双绝热圆柱对水平三角腔内自然对流影响的数值研究

针对含双绝热圆柱的底部加热水平等腰三角腔内空气的稳态层流自然对流开展研究.通过有限容积法对控制方程进行了数值求解,其中瑞利数的变化范围为104 ～106,圆柱体的尺寸比则分别为0（无圆柱体）、1/8和1/4.基于计算结果对自然对流的流动与传热特性随瑞利数和尺寸比的变化规律进行了分析和讨论.结果表明,双绝热圆柱的存在较大程度上改变了三角腔内自然对流的流型和温度场分布,但对整体传热影响较小,仅略微提高了平均努赛尔数,强化传热的效果在尺寸比为1/8时较为明显.     

Mixed convection of nanofluid in a square enclosure with a hot bottom wall and a conductive half-immersed rotating circular cylinder

In this study. The mixed convection in a square enclosure with a hot bottom wall and a conductive half-immersed rotating cylinder from its top wall is investigated numerically. The enclosure is filled with a copper-water nanofluid. The upper half of the cylinder is cooled by the surrounding air, whereas its solid lower half is exposed to the nanofluid. The two left and right sidewalls of the enclosure, together with the remaining regions of its top wall, are assumed to be adiabatic. The dimensionless governing equations are expressed for the velocity and the temperature formulation, and they are modeled by using COMSOL code based on the Galerkin finite element method. In the present work, the geometrical aspect ratio is considered to be varied as (0.2 ≤ R/L ≤ 0.5), the thermal conductivity ratio is considered to be varied as 1 ≤ K_r ≤ 10, the angular rotational velocity is considered to be varied as 0 ≤ $\mathrm{\Omega }$ ≤ 1000, and the ambient convection heat transfer coefficient is considered to be varied as 5 ≤ h ≤ 20. However, the solid volume fraction (ϕ), the Prandtl number (Pr), and the Rayleigh number (Ra) are considered to be fixed at ϕ = 0.02, Pr = 6.2, and Ra = 10⁵. It was found that the convection effect becomes more pronounced when the angular rotational velocity increases, whereas a reverse behavior is observed with an increase in the geometrical aspect ratio. Also, it was observed that the heat explorer depth begins to decrease as the angular rotational velocity increases until the increases of angular rotational velocity effect is diminishing therefore it may be the main target of the present research. This observation is seen for both considered values of the thermal conductivity ratio and the geometrical aspect ratio. Moreover, it was observed that both the local and the average Nusselt numbers increase as the geometrical aspect ratio increases. A comparison with a previously published numerical work is performed, and a good agreement between the results is observed.     

Effects of wall confinement and rheology of non‐Newtonian nanofluids on mixed convection phenomenon of a square cylinder in a vertical channel

The mixed convective momentum and heat transfer phenomena of confined square cylinders in non‐Newtonian nanofluids are numerically investigated. The experimental thermophysical properties of alumina‐water‐based nanofluids are adopted from literature and these nanofluids obey shear‐thinning power‐law type non‐Newtonian behavior. The square cylinder is confined in a vertical channel with a confinement ratio of 0.1333. The flow is assumed to be two‐dimensional and the fluid is allowed to flow in upward direction across the confined square cylinder in the vertical channel. The aiding/opposing buoyancy in the flow is incorporated in terms of Richardson number (Ri ) in the range of –2 to 2. The ranges of other dimensionless parameters considered are: Reynolds number, Re : 1 to 40; and volume fraction of nanoparticles, ?: 0.005 to 0.045. This range of volume fraction of nanoparticles (i.e., ? = 0.005 to 0.045) corresponds to the power‐law index (n ) of a non‐Newtonian nanofluid in the range of n = 0.88 to 0.5, respectively. Prior to obtaining new results, the solution methodology is validated with existing literature counterparts. Finally, effects of the Reynolds number, Richardson number, and the rheology of non‐Newtonian nanofluids on streamline patterns, surface pressure, surface vorticity, drag coefficients, isotherm contours, local and average Nusselt numbers are delineated.     

On the combined influence of Reynolds number and cylinder spacing for flow around a row of heated square cylinders

The characteristics of forced convection heat transfer across a row of heated square cylinders kept in side-by-side arrangement are numerically investigated to examine the combined effects of Reynolds number and cylinder spacing for Ri = 0, 60 ≤ Re ≤ 160, Pr = .71, and s/d = 1.0–8.0, where the space between cylinder surfaces is s and the cylinder size is d. A numerical study was carried out using the thermal lattice Boltzmann method. The goal of this work is to explore the transitions in heat transfer phenomenon that occurs behind the cylinder and to report the corresponding regimes for heat transfer namely synchronous, quasiperiodic, and chaotic. The proposed regime of heat flow is a function of Reynolds number and spacing. The synchronous heat regime is obtained for s/d ≥ 5.0 and quasiperiodic, chaotic regimes are observed for 3.0 ≤ s/d < 5.0, s/d < 3.0, respectively at Re = 100. The instantaneous isotherms, the power spectra of the corresponding Nusselt number signals, and the significance of cylinder Nusselt number frequency are used to examine these heat flow regimes. The heat transfer regimes for a row of heated cylinders and flow regimes for a row of unheated cylinders both have comparable appearances except for the fact that the heat transfer regime is synchronous at s/d ≥ 5.0 and flow is synchronous at s/d ≥ 4.0. The chaotic or quasiperiodic heat transfer regimes occur due to merging and strong interactions between thermal blobs shed from the cylinders. Heat transfer is synchronous at a higher spacing and characterized by independent thermal blobs shedded from the cylinders. It is reported that as spacing reduces and Reynolds number increases, the mean value of the Nusselt number experienced by all cylinders increases. The important outcome of the present numerical work is that for understanding heat transfer from bluff body, the transitions that occur in heat transfer are useful.     

Influence of thermal boundary conditions on natural convection in a square enclosure partially heated from below

Natural convection in air-filled 2D square enclosure heated with a constant source from below and cooled from above is studied numerically for a variety of thermal boundary conditions at the top and sidewalls. Simulations are performed for two kinds of lengths of the heated source, i.e., a small and a large source corresponding to 20% and 80% of the total length of the bottom wall, respectively. The Rayleigh number varied from 10³ to 10⁷. Results are presented in the form of streamline and isotherm plots as well as the variation of the Nusselt number and maximum temperature at the heat source surface. Comparisons among the different thermal configurations considered are reported.     

Heat transfer regulation in a rectangular enclosure using a rotating plate

The effects of an inner rotating plate with horizontal axis on the heat transfer in a differentially heated vertical enclosure were investigated experimentally. The aspect ratio of the enclosure height/width was 1 throughout the experiments. An acrylic plate with a small thermal conductivity was installed horizontally at the center of the square enclosure, and was rotated at various speeds for normal and reverse rotations by using the motor attached outside of the enclosure. Purified water was used as the working fluid. The flow pattern was sketched by a visualization experiment using aluminum powder. The heat transfer results were also compared with those from a previous paper on a rotating cylinder. It is clarified here that the heat transfer rate of the enclosure depends largely on the parameter Gr_w/Re_ω², and is characterized by three regions. The heat transfer rate of the enclosure with a rotating plate is somewhat larger than that of a rotating cylinder in the forced convection region. The rotating plate used here will be useful for regulation of wide‐ranging heat transfer. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(4): 342–353, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10099     

Two-dimensional mixed convection heat transfer from confined tandem square cylinders in cross-flow at low Reynolds numbers

A two-dimensional numerical simulation is carried out to understand the effects of thermal buoyancy and Prandtl number on flow characteristics and mixed convection heat transfer over two equal isothermal square cylinders placed in a tandem arrangement within a channel at low Reynolds numbers. The spacing between the cylinders is fixed with four widths of the cylinder. The numerical results are presented for the range of conditions as: 1 ≤ Re ≤ 30, 0.7 ≤ Pr ≤ 100 (the maximum value of Peclet number being 3000) and 0 ≤ Ri ≤ 1 for a fixed blockage parameter B = 10%. The unsteady numerical simulations are performed with a finite volume code based on the PISO algorithm in a collocated grid system. The representative streamlines, vortex structures and isotherm patterns are presented and discussed. In addition, the overall drag and lift coefficients, recirculation length and average Nusselt numbers are determined to elucidate the role of Reynolds, Prandtl and Richardson numbers on flow and heat transfer. It is found that the flow is completely steady for the chosen ranges of the parameters.     

Effects of diameter ratio of adiabatic circular cylinder and tilt angle on natural convection from a square open tilted cavity

A numerical analysis is carried out to study the performance of natural convection inside a square open tilted cavity filled with air. An adiabatic circular solid cylinder is placed at the center of the cavity and the sidewall in front of the breathing space is heated by a constant heat flux. The top and bottom walls are kept at the ambient constant temperature. Two‐dimensional forms of Navier–Stokes equations along with the energy equations are solved using the Galerkin finite element method. Results are obtained for a range of Grashof numbers from 10³ to 10⁶ at Pr = 0.71 while the tilt angle varies from 0 to 45° and the diameter ratio of the cylinder is considered to be 0.2, 0.3, and 0.4 with constant physical properties. The parametric studies for a wide range of cylinder diameter ratios and cavity tilt angles show significant features of the present problem in terms of stream functions and temperature profiles. The computational results indicate that the heat transfer coefficient is strongly influenced by the above governing parameters. It is also found that the average Nusselt number decreases when the diameter ratio increases. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21001     

Natural-convection heat transfer to air from a horizontal array of cylinders with different surface temperatures

Heat transfer measurements were made on natural convection around horizontal in-line arrays of cylinders whose surface temperatures were different from each other. Through the experiments for a three-cylinder array, a correlation was obtained for the heat transfer coefficient of the array-center cylinder. By using the correlation with some assumptions, the heat-flux distributions could be estimated for an array of five cylinders which were heated to their respective temperatures. Consequently, it was found that both the correlation and the method proposed here were useful in the estimation of heat-flux distributions for a horizontal array of cylinders. © 1998 Scripta Technica, Inc. Heat Trans Jpn Res, 26(2): 116–121, 1997     

Enhanced thermal performance and entropy generation analysis in a novel cavity design with circular cylinder

Analyzing fluid dynamics and heat transfer holds significant importance in the design and enhancement of engineering systems. The current investigation utilizes the finite element method to explore natural convection and heat transfer intricacies within a novel cavity containing an inner circular cylinder under steady and laminar flow conditions. The principal aim of this study is to assess the impact of Rayleigh number (Ra), Bejan number (Be), and the presence of adiabatic, hot, and cold cylinders on heat transfer, entropy generation, and fluid flow. The range of Ra considered in this investigation spans from 10³ to 10⁶, while the Prandtl number for the air is fixed at 0.71. The findings illustrate that the presence of a cylinder leads to higher Be as Ra increase, compared to scenarios where no cylinder is present. This observation suggests that buoyancy forces dominate in the absence of a cylinder, resulting in significantly enhanced convective heat transfer efficiency. However, the presence of a heated cylinder within the tooth-shaped cavity exerts a substantial influence on the overall thermal performance of the system. Notably, the average Nusselt Number (Nu) experiences a remarkable increase of 41.97% under the influence of a heated cylinder, when compared to situations where a cold cylinder is present. This elevated average Nu signifies improved heat transfer characteristics, ultimately resulting in an overall improvement in the thermal system's efficiency.     

Vibration effects on the average heat transfer characteristics of the natural convection field in a square enclosure

In order to study the chaotic behavior of vibrational thermal convection in a square enclosure, a calculation method and the features of the average Nusselt number with vibration frequency were precisely examined. In the computation, the Prandtl number, the Rayleigh number, and the vibration Grashof number were held constant at 0.71, 10⁴, and 10⁶, respectively. The angular frequency of vibration was changed in the range between 10 and 7680. The results showed that the phenomena could be predicted with the calculation method adopted in this paper and the change in the time‐dependent characteristics of surface‐averaged Nusselt number with the angular frequency of vibration could be analyzed well with the power spectra. These changes were characterized by the five regimes proposed by Fu and Shieh. Moreover, it was clarified that the region where the hysteresis phenomena were detected corresponded to the one where the variation of the surface‐averaged Nusselt number was irregular and aperiodic. © 2000 Scripta Technica, Heat Trans Asian Res, 29(7): 545–558, 2000     

Flow and heat transfer around a single row of circular cylinders

A numerical investigation of flow and heat transfer around a single row of circular cylinders was conducted using a boundary-fitted coordinate system. Numerical calculations for center-to-center distance between cylinders L/d=2.0, 2.5, 3.3, and ∞ were made of water flows in the Reynolds number range from 75 to 500. Numerical values of average Nusselt number for uniformly heated cylinders are in relatively good agreement with those obtained from experiments in water (Prandtl number Pr ≒ 8). The interaction of wake flows behind cylinders, observed in the experiments, was also found to occur with decreasing cylinder spacing L/d. © 1997 Scripta Technica, Inc. 25(3): 192–200, 1996     

Heat transfer enhancement of mixed convection in a square cavity with inlet and outlet ports due to oscillation of incoming flow

A numerical study of unsteady laminar mixed convection flow in a square cavity with ventilation ports due to an oscillating velocity at the inlet port is performed. It is found that after certain time duration, a periodic variation in the fluid flow and temperature field in the cavity are created. It is observed that the heat transfer is enhanced for all the Strouhal numbers investigated in comparison to its steady state case. To realize the optimizing Strouhal number to reach the best performance of the system, the total Nusselt number and the coefficient of pressure drop in a cycle of the oscillation is evaluated with respect to the Strouhal number. It is found that for a region of the Strouhal number between 0.5 and 1, the performance of the system will be desirable with considering both the maximum heat transfer rate and minimum pressure drop in the cavity.     

An Experimental and Numerical Study of Natural Convection Heat Transfer in Horizontal Annuli between Eccentric Cylinders

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Heat and mass transfer under MHD mixed convection in a four-sided lid-driven square cavity

This paper investigates the heat and mass transfer under magnetohydrodynamic mixed convection flow of a binary gas mixture in a four-sided lid-driven square cavity. The enclosure's left wall is sinusoidally heated and acts as a source term, while the right wall functions as a sink. The cavity's horizontal walls are adiabatic and impermeable to mass transfer. The governing equations under Boussinesq approximation and stream function-vorticity formulation are solved using the alternating-direction-implicit scheme, a finite-difference method. The numerical scheme's consistency and stability are demonstrated using the matrix method. The MATLAB code is written, validated against some existing studies, and used to perform numerical simulations. The numerical solutions are graphically examined by visualizing the streamline, isotherm, and concentration contours for nondimensional parameters, such as Hartmann number $\left(0\le Ha\le 100\right)$, heat absorption or generation coefficient $\left(-2\le \varphi \le 2\right)$, Richardson number $\left(0.01\le Ri\le 100\right)$, and buoyancy ratio $\left(-6\le N\le 6\right)$. The magnetic field modifies the temperature and concentration distribution in the cavity, depending on the convection mode. The magnetic field forces the fluid to stagnate in different regions of the cavity, depending on the mode of convection. It was found that the difference between the maximum and minimum temperature and concentration at the cavity's midpoint increases up to 13 and 10 times, respectively, in the natural convection compared with the forced convection. The average Nusselt number on the vertical walls of the cavity is maximum in natural convection in the absence of a magnetic field but reaches a minimum value at $Ha=100$ in forced and mixed convection. The average Sherwood number on the cavity's vertical walls decreases with the magnetic field in mixed and natural convection.     

The structures of attractors reconstructed with time–evolution data of average heat transfer on thermal convection field in a vibrating square enclosure

In this paper the time‐dependent characteristics of surface‐averaged Nusselt number in a square enclosure with hot and cold side walls exposed to vertical vibrations were numerically examined. In the computation, the Prandtl number, the Rayleigh number, and the vibration Grashof number were held constant at 0.71, 10⁴, and 10⁶, respectively. The angular frequency of vibration was changed in the range between 10 and 7680. The results showed that the change in the characteristics of the surface‐averaged Nusselt number proposed by Fu and Shieh corresponded to the change in the shape of reconstructed attractor and that these regions could also be characterized by the three indices defined in phase space: average location of trajectory, the largest Lyapunov exponent, and the correlation dimension. Moreover, the time scale with which the autocorrelated coefficient of the surface‐averaged Nusselt number becomes 1/e was found to be a very important parameter for the time‐ and surface‐averaged Nusselt number. © 2000 Scripta Technica, Heat Trans Asian Res, 30(1): 11–21, 2001     

The study of buoyancy influence on mean flow and heat transfer under conditions of mixed convection in annular channels

Laser Doppler anemometry (LDA) measurements are reported on mean flow and turbulence in water as it flows downwards through a long vertical passage of annular cross‐section having an inner surface which can be uniformly heated and an outer one which is adiabatic. Under buoyancy‐opposed conditions, which can be achieved by heating the core and operating at a reduced mass flow rate, the flow near the inner surface is retarded, turbulent velocity fluctuations and turbulent shear stress are increased and the effectiveness of heat transfer is enhanced. When the influence of buoyancy is very strong, flow reversal occurs near the inner surface. Under such conditions, turbulence is produced very readily and the heat transfer process remains very effective, even when the Reynolds number is reduced to values at which the flow is laminar in the absence of heating. The measurements of turbulence in buoyancy‐opposed flow made in this study provide direct confirmation of the validity of the ideas currently used to explain the influences of buoyancy on mixed convection in vertical passages. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(1): 9–17, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20041     

Numerical investigation of mixed convection of non-Newtonian fluid in a vented square cavity with fixed baffle

This paper numerically investigates mixed convective heat transfer in a vented square cavity incorporated with a baffle that is subjected to external non-Newtonian fluids (NNFs). Adiabatic conditions are imposed on the top and bottom walls, while cold temperature conditions are applied to the right and left solid boundaries. Heated NNF enters the cavity through the inlet and goes out through the outlet at three different locations, and it passes on a vertical baffle fixed at the base placed at different lengths. To examine the impact of the inlet and outlet positions, three different shapes of the outlet port located on the right wall and the inlet port on the left bottom wall were investigated. The impacts of Reynolds number (Re) of 100 ≤ Re ≤ 1000, Richardson number (Ri) of 0.1 ≤ Ri ≤ 3, power law index (n) of 0.6 ≤ n ≤ 1.4, length of baffle (L_b) of 0.2 ≤ L_b ≤ 0.6 and the outlet hole positions (S) of $0\le S\le 0.9$ on the thermal and flow distributions in the cavity are taken into consideration in this paper. The results demonstrated that the flow's intensity and heat transfer increase with improvement in the Re and n at any baffle length. When the Ri increased from 0.1 to 3, $N{u}_{\mathrm{avg}}$ increased by 23.3% at $n=0.6$, and 13.8% at $n=1.2$. Also, the Ri increment results in the augmentation of the average heat transfer.     

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.     

Cooling strategy by mixed convection of a discrete heater at its optimum position in a square cavity with ventilation ports

We studied cooling strategy in a square enclosure with ventilation ports and a discrete heat source at its optimum position. We searched the optimum heater position by maximizing the global conductance at different Rayleigh and Reynolds numbers and considered three different ventilation ports arrangements. We solved the conservation equations of mass, momentum and energy for mixed convection. We found that the heater position is at off center in all cases, its optimum position is insensitive to the variation of Ra and Re; it solely depends on the ventilation ports arrangement. The Nusselt number is dependent on Ri = Ra/Re²: at its low values, Nu is a decreasing function of Ri and at its high values, it is an increasing function of it.