerably enhance the heat transfer rate.     

Natural convection heat transfer between horizontal concentric rectangular pipes

Natural convection heat transfer between concentric rectangular pipes was studied numerically. It has been found that rolls of even numbers form in the region on the top surface of the inner pipe. The number of rolls depends on both the Rayleigh number and the aspect ratio. An oblong circulation of flow forms in the region between the side surface of the inner pipe and the surface of the outer pipe. The aspect ratio does not have much effect on the average Nusselt number at the side surface of the inner pipe. The relation between the Nusselt and Rayleigh numbers at the top surface resembles that of the Rayleigh-Bénard convection obtained by Silveston (Chandrasekhar, S. 1961. Hydrodynamic and Hydromagnetic Stability, Oxford University Press, 68). The average Nusselt number at the bottom surface of the inner pipe decreases with increasing aspect ratio because the region where heat transfer is affected significantly by convection is limited. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(4): 271–283, 1998     

Three-Dimensional Numerical Study of Natural Convective Heat Transfer of Liquid in a Cubic Enclosure

ABSTRACT

Steady-state laminar natural convection in a cubic enclosure with a cold vertical wall and two hot square heaters with constant temperature on the opposite wall is studied numerically. The enclosure is filled with various liquids. Three-dimensional Navier–Stokes Equations are solved by employing the SIMPLE algorithm. Computations are performed for a range of Rayleigh number from 10³ to 10⁷ while enclosure aspect ratio varies from 0.05 to 1.6. The effects of Rayleigh number, enclosure aspect ratio, and Prandtl number on heat transfer characteristics are studied in detail. The results show that the flow field is very complex and heat transfer from the two heaters is not the same. The effects of Prandtl number are negligible in the range from 5 to 140 with other parameters kept constant. This allows the use of liquids such as water for studying other dielectric liquids, provided the flow geometry and other nondimensional parameters are similar. The overall Nusselt number increases markedly with Rayleigh number. It is also affected by enclosure aspect ratio. It attains the maximum value when aspect ratio is in the range of 0.1–0.2 and decreases as enclosure aspect ratio varies from 0.2 to 1.6. Also, various settings of cooling face and arrangement of heaters are investigated, and the results show that they have considerable effects on heat transfer of both heaters.     

Numerical Study of Laminar Natural Convection in a Side-Heated Trapezoidal Cavity at Various Inclined Heated Sidewalls

Steady natural convection of air flow in a two-dimensional side-heated trapezoidal room was investigated numerically using a non-orthogonal, collocated finite-volume grid system. The considered geometry has an inclined left heated sidewall, a vertical right cooled sidewall, and two insulated horizontal upper and lower walls. Computations are performed for seven values of the heated sloping wall angle, three different values of aspect ratio, and five Rayleigh number values. Results are displayed in terms of streamlines, isotherms, and both local and average Nusselt number values. The principal result of this work is the great dependence of the flow fields and the heat transfer on the inclination angle, the aspect ratio, and the Rayleigh number. A correlation between the average Nusselt number, Rayleigh number, heated sloping wall angle, and aspect ratio is proposed.     

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.     

The Effect of Alumina–Water Nanofluid on Natural Convection Heat Transfer Inside Vertical Circular Enclosures Heated from Above

Experimental investigation on natural convection heat transfer is carried out inside vertical circular enclosures filled with Al₂O₃–water nanofluid with different concentrations; 0.0%, 0.85% (0.21%), 1.98 (0.51%), and 2.95% (0.75%) by mass (volume). Two enclosures are used with 0.20 m inside diameter and with two different aspect ratios. The top surface of the enclosure is heated using a constant-heat-flux flexible foil heater while the bottom surface is subject to cooling using an ambient air stream. Various heat fluxes are used to generate heat transfer through the nanofluid. The average Nusselt number is obtained for each enclosure and correlated with the modified Rayleigh number using the concentration ratio as a parameter. A general correlation for the average Nusselt number with the modified Rayleigh number is obtained using the volume fraction and the aspect ratio as parameters to cover both enclosures. The results show that the Nusselt number for the alumina–water nanofluid is less than that of the base fluid. This means that using the alumina–water nanofluids adversely affects the heat transfer coefficient compared to using pure water. It is also found that the degree of deterioration depends on the concentration ratio as well as the aspect ratio of the enclosure.     

Effect of nanofluid variable properties on natural convection in enclosures

In this work, the heat transfer enhancement in a differentially heated enclosure using variable thermal conductivity and variable viscosity of Al₂O₃–water and CuO–water nanofluids is investigated. The results are presented over a wide range of Rayleigh numbers (Ra = 10³–10⁵), volume fractions of nanoparticles (0 ≤ φ ≤ 9%), and aspect ratios (½ ≤ A ≤ 2). For an enclosure with unity aspect ratio, the average Nusselt number of a Al₂O₃–water nanofluid at high Rayleigh numbers was reduced by increasing the volume fraction of nanoparticles above 5%. However, at low Rayleigh numbers, the average Nusselt number was slightly enhanced by increasing the volume fraction of nanoparticles. At high Rayleigh numbers, CuO–water nanofluids manifest a continuous decrease in Nusselt number as the volume fraction of nanoparticles is increased. However, the Nusselt number was not sensitive to the volume fraction at low Rayleigh numbers. The Nusselt number demonstrates to be sensitive to the aspect ratio. It was observed that enclosures, having high aspect ratios, experience more deterioration in the average Nusselt number when compared to enclosures having low aspect ratios. The variable thermal conductivity and variable viscosity models were compared to both the Maxwell-Garnett model and the Brinkman model. It was found that at high Rayleigh numbers the average Nusselt number was more sensitive to the viscosity models than to the thermal conductivity models.     

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.