A Numerical Study on Natural Convention Heat Transfer From a Horizontal Isothermal Cylinder Located Underneath an Adiabatic Ceiling

A numerical analysis is performed for steady-state and two-dimensional natural convection heat transfer from a horizontal isothermal cylinder located underneath a horizontal adiabatic ceiling. The finite-volume method based on the SIMPLE algorithm and a nonorthogonal grid discretization scheme are used to solve the continuity, momentum, and energy equations for the Rayleigh numbers in the range from 10^?1 to 10⁴. The Poisson equations are solved to find the grid points, which are distributed in a nonuniform manner with higher concentration close to the solid regions. In addition, the HYBRID differencing scheme is used for the approximation of the convective terms in the curvilinear coordinate. The effects of the Rayleigh numbers and cylinder spacing from the adiabatic ceiling on both the local and average Nusselt numbers around the cylinder are investigated. Numerical results are performed for the plate-to-cylinder spacing ranging from 0.1 to 1.4.     

Experimental Study of Air Pressure Effects on Natural Convection From a Horizontal Cylinder

The topic of this research is the importance of convection heat transfer coefficient and the effect that ambient pressure has on it. Toward this end, an experimental study was performed to investigate the effects of air pressure on natural convection heat transfer from a horizontal cylinder. Pressure was varied from 1 to 220 kPa and the convection coefficient was obtained in the temperature range from 50 to 100°C. Various diagrams and tables were obtained to show the dependence of natural convection on pressure. A correlation was derived to describe the heat transfer coefficient and Nusselt number as a function of pressure and Knudsen number or Rayleigh and Knudsen number. The rate of heat transfer by radiation was also compared with convection at different temperatures and pressures.     

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.     

Laminar Free Convection Around a Horizontal Cylinder with External Longitudinal Fins

The numerical solution of the laminar free convection of air around a horizontal cylinder with external longitudinal fins has been reported in this paper. The cylinder surface as well as the surfaces of each fin were assumed to be at a uniform temperature. The fluid drawn over a large angular domain moves out through a narrow, almost vertical strip known as plume, the thickness of which reduces with increasing buoyancy. The heat transfer increases with an increase in Grashof number, the number of fins, and fin length. For a constant fin surface, more fins of lower length result in a better heat transfer for Gr beyond about 10 ³ .     

Non-Darcy Non-Newtonian Free Convection Flow Over a Horizontal Cylinder in a Saturated Porous Medium

Steady state solutions are obtained for non-Darcy free convection flow along a horizontal cylinder in a non-Newtonian fluid saturated porous medium. The boundary-layer equations governing the flow are solved numerically by using an implicit finite-difference method developed by Keller. Numerical results are obtained for the velocity and heat transfer at the wall for various values of the parameters namely, the Ergun number, Rayleigh number, power-law index and transpiration parameter.     

Free-Forced Convection from a Heated Longitudinal Horizontal Cylinder

Abstract

Finite-difference solutions of a longitudinal three-dimensional boundary layer along a heated horizontal cylinder are presented for Pr = 1 and 10. The numerical results are compared with earlier asymptotic solutions. The comparison shows that the asymptotic solution is valid only for a narrow region close to the leading edge. Downstream from this narrow region, the asymptotic solution overpredicts the buoyancy effect along the bottom of the cylinder and underpredicts it along the top. The numerical solutions indicate that the flow becomes free-convection dominant far downstream from the leading edge even when Gr/Re² is small.     

Non-Newtonian Mixed Convection Flow along an Isothermal Horizontal Circular Cylinder

The mixed convective laminar two-dimensional boundary-layer flow of non-Newtonian pseudo-plastic fluids is studied along an isothermal horizontal circular cylinder using a modified power-law viscosity model. In this model, there are no unrealistic limits of zero or infinite viscosity; consequently, no irremovable singularities are introduced into boundary-layer formulations for such fluids. Therefore, the boundary-layer equations can be solved numerically by using marching order implicit finite difference method with double sweep technique. Numerical results are presented for the case of shear-thinning fluids in terms of the fluid velocity and temperature distributions, shear stresses and rate of heat transfer in terms of the local skin-friction and local Nusselt number respectively. Here, it is found that heating the cylinder delays separation and if the cylinder is warm enough, suppress it completely. Cooling the cylinder brings the separation point nearer to the lower stagnation point and for a very cold cylinder there will not be boundary-layer on the cylinder.     

Neuro-Fuzzy Modeling of the Free Convection Heat Transfer From a Wavy Surface

In this paper an adaptive neuro-fuzzy inference system (ANFIS) is applied to model and predict the experimental results of free convection heat transfer from a vertical array of attached cylinders, which can be considered as a wavy surface, in the presence of a vertical wall. The effects of the wall–wavy surface spacing and Rayleigh number variation on average heat transfer from the wavy surface are considered via this prediction. The training data for optimizing the ANFIS structure are based on available experimental data. A hybrid learning algorithm consisting of gradient descends method and least-squares method is used for ANFIS training. The proposed ANFIS model is developed using MATLAB functions. For the best ANFIS structure obtained in this study, the mean relative errors of the train and test data were found to be 0.02% and 1.2%, respectively. The predicted results showed that ANFIS can predict the experimental results precisely.     

Experimental and Numerical Investigation on Forced Convection in Circular Tubes With Nanofluids

In this paper an experimental and numerical study to investigate the convective heat transfer characteristics of fully developed turbulent flow of a water–Al₂O₃ nanofluid in a circular tube is presented. The numerical simulations are accomplished on the experimental test section configuration. In the analysis, the fluid flow and the thermal field are assumed axial-symmetric, two-dimensional, and steady state. The single-phase model is employed to model the nanofluid mixture and the k-? model is used to describe the turbulent fluid flow. Experimental and numerical results are carried out for different volumetric flow rates and nanoparticles concentration values. Heat transfer convective coefficients as a function of flow rates and Reynolds numbers are presented. The results indicate that the heat transfer coefficients increase for all nanofluids concentrations compared to pure water at increasing volumetric flow rate. Heat transfer coefficient increases are observed at assigned volumetric flow rate for nanofluid mixture with higher concentrations, whereas Nusselt numbers present lower values than the ones for pure water.     

A Numerical Study of Combined Forced Convection and Gas Radiation From a Circular Cylinder in Cross Flow

A numerical study of combined forced convection and gas radiation from a circular cylinder is carried out. The fluid is assumed to be radiatively participating. Simulations are carried out for both laminar and turbulent flows. The Reynolds numbers considered are 100 and 500 for laminar flow and 7190, 21,580, 35,950, and 50,350 for turbulent flow. To check the effect of three-dimensionality on heat transfer characteristics, numerical simulations are also carried out for three-dimensional geometry. All the thermophysical properties of the working fluid are taken as those of air and are assumed to be constant for the range of temperature considered in the present study. In order to understand the effects of absorption and scattering of thermal radiation, a detailed parametric study is carried out by varying the absorption and scattering coefficients from 0 to 60 (m^?1). It is observed that the contribution of radiative heat transfer on total heat transfer is significant when the flow is laminar. The radiative Nusselt number decreases with the increase of absorption coefficient.     

Numerical Investigation on the Steady State Natural Convection in a Horizontal Open-Ended Cavity with a Heated Upper Wall

In this article, the investigation is focused on a configuration made of two horizontal parallel plates with the upper plate heated at uniform heat flux and the lower one adiabatic. Results are presented in terms of velocity and temperature fields, and both the temperature and the velocity profiles at different sections are shown. They are reported at two Rayleigh numbers, 10³ and 10⁵, and for two aspect ratio values, 1 and 10. Results are also shown in terms of the upper and lower wall temperature profiles. Correlations for average Nusselt numbers and maximum dimensionless wall temperature, in terms of Rayleigh number and aspect ratio, are given for 10³ ≤ Ra ≤ 10⁵ and 1 ≤ L/b ≤ 10.     

Natural Convection in a Horizontal Cylinder with Partial Heating: Energy Efficiency Analysis

The current study reports a numerical analysis of free convection of air in an isothermal horizontal cylinder, cooled and heated at different wall locations. Three heater sizes are discussed in this study. The first heated zone is spread across one-quarter of the sidewall; the second is uniformly distributed over the half of the wall and the third active wall covers three-quarters of the cylinder. Five various locations are considered and examined for each active zone of the sidewall. The comput...     

Influences of Physical Parameters on Mixed Convection in a Horizontal Lid-Driven Cavity with an Undulating Base Surface

The problem of steady, laminar, and incompressible mixed convection flow in a horizontal lid-driven cavity is studied. In this investigation, two vertical walls of the cavity are perfectly insulated and the wavy bottom wall is considered at an identical temperature higher than the top lid. The enclosure is assumed to be filled with a Bousinessq fluid. The study includes computations for different physical parameters, such as cavity aspect ratio (AR) from 0.5 to 2, amplitude of undulating wall (A) from 0 to 0.075, and number of undulations (λ) from 0 to 3. The pressure-velocity form of Navier-Stokes and energy equations are used to represent the mass, momentum, and energy conservations of the fluid medium in the cavity. The governing equations and boundary conditions are converted to dimensionless form and solved numerically by the penalty finite element method with discretization by triangular mesh elements. Flow and heat transfer characteristics are presented in terms of streamlines, isotherms, average Nusselt number (Nu), and maximum temperature (θ _max ) of the fluid. Results show that the wavy lid-driven cavity can be considered an effective heat transfer mechanism at larger wavy surface amplitude, as well as the number of waves and cavity aspect ratio.     

Numerical Analysis of Natural Convection in a Cylindrical Envelope with an Internal Concentric Cylinder with Slots

Detailed numerical analysis is presented for natural convection heat transfer in a cylindrical envelope with an internal concentric cylinder with slots. Governing equations are discretized using the finite volume method, and solved using SIMPLE algorithm with QUICK scheme. The results show that the system can reach steady state and be symmetric when the Rayleigh number is below 4 × 10⁵. When the Rayleigh number is greater than 6 × 10⁵, an asymmetric periodical solution is obtained although the initial field and boundary conditions were symmetric. As the Rayleigh numbers increase further, a quasi-periodic solution of the system is achieved at Ra = 2 × 10⁶, and the periodicity is lost at Ra = 6 × 10⁶. It is ascertained that the oscillatory flow undergoes several bifurcations and ultimately evolves to a chaotic flow.     

Experimental Study of Free Convection Heat Transfer from Horizontal Isothermal Cylinders Arranged in Vertical and Inclined Arrays

Laminar free convection heat transfer from vertical and inclined arrays of horizontal isothermal cylinders in air were investigated experimentally. Experiments were carried out using a Mach-Zehnder interferometer. For the vertical array, the cylinder spacing (center to center) varied from 2 to 5 cylinder diameter. The same range of vertical spacing also was used for the inclined array. The horizontal spacing varied from 0 to 2 cylinder diameter in the inclined array. The Rayleigh number based on the cylinder diameter varied between 10³ and 3× 10³. The effect of vertical and horizontal cylinder spacing and Rayleigh number on the heat transfer from each individual cylinder and the whole array were investigated. It is found that the free convection heat transfer from any individual cylinder in the array depends on its position relative to the others. Heat transfer correlations have been developed for any individual cylinder in the vertical and inclined arrays and for the arrays. Also the experiment was carried out on a single cylinder for a comparison with the results from other research.     

A Parametric Study of Prandtl Number Effects on Laminar Natural Convection Heat Transfer From a Horizontal Circular Cylinder to Its Coaxial Triangular Enclosure

A parametric study of Prandtl number effects on laminar natural convection heat transfer in a horizontal equilateral triangular cylinder with a coaxial circular cylinder is conducted. The Prandtl number is varied over a wide range from 10^?2 to 10⁵, which corresponds to a variety of working fluids. The governing equations with the Boussinesq approximation for buoyancy are iteratively solved using the finite volume approach. It is shown that the flow patterns and temperature distributions are unique for low-Prandtl-number fluids (Pr ≤ 0.1), and are nearly independent of Prandtl number when Pr ≥ 0.7. In addition, the inclination angle of the triangular enclosure is found to noticeably affect the variations of the local Nusselt number, and to have insignificant influence on the average Nusselt numbers for low Rayleigh numbers when Pr ≥ 0.7.     

水平高速旋转圆柱表面对流换热的实验研究

应用红外热像技术研究了静止空气的大空间环境下水平旋转圆柱表面的对流换热与转速的关系。在本文的实验范围内，当Re在7300以下时，对流换热随Re的增大而迅速增加，Re超过7300时，其增加速度逐渐变缓，当Re增大到9600时，对流换热反而随Re的增加而减弱，实验结果与理论分析一致。     

Experimental and Numerical Investigation on a Water-Filled Cavity Natural Convection to Find the Proper Thermal Boundary Conditions for Simulations

In this study, the laminar natural convection flow inside a water-filled cavity with differentially heated vertical walls is investigated experimentally and numerically. Both of the walls are heated and cooled by two special heat exchangers that are attached to the walls and the rest are insulated. The main purpose of each test is to reach a uniform constant temperature on both of the heated and cooled walls. Early tests for an air-filled cavity showed that a uniform temperature on the walls is feasible, while a different trend was observed for a water-filled cavity with a nonuniform distribution of temperature. ANSYS FLUENT 15 employed four approaches in terms of boundary conditions for computational purposes. None of the three-dimensional (3D) and two-dimensional (2D) models of the cavity with a uniform wall temperature (the wall average temperature from the experiment) were suitable for predicting the Nusselt number. Therefore, it was essential to use the full model to properly predict the real distribution of temperature and Nusselt number on the walls. The 3D model of the cavity with a nonuniform wall temperature, which was borrowed from the experiment, also provided good results for the Nusselt number, but a measured temperature was still needed from the experiments. The 2D simulation's findings showed a weakness in properly capturing the streamlines for all ranges of Rayleigh numbers.     

Experimental Investigations on Natural Convection Heat Transfer Around Horizontal Triangular Ducts

Experimental investigations have been reported on steady-state natural convection from the outer surfaces of horizontal ducts with triangular cross sections in air. Two different horizontal positions are considered; in the first position, the vertex of the triangle faces up, while in the other position, the vertex faces down. Five equilateral triangular cross-section ducts have been used with cross-section side length of 0.044, 0.06, 0.08, 0.10, and 0.13 m. The ducts are heated using internal constant-heat-flux heating elements. The temperatures along the surface and peripheral directions of the duct wall are measured. Longitudinal (perimeter-averaged) heat transfer coefficients along the side of each duct are obtained for natural convection heat transfer. Total overall averaged heat transfer coefficients are also obtained. Longitudinal (perimeter-averaged) Nusselt numbers and the modified Rayleigh numbers are evaluated and correlated using different characteristic lengths. Furthermore, total overall averaged Nusselt numbers are correlated with the modified Rayleigh numbers. Moreover, a dimensionless temperature group was developed and correlated with the modified Rayleigh number. For the upward-facing case, laminar and transition regimes are obtained and characterized. However, for the downward-facing vertex case, only the transition regime is observed. The local (perimeter-averaged) or the overall total Nusselt numbers increase as the modified Rayleigh numbers increase in the transition regime. However, Nusselt numbers decrease as the modified Rayleigh numbers increase in the laminar regime.     

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.