Numerical study of the laminar natural convection flow around an array of two horizontal isothermal cylinders

Natural convection heat transfer from an array of heated cylinders has received attention in recent years. However, most of the previous investigations has been experimental and has been restricted to the influence of geometrical parameters on the overall heat transfer. The present work is devoted to the numerical study of lanunar natural convection flow from an array of two horizontal isothermal cylinders. This work, that enters within the framework of general study dealing with an array of several cylinders, states the problem in Cartesian coordinates system, involves the use of a control-volume method and solves the full vorticity transport equation together with the stream function and energy equations. The modifications of the average Nusselt number evolution compared with the single cylinder are explained in terms of velocity and temperature fields of the flow around the cylinders. Results are obtained for variety of combinations of spacing and numbers of Rayleigh.     

Separated laminar natural convection above a horizontal isothermal square cylinder

Laminar natural convection over a horizontal isothermal square cylinder situated in an infinite fluid medium is studied by a finite difference technique. Difficulty associated with the complex physical domain is overcome by a body-fitted coordinate transformation. We found that there is boundary layer separation past the sharp edges of the upper horizontal surface of the square cylinder, in the range of Rayleigh number based on the one side length of a square cylinder greater than 5×10³. Well-defined symmetric twin vortices exist above the upper horizontal surface, embedded at the base of the rising plume.     

Effect of natural convection on freezing of water around an isothermal,horizontal cylinder

Freezing of superheated water around an isothermal, horizontal cylinder has been studied experimentally. The shadowgraph technique was used to visualize the flow (plume) development in the water, and the contour of the ice layer around the heat sink was recorded photographically. Freezing of water was always accompanied by natural convection and produced nonuniform ice growth. Benard-Goertler instabilities resulted in secondary flows which produced waviness (nonuniform) ice growth along the axis of the cylinder. The number, location and magnitude of the ripples were found to depend on the initial water superheat and on the heat sink temperature.     

Mixed laminar convection in a horizontal tube with natural convection around its boundaries

The laminar flow and heat transfer within a horizontal tube surrounded by a liquid medium are studied both experimentally and numerically. Emphasis is given to flow regimes where a buoyant effect on the forced flow is exhibited inside the tube. The outer surface of the tube is also subjected to natural convection resulting from the temperature difference between the wall and the surrounding fluid. Detailed analyses are performed for a number of cases with various fluids, inlet temperatures and fluid flows. It is found that the variable wall temperature has a marked effect on the secondary flow patterns within the tube as well as on the heat transfer.     

Numerical study of laminar free convection about a horizontal cylinder with longitudinal fins of finite thickness

Conjugate numerical solution of laminar free convection about a horizontal cylinder with external longitudinal fins of finite thickness has been carried out. Fins alone contribute very small to the total heat transfer but they greatly influence the heat transfer from the uncovered area of the cylinder. Among the various fin parameters, thickness has the greatest influence on heat transfer. The rate of heat transfer is above that for the free cylinder only when the attached fins are very thin. For thin fins, there exist a fin length, which maximizes the rate of heat transfer. The optimum number and dimensionless length of the fins were obtained as 6 and 0.2 respectively when fin thickness is 0.01, the thinnest among those investigated in this study.     

An experimental study of mixed convection around a rotating isothermal cylinder

The mixed convective flows generated by a heated rotating horizontal cylinder have been investigated experimentally. The presence of rotation represents an important complication and extension of previous studies on convective flow and heat transfer around heated stationary horizontal cylinders in an otherwise quiescent medium. Significant qualitative, as well as quantitative, differences in the heat transfer characteristics and flow patterns generated by the rotating cylinders are observed as compared to those for stationary cylinders. When the Reynolds number reaches a value corresponding to the rotational parameter σ ≡ Gr/Re² being just below unity, the thermal plume becomes unstable and eventually breaks down. This event corresponds to the onset of a secondary mean flow which appears to be periodic in the axial direction. Mean Nusselt number measurements are presented, which show a dramatic increase in heat transfer at the onset of the secondary flow. Also, the structure of the secondary flow and the behavior of the plume are elucidated through Schlieren photography.     

Entropy generation due to natural convection from a horizontal isothermal cylinder in oil

Local entropy generation due to natural convection from a heated horizontal isothermal cylinder in oil was investigated numerically. The effect of viscous dissipation on entropy generation profiles was studied over a wide range of Rayleigh and Brinkman numbers. The results showed that viscous dissipation had minimal effect on entropy generation even when using a highly viscous oil.     

Experimental study of the natural convection flow around an array of heated horizontal cylinders

Natural convection heat transfer from an array of heated cylinders has recently attracted much attention. However, in almost all of the investigations, attention has been restricted to the influence of geometrical parameters on the overall heat transfer. The present work deals with an experimental study of natural convection flow from a vertical array of two heated horizontal cylinders. A detailed analysis of the local temperature and velocity fields is performed. The modifications of the average Nusselt number evolution compared with the single cylinder are explained in terms of velocity and temperature fields of the flow around the cylinders. Results that are obtained for a variety of combinations of spacings and Rayleigh numbers are compared with known numerical results. The comparison shows a satisfactory agreement.     

Mixed convection boundary layer flow past an isothermal horizontal circular cylinder with temperature-dependent viscosity

The problem of steady laminar mixed convection boundary layer flow past an isothermal horizontal circular cylinder placed in a viscous and incompressible fluid of temperature-dependent viscosity is theoretically considered in this paper. The partial differential equations governing the flow and heat transfer are shown to be non-similar. Full numerical solutions of these governing equations are obtained using an implicit finite-difference scheme known as the Keller-box method. The solutions are obtained for various values of the Prandtl number Pr, the mixed convection parameter λ and the viscosity/temperature parameter θ_r. The obtained results show that the flow and heat transfer characteristics are significantly influenced by these parameters.     

Numerical solution of the phase change problem around a horizontal cylinder in the presence of natural convection in the melt region

This paper deals with the numerical study of melting of phase change material around a horizontal circular cylinder in the presence of the natural convection in the melt phase. A two dimensional unsteady mathematical model has been formulated in terms of primitive variables and a coordinate transformation technique has been used to fix the moving front. The finite volume approach was used to discretize the system of governing equations, boundary and initial conditions and obtain a system of linear algebraic equations. In the numerical solution an implicit scheme was used for the momentum and energy equations and an explicit scheme for the energy balance at the interface. The numerical predictions were compared with available results to establish the validity of the model and the numerical approach.     

Numerical prediction of entropy generation due to natural convection from a horizontal cylinder

Entropy generation due to natural convection has been calculated for three radii and a wide range of Rayleigh numbers for an isothermal cylinder. It was predominantly caused by conduction. The viscous contribution was negligible. Locations of high local entropy generation were identified for different configurations. The total entropy generation decreased with increasing cylinder size for a given value of the Rayleigh number.     

A numerical study of natural convection around a square,horizontal, heated cylinder placed in an enclosure

In this paper, natural convection around a tilted heated square cylinder kept in an enclosure has been studied in the range of 10³ ⩽ Ra ⩽ 10⁶. Streamfunction-vorticity formulation of the Navier–Stokes equation is solved numerically using finite-difference method in non-orthogonal body-fitted coordinate system. Detailed flow and heat transfer features for two different thermal boundary conditions are reported. Effects of the enclosure geometry has been assessed using three different aspect ratio placing the square cylinder at different heights from the bottom. The concept of heatfunction has been employed to trace the path of heat transport. It is found that the uniform wall temperature heating is quantitatively different from the uniform wall heat flux heating. Flow pattern and thermal stratification are modified, if aspect ratio is varied. Overall heat transfer also changes for different aspect ratio.     

Experimental and numerical study of the natural convection from a heated horizontal cylinder

Natural convection heat transfer from a horizontal cylinder is studied experimentally and numerically. Experimental study had taken place in different environmental temperature in a conditioned room which can be maintained at a stable required value and inside a sufficiently designed test cabin. The environmental and cylinder surface temperatures varied between 10 °C–40 °C and 20 °C–60 °C respectively. In the experimental study, two cylinders having different diameters of 4.8 mm–9.45 mm are used and constant heat flux was applied. On the basis of the experimental data, a correlation for the average Nusselt number over the cylinder is proposed in the range of 7.4 10¹ < Ra < 3.4 10³. The proposed correlation is compared with the well known correlations on natural convection heat transfer from a horizontal cylinder in the specified range of Rayleigh number, and it is shown that the results are in satisfactory agreement. The problem is also investigated numerically. The experimental data and the numerical results fall in ± 20% band. The numerical results obtained in this study are also compared with the results of Merkin. The characteristics of trend lines are similar.     

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.     

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.     

A theoretical study of laminar mixed convection from a horizontal cylinder in a cross stream

The problem of laminar mixed convection from a horizontal isothermal cylinder is considered. The free stream direction is assumed to be horizontal and perpendicular to the cylinder axis. The study is based on the solution of the full Navier-Stokes and energy equations for 2-dim. flow of a Boussinesq fluid. The free stream is assumed to start impulsively from rest and the velocity and thermal boundary layers are developed in time until reaching steady conditions. The investigation covered the ranges of Reynolds number 1 < Re < 40 and Grashof numbers up to Gr = 5 Re² while keeping Prandtl number at a constant value of 0.7. Comparison of results with previous experimental correlations shows a good agreement. The streamline and isotherm patterns are plotted and different aspects of the phenomenon are discussed.     

Numerical study of laminar mixed convection of a nanofluid in horizontal curved tubes

Fully developed laminar mixed convection of a nanofluid consisting of water and Al₂O₃ in a horizontal curved tube have been studied numerically. Three-dimensional elliptic governing equations have been used. Simultaneous effects of the buoyancy force, centrifugal force and nanoparticles concentration has been presented and discussed. The nanoparticles volume fraction does not have a direct effect on the secondary flow, axial velocity and the skin friction coefficient. However, its effect on the entire fluid temperature could affect the hydrodynamic parameters when the order of magnitude of the buoyancy force becomes significant compared to the centrifugal force. For a given Reynold number, buoyancy force has a negative effect on the Nusselt number while the nanoparticles concentration has a positive effect on the heat transfer enhancement and also on the skin friction reduction.     

Laminar boundary-layer analysis of simultaneous mass and heat transfer in natural convection around A horizontal cylinder

An analytical study is presented of the combined heat and mass transfer characteristics of natural convection flow around a horizontal circular cylinder. The surface of the cylinder is assumed to be at uniform temperature and uniform concentration. Specific cases of diffusion of water vapour and naphthalene into air are studied. The results indicate that the local Nusselt number and the local wall shear stress increase and decrease from the pure free convection values as the buoyancy force from species diffusion assists and opposes, respectively, the thermal buoyancy force. The local Nusselt number and the local wall shear stress are found to increase with the decrease of the Schmidt number, whereas the surface mass transfer increases with increasing Schmidt number. The Sherwood number is found to become more effective as the thermal buoyancy force increases. The cumulative tangential mass flow rate is found to increase with the increase of the polar angle from the lower pole and is strongly dependent on the nature and magnitude of the concentration to thermal buoyancy force ratio, especially at low Schmidt number.     

Transient natural convection heat transfer from a horizontal circular cylinder

The transient natural convection from a horizontal circular cylinder subject to a sudden temperature change was investigated numerically. To solve the stream-function vorticity form of the Navier-Stokes equation and energy equation, the Euler explicit finite difference scheme was used for the transport equation and a noniterative direct elliptic solver for the Poisson equation. An overshoot in the heat transfer coefficient was calculated associated with the conduction-convection transition whose magnitude was influenced by the Pr and Ra numbers. The onset time of convection was nearly proportional to Ra^−0.5 in the range 10³6 for Pr=0.7 or 7.0. In order to validate the numerical result, an experiment was also conducted from which Schlieren pictures were obtained. They showed good qualitative agreement for the different stages of the plume development.     

The effect of temperature-dependent viscosity on the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section

This work examines the natural convection heat transfer from a horizontal isothermal cylinder of elliptic cross section in a Newtonian fluid with temperature-dependent viscosity. Results for the local Nusselt number and the local skin-friction coefficient are presented as functions of eccentric angle for various values of viscosity-variation parameter, aspect ratio, and Prandtl number. The total heat transfer rate and the total skin friction of the elliptical cylinder with slender orientation are higher than those of the elliptical cylinder with blunt orientation. Moreover, increasing the viscosity-variation parameter tends to enhance the heat transfer rates from a horizontal elliptical cylinder.