Developing Flow of Mixed Convection in a Vertical Rectangular Duct with One Heating Wall

Heat transfer and flow patterns of laminar mixed confection in the developing region of a vertical rectangular duct with one heating wall have been investigated numerically in this study. The parabolic boundary layer model is adopted to predict the three-dimensional buoyancy-assisted flow field. Governing equations art solved by using the SIMPI.KC method coupled with a forward marching, implicit finite difference scheme. The velocity and temperature distributions as well as the stream wise variations of local heat flux and fluid pressure are calculated under various geometric parameters. Results show that the flow characteristics are significantly dependent on the buoyancy effect (Gr / Re), the aspect ratio of cross section of duct (H). and the Prandtl number (Pr). The numerical solutions obtained have been compared and verified with existing studies. Meanwhile, the analytical solutions of fully developed flaw recently reported 181 are found to exactly portray the behavior of flow far downstream.     

Coupled Natural Convection and Radiation in a Horizontal Rectangular Enclosure Discretely Heated from Below

A numerical study is carried out to investigate the interaction between natural convection and thermal radiation in a horizontal enclosure filled with air and heated discretely from below. The results are presented for a cavity having an aspect ratio A _r  = L′/H′ = 10, while the Rayleigh number and the emissivity of the walls are varied in the ranges 10³ ≤ Ra ≤ 10⁶ and 0 ≤ ε ≤ 1, respectively. The results of the study, presented in terms of flow and temperature patterns, average convective, radiative and total Nusselt numbers, evaluated on the cold wall, show that the problem has multiple solutions. Each of these solutions is characterized by a specific flow structure, and its appearance and range of existence depend strongly on the parameters Ra and ε. The amount of heat evacuated through the cold surface is dependent on the type of solution.     

Three-Dimensional Mixed Convection Heat and Mass Transfer in a Rectangular Duct: Case of Longitudinal Rolls

This article presents numerical study of 3-D thermosolutale mixed convection (TSMC) in horizontal rectangular channels. The contribution of this work is to characterize the travelling wave's appearance and to generalize the behavior of Poiseuille-Rayleigh-Benard (PRB) systems for a broad range of dimensionless parameters, which control the double diffusive mixed convection. The numerical results consist of analyzing the flow regimes of the steady longitudinal thermoconvectives rolls for the case of purely thermal mixed convection (TMC) and for both thermal and mass transfer (TSMC). The transition from opposed volume forces to cooperating ones at fixed Rayleigh (Ra), Reynolds (Re), and Lewis (Le) numbers, considerably affects the birth and the development of the longitudinal rolls (noted R_//). The heat and mass transfers distribution, presented by the average Nusselt and Sherwood numbers, are also examined.     

Studies on Three-Dimensional Mixed Convection with Surface Radiation in a Rectangular Channel with Discrete Heat Sources

The flow behavior and heat transfer characteristics of conjugate heat transfer under mixed convection for a three-dimensional laminar flow in a rectangular channel with six protruding heat sources, mounted on the lower wall of the channel, have been studied numerically and experimentally. At higher temperatures, radiation plays an important role. This work reports the effect of radiation on conjugate mixed convection heat transfer. Air is taken as a cooling medium and is considered to be radiatively non-participating medium. The parameters considered for the study are positions (streamwise and spansise) of the heat sources, Reynolds number, emissivity of the heat sources, and the thermal conductivity of a printed circuit board (PCB) having constant fluid properties with the Prandtl number being 0.707. The Boussinesq approximation has been used. Commercial software ANSYS Fluent has been used for numerical analysis, and experiments have been carried out in a small-sized wind tunnel. The ranges of Reynolds number, emissivity, and thermal conductivity of PCB are 115–690 (corresponding inlet velocity of 0.25–1.5), 0–0.9, and 0.038–1.4 W/mK, respectively. Results indicate that the radiative heat transfer is significant at lower Reynolds number and lower thermal conductivity of PCB. The streamwise spacing of heat sources has larger influence compared to the spanwise spacing.     

Enhanced Three-Dimensional Mixed Convection in a Horizontal Channel Using a Baffle

Three-dimensional mixed convection inside a horizontal rectangular channel with a square heated surface on one of the vertical sidewalls and an infinitely thin baffle installed on the opposite insulated sidewall is numerically investigated. Attention is focused on the influence of the baffle position (?2 to 2), the inclination angle between the baffle and the horizontal (15° to 90°), and the baffle height (0.2 to 0.9) on the flow and thermal characteristics. The other parameters remain unchanged: the Reynolds number (100), Grashof number (50,000) and Prandtl number (0.71). The results show recirculation around the top portion of the heated surface due to strong buoyancy. The heat transfer depends strongly on the relative positions of the baffle and the recirculation. Heat transfer enhancement is obtained with a higher baffle and a larger inclination angle if the baffle is close to the cold main stream. In contrast, the average Nusselt number is slightly smaller if the baffle is surrounded by the recirculation than it is without the baffle. An accurate correlation is proposed for calculating the average Nusselt number over the investigated range of the baffle position and the inclination angle for a fixed baffle height (0.75).     

Inverse Natural Convection Problem with Radiation in Rectangular Enclosure

Inverse thermal problem is applied to natural convective flow with radiative heat transfer. The bottom wall temperature in the 2-D cavity domain is estimated by using gas temperature measurements in the flow field. The inverse problem is solved through a minimization of an objective function using the conjugate gradient method with adjoint problem. The effects of functional form of bottom wall temperature profile, the number and the position of measurement points, and the measurement errors are investigated and discussed. The conjugate gradient method is found to work well in estimating the bottom wall temperature, even when natural convection with radiation phenomena is involved.     

Entropy Generation due to Combined Natural Convection and Thermal Radiation within a Rectangular Enclosure

ABSTRACT

The present work investigates entropy production due to coupled natural convection/radiation heat transfer phenomenon in an inclined rectangular enclosure, isothermally heated from the bottom side and isothermally cooled from the other sides. The discrete-ordinate method is used in modeling the radiative transport equation while the statistical narrow band correlated-k model is adopted to deduce the radiative properties of the medium. The influence of pertinent parameters such as aspect ratio, inclination angle and walls emissivities on entropy generation is studied. It is found that the volumetric entropy generation is reduced when increasing the inclination angle of the enclosure. Moreover, it is shown that the minimum entropy production due to radiation heat transfer in participating media occurs at aspect ratio equal to unity.     

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.     

Natural Convection in a Vertical Rectangular Cavity Filled with a Non-Newtonian Power Law Fluid and Subjected to a Horizontal Temperature Gradient

A study of natural convection, in a vertical rectangular cavity filled with a non-Newtonian fluid and subjected to uniform heat flux along the vertical side walls, is carried out numerically by solving the full governing equations. In the limit of a tall enclosure, these equations are considerably reduced by using the parallel flow approximation. Solutions for the flow and temperature fields, and the heat transfer rate, are obtained as functions of the governing parameters. Good agreement is found between the results of the two approaches for a wide range of governing parameters.     

Radiation Effects on Turbulent Mixed Convection in an Asymmetrically Heated Vertical Channel

The purpose of present study is to numerically investigate the radiation effects on turbulent mixed convection flow between two differentially heated vertical parallel plates. Two flow situations known as aiding and opposing flow are considered. Frictional Reynolds number and Grashof number are assumed to be 150 and 1.6 × 10⁶, respectively. Both hydrodynamically and thermally developing and fully developed regions in the channel are investigated. Three Reynolds-averaged Navier–Stokes-based low Reynolds turbulence models are evaluated and the model with better overall performance is applied to the simulations. The radiative transfer equation for the gray and participating fluid is solved using the discrete-ordinates method, adopting its eighth-order quadrature scheme. The effects of two radiative parameters, namely, wall emissivity and optical thickness, on the flow and thermal fields, Nusselt number, and friction factor are addressed. Present results indicate that the presence of thermal radiation has a significant influence on flow and thermal fields. With an increase in wall emissivity and optical thickness, influence of radiation on the mean velocity, mean temperature, and turbulence kinetic energy profiles grows in both aiding and opposing regions. This results in an increase in bulk temperature, centerline velocity, and Nusselt number and a decrease in friction factor on both sides.     

水平放置离散矩形直翅片强制对流的传热研究

实验了不同空气流速时水平放置离散矩形直翅片组的稳态传热着重探讨了翅片列间距对翅片组散热性能和阻力损失的影响,用离散翅片的长度作为定性尺寸,得到了计算直线排列的离散翅片组平均对流传热系数的无量纲传热准数关系式     

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.     

Varying Heating Effect on Mixed Convection of Nanofluids in a Vented Horizontal Cavity with Injection or Suction

The problem of mixed convection heat transfer inside a horizontal vented enclosure through the lower and upper parts, respectively, of its left and right vertical walls is studied numerically using Al₂O₃-water nanofluid as working fluid. The bottom wall is subjected to a linearly varying (increasing or decreasing) heating temperature profiles, while the other boundaries are considered thermally insulated. The fresh fluid is admitted from the bottom part of the left vertical wall by injection or by the suction imposed on the opening of the right vertical wall. Based on numerical predictions, the conjugate effect of the Reynolds number and the nanoparticle concentration on fluid flow and heat transfer characteristics is studied. The obtained results demonstrate clearly the positive role of the nanoparticles addition on the improvement of the heat transfer rate and the mean temperature within the cavity. In addition, the flow structure and the temperature distribution inside the cavity are seen to be very sensitive to the variations of the Reynolds number, the imposed external flow mode, and the heating type. Results presented show that, in general, the decreasing heating mode is more favorable to the heat transfer in comparison with the case of the increasing heating mode. The cooling efficiency is found to be more pronounced by the injection/suction mode by applying the increasing/decreasing heating type.     

Numerical Investigation of Natural Convection in a Partitioned Rectangular Enclosure

This work presents a numerical analysis using the finite-element method of natural-convection heat transfer and flow patterns in a square partitioned enclosure with two partitions protruding centrally from the end walls of the enclosure. The enclosure has opposite isothermal walls at different temperatures. The length of the partitions is fixed and equal to one-fourth the height of the enclosure. Three partition positions and thicknesses are considered. Computation of Nusselt numbers for Rayleigh numbers in the range 10⁴–10⁶ is done. “Standard” boundary conditions are introduced as being more appropriate to simulate situations of practical engineering interest. Results clearly demonstrate that partition location and thickness have a significant effect on heat transfer.     

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.     

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.     

Effect of Radiation on Mixed Convection Inside a Lid-Driven Square Cavity With Various Optical Thicknesses and Richardson Numbers

This work studies numerically the effect of the radiative heat transfer on the flow and thermal behaviors of the mixed convection in a lid-driven square cavity in the presence of radiatively emitting, absorbing, and isotropically scattering gray medium. The Boussinesq approximation has been used in modeling the governing equations, and the SIMPLE (semi-implicit method for pressure-linked equations) algorithm is used in coupling the velocity and pressure fields. The radiative transfer equation and the governing equations have been solved respectively by the discrete ordinates method and the finite-volume method in order to obtain the temperature, velocity, and heat flux distributions in the participating medium. The present numerical simulations are validated by comparison with several earlier studies. Then, the temperature and velocity distributions and Nusselt numbers have been analyzed in a broad range of optical thicknesses from 0 to 100 and Richardson numbers from 0.01 to 100. The results show that the radiation has a significant role on the flow and thermal behaviors in the lid-driven square cavity. As an example, we can refer to a sweep behavior that is detected in the velocity distributions of the lid-driven cavity.     

Convective Heat Transfer in a Vertical Rectangular Duct Filled with a Nanofluid

An analysis is performed to study natural convective heat transfer in a vertical rectangular duct filled with a nanofluid. One of the vertical walls of the duct is cooled by a constant temperature, while the other wall is heated by a constant temperature. The other two sides of the duct are thermally insulated. The transport equations for a Newtonian fluid are solved numerically with a finite volume method of second‐order accuracy. The influence of pertinent parameters such as Grashof number, Brinkman number, aspect ratio and solid volume fraction on the heat transfer characteristics of natural convection is studied. Results for the volumetric flow rate and skin friction for Copper and Diamond nanoparticles are also drawn. The Nusselt number for various types of nanoparticle such as silver, copper, diamond and titanium oxide are also tabulated. The results indicate that inclusion of nanoparticles into pure water improves its heat transfer performance; however, there is an optimum solid volume fraction which maximizes the heat transfer rate.     

Asymmetrical Non-Uniform Heat Flux Distributions For Laminar Flow Heat Transfer With Mixed Convection In a Horizontal Circular Tube

Non-symmetric heat flux distributions in terms of gravity in solar collector tubes influence buoyancy-driven secondary flow which has an impact on the associated heat transfer and pressure drop performance. In this study the influence of the asymmetry angle (0°, 20°, 30° and 40°) with regard to gravity for non-uniform heat flux boundaries in a horizontal circular tube was investigated numerically. A stainless steel tube with an inner diameter of 62.68 mm, a wall thickness of 5.16 mm, and a length of 10 m was considered for water inlet temperatures ranging from 290 K to 360 K and inlet Reynolds numbers ranging from 130 to 2000. Conjugate heat transfer was modelled for different sinusoidal type outer surface heat flux distributions with a base-level incident heat flux intensity of 7.1 kW/m². It was found that average internal heat transfer coefficients increased with the circumferential span of the heat flux distribution. Average internal and axial local heat transfer coefficients and overall friction factors were at their highest for symmetrical heat flux cases (gravity at 0º) and lower for asymmetric cases. The internal heat transfer coefficients also increased with the inlet fluid temperature and decreased with an increase in the external heat loss transfer coefficient. Friction factors decreased with an increase in fluid inlet temperature or an increase in the external heat loss transfer coefficients of the tube model.     

矩形微通道内液体流动与传热的数值模拟研究

本文针对矩形微通道内单相流动和传热特性,利用CFD模拟分析软件对其进行三维数值模拟研究.微矩形通道宽为50μm,高为200μm,工质采用去离子水.模型以有限体积法离散,SIMPLEC方法求解速度、压力和温度耦舍方程组.讨论了流体热物性随温度变化和雷诺数对速度场和温度场的影响.并与理论预测值、参考文献值比较.分析结果显示,流体粘度随温度对触的影响和粘性耗散对热起始段的作用不能忽略.fRe数随Re数的增加而减小,Nu数不受Re数的变化影响.