Visualization and analysis of surface tension and cooling effects on differentially heated cavity using heatline concept

Convection in a square cavity with a free surface and heated from the side is visualized and analyzed by the heatline concept. The temperature gradient is applied along the top free surface and the heat balance at the surface is assumed to obey Newton’s law of cooling. The finite difference method has been used to solve the dimensionless governing equations. The governing parameters considered are the Marangoni number (0 ? Ma ? 1000), the Biot number (0 ? Bi ? 6) and the Prandtl number (0.054 ? Pr ? 6.2). The flows of heat and fluid are of a similar type except at a strong cooling condition. The heat transfer performance presents a minimum at Marangoni number of roughly 100, 200 and 600 for the cavity filled with liquid metal, mixture of noble gases and air, respectively.     

Numerical simulation of natural convection heat transfer in a porous cavity heated from below using a non-Darcian and thermal non-equilibrium model

The present paper investigates the numerical simulation of steady laminar incompressible natural convection heat transfer in an enclosed cavity that is filled with a fluid-saturated porous medium. The bottom wall is subjected to a relatively higher temperature than the top wall while the vertical walls are considered to be insulated. The flow field is modeled upon incorporating different non-Darcian effects, such as the convective term, Brinkman effect and Forchhiemer quadratic inertial effect. Moreover the two-equation model is used to separately account for the local fluid and solid temperatures. The numerical solution is obtained through the application of the finite volume method. The appraisals of the sought objectives are performed upon identifying key dimensionless groups of parameters. These dimensionless groups along with their operating domains are: Rayleigh number 1 ⩽ Ra ⩽ 400, Darcy number 10⁻⁴ ⩽ Da ⩽ 10⁻³, effective fluid-to-solid thermal conductivity ratio 0.1 ⩽ κ ⩽ 1.0, and the modified Biot number 1 ⩽ χ ⩽ 100. The non-Darcian effects are first examined over a broad range of Rayleigh number. Next, the implications of the group of parameters on the flow circulation intensity, local thermal non-equilibrium (LTNE) and average Nusselt number are highlighted and pertinent observations are documented.     

The effect of the position of the heated thin porous fin on the laminar natural convection heat transfer in a differentially heated cavity

Laminar natural convection heat transfer in a differentially heated cavity with two thin porous fins attached to the hot wall and bottom insulated surface was studied numerically for various pertinent parameters. Such parameters include Richardson number, Darcy number, thermal conductivity ratio, and location of the porous fin. The left wall of the cavity is assumed to be uniformly heated while the right wall is kept at a lower temperature. In addition, the horizontal walls of the cavity were considered insulated. Furthermore, the governing transport equations within the porous media were written according to the volume-average theory. The governing equations are solved using a finite element formulation based on the Galerkin method of weighted residuals. The results of this investigation showed that the presence of a horizontal porous fin increases the average Nusselt number when compared with the differentially heated cavity for various Richardson numbers and thermal conductivity ratios. However, a vertical porous fin attached to the bottom insulated surface exhibited a lower average Nusselt number than the no-fin case.     

Numerical visualization of mass and heat transport for conjugate natural convection/heat conduction by streamline and heatline

The method of numerical visualization of mass and heat transport for convective heat transfer by streamlines and heatlines are comprehensively studied. Functions are directly defined in terms of dimensionless governing equations or variables. Some basic characteristics of the functions are illustrated in detail, knowledge of which is essential to perceive the results and the philosophy of heat and fluid flow. The consistency of the formulations is especially addressed when dealing with conjugate convection/conduction problem. The functions/lines are unified for both fluid and solid regions, and the diffusion coefficients of the function equations are invariant. The method has been used to visualize the heat and fluid flow structures for natural convection in an air (Pr=0.71) filled square cavity over a wide range of Ra=10³−10⁶, and those for conjugate natural convection/heat conduction problem where the conduction effect of solid body on heat transfer is investigated. As to exhibiting the nature of convective heat transfer, streamlines and heatlines provide a more practical and efficient means to visualize the results than the customary ways.     

辐射侧加热腔内自然对流传热特性研究

为了明确辐射侧加热封闭方腔内半透明流体的自然对流传热现象及规律,采用有限体积法进行数值模拟研究,分析了瑞利数和光学厚度对流场、温度场以及传热特性的影响。结果表明：与传统侧壁加热腔内自然对流相比,辐射侧加热腔内等温线和流场分布规律不一致;随着瑞利数和光学厚度增加,涡心由中心位置沿直线向辐射入射侧斜上方偏移;随着瑞利数增加,等温线变得更均匀;随着光学厚度增加,等温线变密,努塞尔数Nu与瑞利数RaT的标度律指数减小,当光学厚度增加到一定时标度律不再变化,此时传热标度律与传统恒壁温侧加热腔内自然对流相当,满足Nu~Ra0.29T。     

Unsteady natural convection in a water-filled isosceles triangular enclosure heated from below

This study is concerned with transient natural convection in a water-filled isosceles triangular enclosure subject to cooling at the inclined surfaces and simultaneous heating at the base. The unsteady flows over a range of Grashof numbers are visualized using a shadowgraph technique, and corresponding numerical simulations are carried out using a Finite Volume Method. Both the experiments and numerical simulations have revealed that the transient flow development in the enclosure due to abrupt heating and cooling through the boundaries can be classified into three distinct stages, that is, an early stage, a transitional stage, and a steady/quasi-steady stage. The major flow features at each of the three stages are described and the Grashof number effects on the flow development and heat transfer are discussed. It is found that, for a fixed aspect ratio of 0.5, a transition of the unsteady flow from symmetric to asymmetric structures occurs for Grashof numbers above 2.95 × 10⁴. Moreover, the present heat transfer calculations indicate that the average Nusselt number over the inclined and horizontal surfaces approximately scales with Gr^0.2.     

Effects of thin fin on natural convection in porous triangular enclosures

A two-dimensional solution of natural convection in solid adiabatic thin fin attached to porous right triangular enclosures has been analyzed numerically. The vertical wall of the enclosure is insulated while the bottom and the inclined walls are isothermal. The temperature of the bottom wall is higher than the temperature of the inclined wall. Governing equations, which are written using Darcy model, are solved via the finite difference technique. The Successive Under Relaxation (SUR) method was used to solve linear algebraic equations. Dimensionless location of the thin fin from 0.2 to 0.6, the aspect ratio of triangular enclosure from 0.25 to 1, Rayleigh number from 100 to 1000 and the dimensionless height of the fin from 0.1 to 0.4 are used as governing parameters that are effective on heat transfer and fluid flow. Results for the mean Nusselt number, velocity profiles, the contour maps of the streamlines and isotherms are presented. It is observed that the thin fin can use as a passive control element for flow field, temperature distribution and heat transfer.     

Unsteady natural convection heat transfer from a heated horizontal circular cylinder to its air-filled coaxial triangular enclosure

Unsteady natural convection heat transfer in a horizontal annular region bounded by a heated inner circular cylinder and a coaxial outer triangular cylinder is numerically studied for a wide range of Grashof numbers, aspect ratios, and inclination angles of the triangular enclosure. Different phases are identified during the course of flow development through the evolutions of the average Nusselt number over the inner circular wall. Snapshots of streamlines and isotherms for two typical cases are presented to exhibit identification among these phases. The flow development time and time-averaged Nusselt number over the inner circular wall are predicted and scaled with Grashof number. Additionally, the onset and evolution of pitchfork bifurcation are quantitatively investigated.     

MHD natural convection in a laterally and volumetrically heated square cavity

A numerical study is presented of unsteady two-dimensional natural convection of an electrically conducting fluid in a laterally and volumetrically heated square cavity under the influence of a magnetic field. The flow is characterized by the external Rayleigh number, Ra_E, determined from the temperature difference of the side walls, the internal Rayleigh number, Ra_I, determined from the volumetric heat rate, and the Hartmann number, Ha, determined from the strength of the imposed magnetic field. Starting from given values of Ra_E and Ha, for which the flow has a steady unicellular pattern, and gradually increasing the ratio S = Ra_I/Ra_E, oscillatory convective flow may occur. The initial steady unicellular flow for S = 0 may undergo transition to steady or unsteady multicellular flow up to a threshold value, Ra_I,cr, of the internal Rayleigh number depending on Ha. Oscillatory multicellular flow fields were observed for S values up to 100 for the range 10⁵-10⁶ of Ra_E studied. The increase of the ratio S results usually in a transition from steady to unsteady flow but there have also been cases where the increase of S results in an inverse transition from unsteady to steady flow. Moreover, the usual damping effect of increasing Hartmann number is not found to be straightforward connected with the resulting flow patterns in the present flow configuration.     

Entropy generation for natural convection by heated partitions in a cavity

Entropy generation for natural convection in a partitioned cavity, with adiabatic horizontal and isothermally cooled vertical walls, is studied numerically by both a FORTRAN code and the commercially available CFD-ACE software. Effects of the Rayleigh number, the position of the heated partition, and the dimensionless temperature difference on the local and average entropy generation rate are investigated. Proper scale analysis of the problem showed that, while fluid friction term has nearly no contribution to entropy production, the heat transfer irreversibility increases monotonically with the Nusselt number and the dimensionless temperature difference.     

Natural convection heat transfer in an anisotropic porous cavity heated from the side: Part 1. Theory

Natural convection heat transfer and flow structure in an anisotropic porous medium in a square cavity saturated with a Boussinesq fluid have been studied analytically and numerically. Based on an asymptotic analysis, three distinctive regimes are found depending on the magnitude of the permeability ratio K. In the vicinity of K = 1 the average Nusselt number and fluid velocity are scaled with (KRa) ^1/2 when either K or the Rayleigh number Ra is varied. In the limit of K → 0 the heat transfer across the cavity approaches the conductive state, and the convecting velocity, which is primarily in the vertical direction, is scaled with KRa. At the other end of the spectrum, namely, K → ∞, the average Nusselt number and the convecting velocity are scaled with Ra and independent of K. The asymptotic results are verified with two‐dimensional numerical calculations. The ranges of K of the respective regimes are also determined based on the numerical results. © 2000 Scripta Technica, Heat Trans Asian Res, 29(5): 373–384, 2000     

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。     

A numerical investigation of transient natural convection heat transfer of aqueous nanofluids in a differentially heated square cavity

Transient natural convection heat transfer of aqueous nanofluids in a differentially heated square cavity is investigated numerically. The effective thermal conductivity and dynamic viscosity of nanofluids are predicted by using the proposed models that take the contribution of Brownian motion of nanoparticles into account. Three different Rayleigh numbers and five different volume fractions of nanoparticles are considered. The development of natural convection is presented through the evolutions of the average Nusselt number along the cold side wall. The predicted flow development times and time-averaged Nusselt numbers are scaled with Rayleigh number. In addition, the time-averaged Nusselt numbers are presented in terms of volume fraction of nanoparticles. It is shown that at constant Rayleigh numbers, the time-averaged Nusselt number is lowered with increasing volume fraction of nanoparticles.