Experimental study of natural convection heat transfer of air layers in vertical annuli under high rayleigh number conditions

In this paper experimental investigations of natural convection heat transfer of air layers in vertical annuli are presented. In these experiments, the surface of the inner cylinder is maintained at a constant heat flux condition and the outer cylinder is cooled in the atmosphere. In order to obtain the convective contribution, the overall heat transfer data are corrected for thermal radiation and axial conduction losses from the end plates in the annuli. Special emphasis, in these investigations, was placed on the high Rayleigh number region where no experimental data are available in the literature. Data were obtained for Rayleigh numbers greater than 10⁹. The radius ratios studied were 2.03 and 3.92, and the aspect ratios studied were 23.94 and 66.67. Heat transfer correlations for average Nusselt numbers were developed for different Rayleigh number regions. For the low Rayleigh number region the results of this paper agree with the correlations reported in the literature. Much needed data and correlations for the high Rayleigh number region are obtained for the first time. These results improve the predictive ability for the heat transfer characteristics in the high Rayleigh number region. ©1999 Scripta Technica, Heat Trans Asian Res, 28(1): 50–57, 1999     

Analysis of Solidiflcation in the Presence of High Rayleigh Number Convection in an Enclosure

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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     

Transient double-diffusive convection in an enclosure with large density variations

An extension of a slightly compressible flow model to double-diffusive convection of binary mixtures of ideal gases enclosed in a cavity is presented. The problem formulation is based on a low-Mach number approximation and the impermeable surface assumption is not invoked. The main objectives of this work are the statement of the mathematical model used, and the analysis of some significant results showing the influence of density variation on transient solutions for pure thermal or pure solutal convection as well as for thermosolutal convection in the special case where the thermal and solutal buoyancy forces are equal in intensity either for aiding or for opposing cases.     

Numerical research of double‐diffusive natural convection in elliptical cylinders: Effect of thermal Rayleigh number

This paper is the first part of a two‐part study, and it presented numerical research of double‐diffusive natural convection within an annulus area, situated in two horizontal confocal elliptic solids charged by a Newtonian fluid. The elliptical coordinates were used to transform the physical domain into a rectangular one. To resolve the governing equations and the boundary layer conditions, a calculator code based on the finite volume approach was developed. The details of the influences of thermal Rayleigh number on heat and mass transfer were investigated. Results obtained were compared with those existing in other reasearch works.     

Numerical analysis of natural convection in an inclined trapezoidal enclosure filled with a porous medium

A theoretical study of buoyancy-driven flow and heat transfer in an inclined trapezoidal enclosure filled with a fluid-saturated porous medium heated and cooled from inclined walls has been performed in this paper. The governing non-dimensional equations were solved numerically using a finite-difference method. The effective governing parameters are: the orientation or inclination angle of the trapezoidal enclosure , which varies between 0° and 180°, the Rayleigh number Ra, which varies between 100 and 1000, the side wall inclination angle θ_s and the aspect ratio A. The side wall inclination parameter θ_s is chosen as 67°, 72° and 81° and the calculations are tested for two different values of A=0.5 and 1.0. Streamlines, isotherms, Nusselt number and flow strength are presented for these values of the governing parameters. The obtained results show that inclination angle is more influential on heat transfer and flow strength than that of the side wall inclination angle θ_s. It is also found that a Bénard regime occurs around =90°, which depends on the inclination of the side wall, Rayleigh number and aspect ratio.     

快速冷却条件下凝固潜热处理模型的研究

深入分析了有限差分法模拟凝固过程时，采用等效比热法处理相变潜热的原理；从理论和实际计算角度分析了快速冷却条件下常规的等效比热法会造成热量“虚增”，模拟计算结果失真的原因和影响程度；并进一步建立了快速冷却条件下凝固潜热处理的模型。计算结果表明，该模型可以充分保证模拟计算的精度和效率。     

Heat and mass transfer analysis of combined convection in a horizontal rectangle

In this study, the heat and mass transfer of combined free and forced convection in the horizontal rectangle is explored. The governing equations together with the boundary conditions are solved numerically by using the finite volume method. The innovative idea in this study is to appropriately modify the Semi-Implicit Method for Pressure-Linked Equations algorithm and thereby, the numerical solutions of the flow variables such as the temperature and the concentration in addition to the components of velocity and the pressure are computed. The Richardson numbers (Ri) for distinct gases and liquids are calculated for different Rayleigh numbers at low (Re = 50) and high (Re = 5000) Reynolds numbers. The dimensionless parameters, such as the Reynolds number (Re), the Prandtl number (Pr), and the Schmidt number (Sc) are appropriately chosen to calculate the Richardson numbers. Consequently, combined free and forced convection effects are analyzed. Furthermore, the heat and mass transfer aspect for distinct gases and liquids is critically examined using empirical correlations. The accuracy and the validation of these results are ensured owing to the solutions obtained from correlations being advised in this study and those are existing in the literature.     

含加热圆管方腔内自然对流的数值研究

采用数值计算方法对含不同直径圆管以及相同直径圆管位置不同方腔内的层流自然对流进行了研究。以冷热壁面温度差为基准的瑞利数Rn为10^6,以圆管壁面热流密度为基准的Ra为10^8。计算结果表明,当圆管处于方腔中间位置时,随着圆管直径的增大,圆管表面局部努塞尔数呈减小趋势。当圆管直径不变时,由于在不同位置处浮力作用的强弱不同,随着圆管在方腔内位置的改变,方腔内流场结构和温度场分布也会发生变化。整个计算结果可为工程设计提供参考。     

Natural convection suppression and crystal growth during unidirectional solidification of a binary system

We studied experimentally the interaction between natural convection and dendritic growth in the mushy layer during unidirectional solidification of aqueous ammonium chloride solutions cooled from below. Small amounts of hydroxyethylcellulose were added to the solution to increase its viscosity, leading to the suppression of convection. Natural convection consists of salt fingers in the liquid phase and plumes in the mushy layer for a low‐viscosity solution, but the onset of plumes is suppressed for a high‐viscosity solution. The mushy layer becomes sparsely packed, and the primary and secondary arms of the dendrites grow to noticeable sizes with increasing its viscosity, which yields a low solid fraction, such as 1% on average in the mushy layer for a viscosity ratio of 25.5. This demonstrates that natural convection strongly affects the morphology of dendrites. © 2000 Scripta Technica, Heat Trans Asian Res, 29(2): 120–131, 2000     

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.     

An analytical and numerical study of coupled transient natural convection and solidification in a rectangular enclosure

The transient process of the solidification of a pure liquid phase-change material in the presence of natural convection in a rectangular enclosure is considered both analytically and numerically. One vertical boundary is held at a temperature below the melting-point of the material, the other above; the horizontal boundaries are both assumed adiabatic. A nondimensional analysis of the problem, principally in terms of the Rayleigh (Ra) and Stefan (St) numbers, indicates that some asymptotic simplification is possible for materials often considered in the literature (water, gallium, lauric acid). This observation suggests a way to simplify the full problem when Ra  1 and St  1, giving a conventional boundary value problem for the liquid phase and pointwise-in-space first-order ODEs for the evolution in time of the solidification front. The method is tested against full 2D finite-element-based transient numerical simulations of solidification. In addition, simpler approaches for determining the average thickness of the solid layer, based on boundary-layer and enclosure flow correlations, are also investigated.     

Cavity inclination effect on convection flow in a triangular geometry

In this study, the water convection flow within a right-angled, inclined, and isosceles triangle enclosure for various inclination angles was numerically analyzed using the lattice Boltzmann method with the multirelaxation time model. On the hypotenuse side, the enclosure is thermally insulated, while the left and horizontal walls are kept, respectively, at cold and hot temperatures. This study was conducted to show the effects of two key parameters, the tilt angle $\varphi$ and the Rayleigh number $Ra$, whose changes span from $0^{\circ }$ to $315^{\circ }$ and $5\times 10^3$ to $10^6$, respectively. The effect of these variables is presented in terms of streamlines, isotherms, velocity profiles, temperature plots, and the average Nusselt number. Furthermore, the impact of the size of a hot square obstruction inside the cavity on the isotherms and streamlines has been investigated. The findings demonstrate that the rate of heat transport is enhanced as the Rayleigh number increases. This result is in good agreement with earlier research without tilting the cavity. Depending on the Rayleigh number, the tilt angle has a significant effect on the rate of heat transmission.     

Thermal transport analysis for natural convection in a porous corrugated rhombic enclosure

A numerical study of fluid flow and heat transfer, applying natural convection is carried out in a porous corrugated rhombic enclosure. A uniform heating source is applied from the bottom boundary wall while the inclined side walls are maintained to a constant cold temperature and the top corrugated wall is retained at insulated condition inside the enclosure. The heat transfer and flow features are presented for a wide spectrum of Rayleigh numbers (Ra), 10⁴ ≤ Ra ≤ 10⁶, and Darcy numbers (Da), 10^?3 ≤ Da ≤ 10^?2. The number of undulations (n) for the top and bottom walls have been varied from 1 to 13 keeping the amplitude of undulation fixed. It is revealed that the characteristics of heat transfer are conceivably modulated by changing the parameter of the undulation number on the enclosure walls, specifically at the bottom and top. The influencing control of n in altering the heat transfer rate is felt maximum on the left wall and minimum for the right wall, and there is a strong interplay between Ra and Da together with n on dictating the heat transfer characteristics. The critical value, where heat transfer rate is observed as maximum is at n = 11 and thereafter the values decrease.     

Transient natural convection in an enclosure with vertical solutal gradients

Transient natural convection in an enclosure with vertical solutal gradients has been studied in this paper. Transfers in a rectangular cavity configuration translating hydrodynamic and thermal phenomena are numerically predicted by means of computational fluid dynamics (CFD) in transient regime.The objective of this numerical study is to give a fine knowledge of the hydrodynamic and thermal characteristics during energy storage in an enclosure filled with water stratified by downward salinity gradient. The enclosure is divided into three zones with different salinity level such as salt gradient pond (SGP). Water is heated by a heating device at the bottom of the cavity.The Navier–Stokes, energy and mass equations are discretized using finite-volume method, and a two-dimensional analysis of the hydrodynamic and thermal behaviors generated in transient regime in the cavity are performed. The mathematical modelling has allowed the prediction of the storage performances by developing parametrical study in view to search the convective heat transfer coefficient at the bottom of the enclosure. Velocity vector fields show the presence of recirculation zones caused only in the lower region and permit to explain the increase of the temperature in the lower convective zone (LCZ).This study shows also the importance of the salinity in the preservation of the high temperature in the bottom of the cavity, and the important reduction of the phenomenon of thermal transfer across the non-convective zone (NCZ).     

Role of Prandtl number in the interaction phenomenon of surface radiation with an opposing mixed convection within a differential heated cavity

A numerical analysis has been done for opposing mixed convection resulting due to wall movement and buoyancy induced by a clockwise fluid motion in a differentially heated cavity. The effect of Prandtl number (Pr) and wall surface emissivity (?) has been investigated for different values of Richardson number. The net radiation method has been employed to simulate the effect of surface radiation. The energy equation along with its nonlinear boundary condition is treated with the Newton‐Raphson scheme. As momentum and energy equations are coupled with each other through their source terms, an iterative solution procedure is employed. A vorticity‐stream function formulation of the momentum equation has been adopted and solved by using an underrelaxation parameter of 0.45. The effect of Prandtl number with respect to the transformation of a multi‐cellular structure of streamline into a unicellular structure has been analyzed. For the same Richardson number (Ri) with an increase in Prandtl number, the flow and heat transfer phenomena changes from a buoyancy‐induced dominated flow to a shear‐induced dominated flow, which leads to some exciting results with respect to wall movement as well. Furthermore, the role of surface radiation in this respect has been emphasized. Nusselt number variation with the Prandtl number and surface emissivity has also been presented. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21003     

Microscopic study on the solidification of aqueous solutions using laser interferometry

Solidification of an aqueous solution was studied using a laser interferometry technique combined with an optical microscope. In order to measure the concentration distribution in an aqueous NaCl solution near an ice crystal and the three-dimensional shape of the ice crystal in a known temperature field, a directional solidification stage was used. This was composed of low- and high-temperature blocks and a moving bed. In our experiment, ice crystals showed four shapes: flat, treelike, swordlike, and needlelike. As a result of the interferometry experiment, it was observed that the concentration increases in the bulk solution for thick samples, swordlike ice crystals have an asymmetric triangular cross section, and treelike crystals have a flat and low top. We also studied ice formation response to injection of a high-concentration solution. © 1998 Scripta Technica, Heat Trans Jpn Res, 27(5): 353–364, 1998     

Inhomogeneous flow model of natural convection,entropy generation,and heatlines visualization in wavy I-shaped enclosure with rectangular heater

The present investigation is on examination of the natural convection and entropy generation considering the heatlines visualization of nanofluid I-shaped enclosure with two corrugated walls considering inner rectangular heater of three different heights. The influence of Brownian motion along with thermophoresis had been implemented using Inhomogeneous two-phase model of nanofluid. The governing equations were solved numerically using COMSOL software. Influence of Rayleigh number $$, Buoyancy ratio number $$, Lewis number $$, heater length $$. The results indicate that the influence of Lewis number on heat transfer bettering is stronger at high Rayleigh number $$ while its impact is negligible at a lower value of Rayleigh number (conduction mode). In addition, the total entropy generation gets its highest value at Lewis number $$. Bejan number, fluid flow strength and heat rate increase as the rectangular heater height increases. Also, higher heat transfer augmentation is taken when the heater height is $$ while increasing the heater height to $$ leads to more total entropy generation. The impact of heater height on total entropy generation is highly affected by Rayleigh number as increasing the heater height from $$ into $$, total entropy generation increases by $$ at $$ while it increases by $$ at $$.