Natural Convection from a Heated Elliptic Cylinder with a Different Axis Ratio in a Square Enclosure

A detailed study about the free convection over a heated elliptic cylinder, placed at the center of a square cavity having cooled walls, is performed. Simulations are carried out for three Rayleigh numbers (10⁴, 10⁵, and 10⁶) and two cavity aspect ratios (CR = 2.5 and 5.0) for different axis ratio (AR). The effect of AR on fluid flow and heat transfer characteristics for varying Rayleigh number and cavity aspect ratio are analyzed. The influence of AR is phenomenal at higher Ra and lower CR. At higher Ra, thermal plumes are observed above the cylinder for different ARs. Bicellular vortices are formed at low Ra by changing CR. The surface-averaged Nusselt number (Nu _avg ) increases with increasing AR and Ra. The value of Nu _avg increases with decreasing CR, and a correlation for Nu _avg in terms of AR is obtained for each CR.     

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

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

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.     

Heat and fluid flow across a rotating cylinder dissipating uniform heat flux in 2D laminar flow regime

Free-stream flow and forced convection heat transfer across a rotating cylinder, dissipating uniform heat flux, are investigated numerically for Reynolds numbers of 20–160 and a Prandtl number of 0.7. The non-dimensional rotational velocity (α) is varied from 0 to 6. Finite volume based transient heatline formulation is proposed. For Re = 100, the reasons for the onset/suppression of vortex shedding at a critical rotational velocity is investigated using vorticity dynamics. At higher rotational velocity, the Nusselt number is almost independent of Reynolds number and thermal boundary conditions. Finally, a heat transfer correlation is proposed in the 2D laminar flow regime. Cylinder rotation is an efficient Nusselt number reduction or cylinder-surface temperature enhancement technique.     

NATURAL CONVECTION IN A DIFFERENTIALLY HEATED SQUARE CAVITY WITH INTERNAL HEAT GENERATION

A high-resolution, finite-difference numerical study is reported on natural convection in a square cavity. The vertical sidewatts of the cavity are differentially heated, and a uniform internal heat generation is also present. Two principal parameters are considered, the internal Rayleigh number Ra_I, which represents the strength of the internal heat generation, and the external Rayleigh number Rag, which denotes the effect due to the differential heating of the side walls. The internal Rayleigh number varies in the range 10¹⁰ Ra_I ≤ 10⁷, while the external Rayleigh number is set at Ra_E = 5 x 10⁷ for most computations. As the relative strength of the internal heat generation increases, the flows near the tap portion of the heated sidewall are directed downward. When the effect of the internal heat generation is dominant, the thermal energy leaves the system for the surroundings over the top portion of the heated wall. Only in the bottom pari of the heated wall is heat transfer directed into the system. These numerical solutions are in qualitative agreement with the available experimental measurements.     

Natural convection heat transfer of high temperature gas in an annulus between two vertical concentric cylinders

Water cooling panels have been adopted as the vessel cooling system of the High Temperature Engineering Test Reactor (HTTR) to cool the reactor core indirectly by natural convection and thermal radiation. In order to investigate the heat transfer characteristics of high temperature gas in a vertical annular space between the reactor pressure vessel and cooling panels of the HTTR, we carried out experiments and numerical analyses on natural convection heat transfer coupled with thermal radiation heat transfer in an annulus between two vertical concentric cylinders with the inner cylinder heated and the outer cylinder cooled. In the present experiments, Rayleigh number based on the height of the annulus ranged from 2.0 × 10⁷ to 5.4 × 10⁷ for helium gas and from 1.2 × 10⁹ to 3.5 × 10⁹ for nitrogen gas. The numerical results were in good agreement with the experimental ones regarding the surface temperatures of the heating and cooling walls. As a result of the experiments and the numerical analyses, the heat transfer coefficient of natural convection coupled with thermal radiation was obtained as functions of Rayleigh number, radius ratio, and the temperatures and emissivities of the heating and cooling wall surfaces. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(5): 293–308, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20070     

NATURAL CONVECTION-RADIATION INTERACTIONS IN A CUBE FILLED WITH A NONGRAY GAS

A three-dimensional numerical study was performed on interactions of natural convection and radiation in a cubical enclosure filled with carbon dioxide gas. The enclosure was heated differentially by two opposing vertical walls. Gas radiation was analyzed by the P₁ differential approximation method and the weighted sum of gray gas model. Computations were carried out over a range of the Rayleigh number, Ra, between 10⁵ and 10⁹. The Prandtl number and the overheat ratio were held fixed at 0·68 and 1·0, respectively. Unsteady transitional flows were computed by a direct simulation method, without using any explicit turbulence models. From the predictions, a mean heat transfer correlation has been proposed as Nu = 0·323 Ra^0·342 in the surface/gas radiation mode, where Nu is the time and spatially averaged Nusselt number at the isothermal walls.     

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.     

Numerical investigation of turbulent natural convection in an inclined square cavity with a hot wavy wall

The turbulent natural convection of air flow in a confined cavity with two differentially heated side walls is investigated numerically up to Rayleigh number of 10¹². The objective of the present work is to study the effect of the inclination angle and the amplitude of the undulation on turbulent heat transfer. The low-Reynolds-number k–ε, k–ω, k–ω–SST RANS models and a coarse DNS are used and compared to the experimental benchmark data of Ampofo and Karayiannis [F. Ampofo, T.G. Karayiannis, Experimental benchmark data for turbulent natural convection in an air filled square cavity, Int. J. Heat Mass Transfer 46 (2003) 3551–3572]. The k–ω–SST model is then used for the following test-cases as it gives the closest results to experimental data and coarse DNS for this case. The mean flow quantities and temperature field show good agreement with coarse DNS and measurements, but there are some slight discrepancies in the prediction of the turbulent statistics. Also, the numerical results of the heat flux at the hot wall are over predicted. The strong influence of the undulation of the cavity and its orientation is well shown. The trend of the local heat transfer is wavy with different frequencies for each undulation. The turbulence causes an increase in the convective heat transfer on the wavy wall surface compared to the square cavity for high Rayleigh numbers. A correlation of the mean Nusselt number function of the Rayleigh number is also proposed for the range of Rayleigh numbers of 10⁹–10¹².     

A numerical study of laminar free convection heat transfer between inner sphere and outer vertical cylinder

The effects of height and radius ratio with a Newtonian fluid have been investigated numerically to determine heat transfer by natural convection between the sphere and vertical cylinder with isothermal boundary conditions. The inner sphere and outer vertical cylinder were heated and cooled in a steady change of temperature. Calculations were carried out systematically for a range of the Rayleigh numbers to determine the average Nusslet numbers which are affected by the geometric ratio parameters (HR and RR) on the flow and temperature fields. The governing equations, in terms of vorticity, stream function and temperature are expressed in a spherical polar coordinate system. Results of the parametric study conducted further reveal that the heat and flow fields are primarily dependent on the Rayleigh number and height and radius ratio, for a Prandtl number of 0.7, with the Rayleigh number ranging from 10³ to 10⁶, and the height and radius ratio varying from 1.2 to 5.0. Above all, the specification of different convective configurations has a significant effect on the average heat transfer rate across the composite annulus gap.     

Heat transfer from small objects in microgravity: Experiments and analysis

Heat transfer over a sub-millimeter spheroidal solid is of interest in many engineering processes. One important mechanism of heat transfer in the above processes is natural convection which leads to heat transfer rates many times larger than that of pure conduction. Despite the huge literature devoted to natural convection heat transfer rates over spheres (and to a smaller extent over spheroids) there is not a generally accepted correlation especially for small Rayleigh numbers. Existing correlations for external geometries predict a progressively increasing contribution of natural convection to heat transfer with respect to gravity (starting from zero gravity). To test the validity of these correlations, experiments are performed for the estimation of heat transfer rates at low gravity. Heat pulses are given to a miniature thermistor with a nearly spheroidal shape immersed in a liquid and its thermal response is registered during heating in parabolic flights. The contribution of natural convection to heat transfer is undoubtedly estimated from runs in which acceleration varies from 0 to 1.8 g. Surprisingly enough, the experiments showed that the Rayleigh number must take a minimum value before non-negligible effect of natural convection on heat transfer appears (existence of a threshold Rayleigh number). In the absence of natural convection (below Ra_thr) the experimental thermal response curves can be successfully described by approximating solutions of the transient heat conduction equation for the spheroidal geometry of the thermistor. Apparently, additional research is needed regarding the natural convection around sub-millimeter objects for small Rayleigh numbers.     

Lattice Boltzmann simulation of natural convection around a horizontal elliptic cylinder inside a square enclosure

Natural convection between a square outer cylinder and a heated elliptic inner cylinder has been studied numerically. The inner and outer walls are maintained at temperatures T_h and T_c, respectively, with T_h > T_c. Lattice Boltzmann method (LBM) has been used to investigate the hydrodynamic and thermal behaviors of the fluid at various vertical positions of the inner cylinder for different Rayleigh numbers ranging from 10³ to 10⁶. The results show that streamlines, isotherms, and the number, size and formation of the cells strongly depend on the Rayleigh number and the position of inner cylinder. The changes in heat transfer quantities have also been presented.     

Numerical study of mixed convective heat transfer in a lid‐driven enclosure with rotating cylinders

A numerical simulation is performed to characterize the mixed convective transport in a three‐dimensional square lid‐driven enclosure with two rotating cylinders. The top wall is moving in the positive x‐direction, and the bottom wall is at a higher fixed temperature compared with all other isothermal walls. Both cylinders are rotating in its own plane about their centroidal axis. On the basis of rotation of both cylinders in clockwise or counter‐clockwise directions, four rotational models are studied. Various controlling parameters considered in the present study are Grashof number (10 ³ < Gr < 10 ⁵), rotating speed of the cylinder (5 < ω < 50), and the Reynolds number based on top wall movement is fixed to 100. The effect of cylinder rotation on the heat transfer of bottom wall is reported with the help of streamlines, contour plots of z‐component of vorticity, averaged and local Nusselt number, ratios of secondary flow and drag coefficient. It is observed that the heat transfer at the bottom wall is substantially dependent on the rotational model and rotational speed of the cylinder.     

NATURAL CONVECTION IN A TWO-DIMENSIONAL DIFFERENTIALLY HEATED SQUARE ENCLOSURE UNDERGOING ROTATION

A numerical study of two-dimensional natural convection in a rotating and differentially heated square enclosure has been presented by solving the conservation equations of mass, momentum, and energy in a rotating coordinate system using the finite difference method. Considering air to be the fluid medium in the cavity, the results are presented for a wide range of Rayleigh numbers (Ra), Taylor numbers (Ta), and rotational Rayleigh numbers (Ra _w). It is found that a significant enhancement in heat transfer can be achieved due to rotational effects. At a particular Ra, increase in Ta results in an increase in frequency of oscillations of the dynamical variables and also gives rise to formation of a mushroom-shaped plume in the core of the cavity. For constant Ta, an increase in Ra results in formation of thinner thermal boundary layers at the isothermal walls and stable thermal stratification in the core of the cavity. The stratification becomes unstable when the Ta     

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 of Al2O3 Nanofluid Between Two Horizontal Cylinders Inside a Circular Enclosure

Natural convection heat transfer within horizontal annuli has many engineering applications such as heat exchangers like fire tube heaters. In this paper numerical methods were used for the computational analysis of heat transfer from the fire tube/hot tube to the gas tube/cold tube inside the water medium using alumina nanoparticles. Because of eccentricities of both hot and cold cylinders and different diameters, the geometry is asymmetric. The mathematical model is based on two-dimensional continuity, momentum, energy, and volume fraction equations, which are solved numerically. The simulation was done for different values of particle loading, 1%, 2%, and 5%, at Rayleigh numbers 10³, 10⁴, and 10⁵. The results show that nanoparticles enhance the heat transfer by increasing the volume concentrations of particles. It was observed that the maximum and minimum augmentation of the average Nusselt number are about 30% and 14% at the Ra = 10³ and Ra = 10⁵, respectively. Although the average Nusselt number rises by increasing the Rayleigh number, the ratio of heat transfer using nanofluid to that by pure fluid decreases. Using 5% volume fraction of alumina nanoparticles at Rayleigh number of 10³ increases the heat transfer to cold tube by about 23% compared to the pure water. The effect of nanolayer formation around particles was considered in a thermal conductivity model, which shows approximately 5% increase in the Nusselt number. To verify the solution results, comparisons with previously published work on the basis of special cases are performed.     

Effects of rotation on the trailing vortex and heat transfer from a horizontal rotating cylinder at higher Grashof number

In the present study, effects of rotation on the trailing vortex and heat transfer from a large diameter horizontal rotating cylinder in still air have been experimentally investigated whereas earlier studies considered cylinders with smaller diameters. As the rotational speed n is increased, the trailing vortex would deflect in the rotational direction, the flow state of air near the cylinder would vary from laminar to turbulent, the heat transfer would transit from pure natural convection to mixed convection, and finally to pure forced convection resulted from rotation, the trailing vortex would break down and disappear. The variation of deflection angles ω with the parameter $R{e}_r/\sqrt{Gr}$ can be expressed as $w=32.3R{e}_r/\sqrt{Gr}$ at lower rotational speed. The discriminant to determine the disappearance of trailing vortex can be presented as Re_r²/Gr = 7.51.     

Numerical study of mixed convection in a ventilated square enclosure with the lattice Boltzmann method

In this article, numerical study of heat transfer by convection in a square cavity was investigated. The vertical walls of the cavity are differentially heated and the horizontal walls are considered adiabatic. A ventilation jet is created by a fan placed in the cavity. A lattice Boltzmann model for incompressible flow equation is used to simulate the problem. A parametric study was performed presenting the influence of Reynolds number (20 ≤ Re?≤?500), Rayleigh number (10≤Ra?≤?10⁺⁶), and fan position (0.2?≤?L_F≤0.8). It has been observed that heat transfer rate increases with the Reynolds number increasing and it is maximal for the L_F=0.2.     

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.     

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.