Enhancement of Free Convection Heat Transfer from a Vertical Array of Isothermal Cylinders by Flow Diverters

Free convection heat transfer from a vertical array of five horizontal isothermal cylinders separated by flow diverters is investigated experimentally through a Mach-Zehnder interferometer. Flow diverters with widths of 1, 2, and 3 cylinder-diameter are placed midway between the cylinders with a 45-degree inclination angle. The cylinders vertical center to center spacing is kept constant to three-cylinder diameter. The experiments are carried out for various Rayleigh numbers based on the cylinder diameter in the range of 10³ to 2.5× 10³ and for different flow diverter width. It is observed that the flow diverters enhance the heat transfer of the array from 10% to 27%, depending on their width. By increasing the width of the diverters and the Rayleigh number, enhancement of the heat transfer from the array increases.     

Free Convection Heat Transfer from Vertical Slender Cylinders: A Review

The effect of transversal curvature of a vertical cylinder becomes important where the thermal boundary layer thickness is comparable or thicker then the radius of cylinder. The cylinder slenderness criterion for laminar free convection for fluids of Prandtl numbers from 0.01 to 100 is presented. The classical analysis of the laminar free convection heat transfer from vertical cylinders is shown. Some results of numerical calculations of the turbulent boundary layer on a vertical cylinder using modified integral method are given. Experimental data concerning the laminar-turbulent transition suggest that the critical Grashof number for a vertical flat plate is Gr _cr ≈ 10⁹ and for a vertical cylinder is Gr _cr ≈ 4 × 10⁹. Theoretical, numerical, and experimental data for free convection heat transfer from vertical slender circular cylinders are surveyed. A separate section of the paper is devoted to the presentation of the list of selected correlation equations. Some of them are compared graphically. In the laminar region, the correlation equation based on the numerical calculations is validated with the recent experimental results for Prandtl number of 0.71 and for the cylinder height to diameter ratio from 1 to 60. In the turbulent region, few experimental data are available, and some results indicate that the effect of transversal curvature on the average convective heat transfer is very weak.     

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.     

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.     

等温竖壁自然对流换热的数值模拟

采用相似变换及箱形格式对等温竖壁自然对流换热进行数值模拟,计算结果与传统的相似解结果相符,表明用此方法求解自然对流换热问题是可行的。     

Turbulent Free Convection from a Vertical,Isothermal Plate

Abstract

The temperature and velocity fields adjacent to an isothermal, vertical plate have been calculated by finite-difference methods using the time-averaged equations of conservation. Effective diffusivities for turbulent transfer were computed from differential balances for the turbulent kinetic energy and the rate of dissipation of turbulent energy, using the empirical coefficients previously evaluated for forced convection together with an additional Prandtl-number-dependent coefficient associated with the buoyant production of turbulent kinetic energy. Although the turbulent boundary layer almost approaches an asymptotic condition, the slight development requires a two-dimensional solution proceeding from the leading edge through the laminar and turbulent regimes. It was necessary to trigger the transition from laminar to turbulent motion, but the ultimate turbulent behavior was found to be independent of the point of triggering. The computed velocity fields, temperature fields, and rates of heat transfer are in agreement with prior experimental data for air within their uncertainty. Excellent agreement was also obtained with the data for water, and fair agreement with the data for spindle oil.     

Mixed Convection Heat Transfer from Tandem Square Cylinders in a Vertical Channel at Low Reynolds Numbers

The fluid flow and heat transfer characteristics around two isothermal square cylinders arranged in a tandem configuration with respect to the incoming flow within an insulated vertical channel at low Reynolds number range (1 ≤ Re ≤ 30) are estimated in this article. Spacing between the cylinders (S) is fixed at four widths of the cylinder dimension (d) and, the blockage parameter (B) is set to 0.25. The buoyancy-aided/opposed convection is examined for the Richardson number (Ri) ranges from ?1 to 1 with a fixed Prandtl number (Pr) of 0.7. The transient numerical simulation for this two-dimensional, incompressible, laminar flow and heat transfer problem is carried out by a finite volume code based on the PISO algorithm in a collocated grid system. The results suggest that the flow remains steady for the entire range of parameters chosen in this study. The representative streamlines, vorticity, and isotherm patterns are presented to interpret the flow and thermal transport visualization. Additionally, the time average drag coefficient (C _D ) as well as time and surface average Nusselt number (Nu) for the upstream and downstream cylinders are determined to elucidate the effects of Re and Ri on flow and heat transfer phenomena.     

Conjugate Heat Transfer for Free Convection along a Vertical Plate Fin

<正>In this study,a new and effective improved Semi-Analytic and Semi-Empirical formula f(Pr)= (0.749999437Pr~(1/2))/((0.609+1.221Pr~(1/2)+1.238Pr)~(1/4))has been proposed to solve a conjugate problem with free convection in the incompressible laminar boundary layer flow and heat conduction in a solid wall for the flow passing a flat plate fin. A combination of flat-plate flow and flat-plate fin heat conduction has been considered in the present study.Finite -difference solutions for the interface temperature profiles and the heat transfer rates have been presented over the entire thermo-fluid-dynamic field for Prandtl numbers from 0.001 to 10000.First,the similar flow field has been solved by the Runge-Kutta method and the shooting methods,then the correlation equation of the local heat transfer coefficient have been obtained.Finally,the empirical formula has been substituted into the fin temperature heat conduction calculation processes to obtain the iterative solutions of the conjugate problems.     

CFD Analysis of Steady Laminar Natural Convection Heat Transfer from a Pin Finned Isothermal Vertical Plate

Heat transfer behavior with both the conductive and nonconductive fins have been analyzed by examining variations of the local and average Nusselt numbers in two‐dimensional flow. The main objective of this study is to quantify and compare the natural convection heat transfer enhancement of fin array with different fin aspect ratio and at different angles of inclination. It is found that significant heat transfer augmentation is obtained for both conductive and nonconductive fins. For conductive fins 20% higher augmentation factor is obtained when the fin aspect ratio is 6, angle of inclination is 60° and the pitch‐to‐length ratio is 0.2. For nonconductive fins, 10% higher augmentation factor is obtained when fin aspect ratio is 8, angle of inclination is 45° and pitch‐to‐length ratio at 0.5. A general correlation has been developed to predict the average Nusselt number and heat transfer augmentation factor for conductive and nonconductive fin arrays as a function of different fin configurations.     

Numerical Study on Mixed Convection Heat Transfer in Inclined Triangular Cavities

This article presents a parametric study on flow behavior and heat transfer in an inclined triangular cavity subjected to a moving lid and temperature differential. The systematic study considers three physical parameters (inclination angle, Reynolds number, and Grashof number) and explores the influence of these parameters on flow pattern and heat transfer characteristics. A series of computations were performed for the inclination angle (θ) ranging from 0° to 360° (in increments of 45°), Reynolds number (Re) from 100 to 1,500, and Grashof number (Gr) from 10⁵ to 10⁷. The numerical results show that there are three kinds of flow regime in a triangular cavity inclined from 0° to 360°: buoyancy-dominant, inertia-dominant, and intermediate transition (mixed convection flow). It is interesting that the case with Re = 100, Gr = 10⁷, and θ = 0° exhibits five circulation cells and induces excellent thermal performance, corresponding to wavy profiles in local Nusselt number and local friction factor. The study also reveals that the good thermal performance within a local region can generate higher friction force on the neighboring boundary and this friction force may reduce the strength of the vortex.     

柴油机非水冷却介质自然对流沸腾传热特性研究

对于采用非水冷介质的高温冷却及少冷却柴油机的研究，目前尚需了解冷却介质温度的提高及冷却介质的性质差异，对柴油机的传热及零部件热状况的影响。本文模拟柴油机工作条件，对机油、柴油及不同配比的乙二醇水溶液等液体的自然对流沸腾传热特性进行了试验研究，揭示了各种因素对传热的影响，通过对试验数据的回归分析得出了３种非水冷却介质自然对流沸腾传热关系式。为机油、柴油及乙二醇水溶液用于柴油机高温冷却及少冷却提供了理论依据。     

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.     

Natural Convection Heat Transfer from Vertical Helical Coils in Oil

Abstract

This paper is the first in a two-part study of the pressure-flow characteristics for a range of microchannels. Here, the manufacture of the channels and the resulting quality in terms of the channels' closeness to target dimensions, channel-to-channel variation for each sample, and the difference in area between the assumed perfect rectangular/trapezoidal shape of the channels and their actual cross-section are addressed. Wet etching with KOH produced trapezoidal channels 577 μum wide and 413 μum high. DRIE produced rectangular channels 304 μum wide and 332 μum high. Mechanical sawing produced near rectangular channels in both silicon and plastic. The silicon channels were 52 μum wide and 423 μum deep, and the plastic channels were 203 μum wide × 344 or 382 μum deep. Channel dimensions were measured using a scanning electron microscope. This paper demonstrates the feasibility of producing relatively large microchannels in two materials by three methods.     

大空间管排自然对流的数值模拟

对具有2，4，6根管的管排在大空间内的自然对流进行了数值模拟。参数范围为10^2〈Ra〈10^4，S／D=1．25，2，3，5，9，11，Pr=0．7，流态为层流。数值计算结果表明：Ra和S／D对换热都有重要的影响，在小间距时对流作用处于劣势，管排中的管处于换热削弱状态，随着间距的增大对流作用逐渐占优势，管排中的各管从下至上逐渐受到加强，管排中出现了涡，这种涡起着增强局部换热系数的作用。     

Efficiency of the Horizontal Single Pin Fin Subjected to Free Convection and Radiation Heat Transfer

In this communication, the results of numerical calculations of the heat transfer coefficient and temperature distribution along the horizontal single pin fin in still ambient air, as well as the fin efficiency, are presented and compared with classical analytical results in the case of the constant heat transfer coefficient fin theory. The measured temperature distributions along the two low carbon steel pin fins having a length-to-diameter ratio of 35—one covered with the polished nickel and the other painted mat black—agree very well with the numerical results and are higher than the classical results. The analytically calculated fin efficiency does not differ significantly from the results of the numerical calculations if they are compared for the same dimensionless fin parameter in which the heat transfer coefficient is determined for the fin base temperature. More extended numerical calculations showed that beyond the fin parameter of five, the analytical results of the fin efficiency are higher than the numerical results by no more than about 1%. The largest difference between the classical and numerical fin base efficiencies is about 3.5%, and it was observed at a fin parameter of about 1, where the length of the pin fin has the optimal value based on the classical theory.     

Empirical Correlations for Free Convection in an Isothermal Asymmetrically Heated Vertical Channel

Laminar free convection in an isothermal asymmetrically heated vertical channel has been extensively studied in the past, and empirical correlations for the overall channel convective heat transfer rate are available in the literature. However, this problem has been revisited in order to develop empirical correlations that allow the calculation of the average Nusselt number for each channel wall separately. A numerical solution has been obtained for a Prandtl number of 0.71 and for Rayleigh numbers ranging from the conduction regime to the isolated boundary layer regime. The data have been used to develop correlations for the average Nusselt numbers on the hot and cold walls. These correlations satisfy a heat balance for the overall channel.     

Fully Developed Free Convection Heat and Mass Transfer of a Micropolar Fluid Between Porous Vertical Plates

In this article, we consider the problem of fully developed natural convection heat and mass transfer of a micropolar fluid between porous vertical plates with asymmetric wall temperatures and concentrations. The resulting boundary-value problem is solved analytically by the homotopy analysis method (HAM). Profiles for velocity and microrotation are presented for a range of values of the Reynolds number and the micropolar parameter.     

Free Convective Heat Transfer Structures as a Function of the Width of Isothermal Horizontal Rectangular Plates

Abstract

Results are presented for the experimental investigations of free convection heat transfer from upward facing isothermal horizontal rectangular plates as a function of the plate width. Two models of the convective fluid flow structures above horizontal rectangular plates were proposed as a result of flow visualization. Solutions of these models are presented in the form of Nusselt-Rayleigh relations with the aspect ratio as a parameter. Analysis of the visualization results provided a basis for preferring the radial flow pattern at small values of the Rayleigh number, especially for square plates or at the ends of rectangular plates, and a basis for preferring the parallel flow model at large values of the Rayleigh number. From the previous experimental results and the present experimental and interferometric studies, it is shown that the transition Rayleigh number at which the flow changes from the concentric to the parallel flow pattern is a function of the width of the plate.     

Mixed Convection Heat Transfer from an In-Line Row of Square Cylinders in Cross-Flow at Low Reynolds Number

This article presents a two-dimensional numerical study on the unsteady laminar mixed convection heat transfer from a row of five in-line isothermal square cylinders placed in an unconfined medium and subjected to cross-flow of a Newtonian fluid at low Reynolds number (Re = 125). The hydrodynamic and thermal transport phenomena are captured for the separation ratios (spacing to cylinder size ratio, s/d) of 0.5, 1, 1.5, 2, 3, and 4. The mixed convection heat transfer is studied for Richardson numbers (Ri) ranging from 0 to 3 with a fixed Prandtl number (Pr = 0.71). Numerical calculations are performed by using a PISO algorithm-based finite volume solver in a collocated grid system. The instantaneous vorticity fields along with the isotherm patterns are systematically presented and discussed for different separation ratios and Richardson numbers. Depending on the engineering application, the temperature difference between the surface and the free stream could vary to make buoyancy of primary importance, entailing major modification of the flow field. Additionally, the instantaneous and mean drag and lift coefficients, Strouhal numbers, and mean Nusselt numbers are determined and discussed.     

波纹形内翅片管对流换热实验研究及其应用

通过实验的方法研究了一种新型波纹形内翅片换热管的对流换热和阻力特性,建立了所测Re范围内对流换热和阻力实验关联式,并且在相同质量流量、相同泵功率、相同阻力降的条件下比较了该翅片管与普通光管之间的传热效果.与类似的波纹管的换热效果进行了比较,结果表明,新型波纹形内翅片换热管具有较好的换热效果,特别是在较低Re条件下,效果更加明显.