Natural Convection of Nanofluid in Cylindrical Enclosure Filled with Porous Media

A numerical study has been carried out to investigate the effect of aspect ratio on heat transfer by natural convection of nanofluid taking Cu nano particles and the water as based fluid. The flow is laminar, steady state, axisymmetric two-dimensional in a vertical cylindrical channel filled with porous media. Heat is generated uniformly along the center of the channel with its vertical surface remain with cooled constant wall temperature and insulated horizontal top and bottom surfaces. The governing equations which used are continuity, momentum and energy equations using Darcy law and Boussinesq＇s approximation which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using the MATLAB-7 program. The parameters affected on the system are Rayleigh number ranging within （10≤ Ra ≤ 103）, aspect ratio （1 ≤ As 〈 5） and the volume fraction （0 ≤0 〈 0.2）. The results obtained are presented graphically in the form of streamline and isotherm contour plots and the results show that as ~ increase from 0.01 to 0.2 the value of the mean Nusselt number increase 50.4% for Ra = 1,000.     

The Improved Direct Collocation Meshless Approach for Radiative Heat Transfer in Participating Media

The moving least-squares (MLS) direct collocation meshless method (DCM) is an effective numerical scheme for solving the radiative heat transfer in participating media. In this method the trial function is constructed by a MLS approximation and the radiative transfer equation (RTE) is discretized directly at nodes by collocation. The main drawback of this method is that, like most of the other numerical methods, the solution to the RTE by the DCM also suffers much from nonphysical oscillations in some cases caused by the convection-dominated property of the RTE. To overcome the numerical oscillations, special stabilization techniques are usually adopted, which increases the complexity and computation time of problem. In the present work a new scheme based on the outflow-boundary intensity interpolation correction is proposed that can easily ensure a large reduction in numerical oscillations of results without any complex stabilization technique. Adaptive support domain technique is also adopted, and the size of the support domain of each evaluated point changes with the density of nodes with irregular distribution. Five cases are studied to illustrate the numerical performance of these improvements. The numerical results compare well with the benchmark approximate solutions, and it is shown that the improved moving least-square direct collocation meshless method (iDCM) is easily implemented, efficient, of high accuracy, and excellent stability, to solve radiative heat transfer in homogeneous participating media.     

辐射腔体热源反向优化设计

介绍的待设计热力系统通过辐射加热使目标从初始已知状态按照设定温度进程升温到最终的热稳定状态。对于热源就是寻求满足整个加热过程的热流输入函数,在空间结构和腔体表面性质已知的条件下,热流输入函数可以通过目标的步时确定,问题转变成非稳态问题。非稳态问题的引入使问题更具有实际应用的价值,采用截断奇异值分解法来求解。     

Extension of the Discrete Ordinates Interpolation Method to Combined Convection-Radiation Problems with Fluid Flow in Three-Dimensional Geometries Filled with Gray Participating Media

Combined convection-radiation problems in gray absorbing/emitting/scattering media are investigated numerically. The discrete ordinates interpolation method (DOIM) is incorporated into commercial software (FLUENT) using userdefined functions (UDFs). As preliminary tests, combined conduction/natural convection-radiation problems in a rectangular geometry are solved to validate the accuracy. The original DOIM is modified to solve the radiative heat transfer in an irregular geometry with internal obstacles. Then the combined turbulent forced convection-radiation problem is solved, and the radiation effects are discussed through the profiles of velocity and temperature. Fine agreement with other reference solutions is found. The DOIM promises reliable accuracy and excellent versatility for incorporation into fluid flow codes. Further computational issues are also discussed.     

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.     

Heat Transfer in a Lid-Driven Enclosure Filled with Water-Saturated Aluminum Foams

Mixed convection in a lid-driven square enclosure filled with water-saturated aluminum foams is investigated numerically. The driving forces of fluid flow in such a system include the buoyancy force due to temperature gradient and the shear force due to lid movement, while the interaction of these forces results in various heat transfer modes. This work uses the Brinkman-Forchheimer model for fluid flow and the two-equation model for heat transfer. The top moving wall and the bottom heated wall are maintained at different constant temperatures, while the other walls are thermally insulated. The relevant parameters are the porosity of aluminum foams (ε = 0.91, 0.97), the Grashof number (Gr = 10⁴–3 × 10⁶) and the Reynolds number (Re = 10^?2–10⁴). The fluid flow and heat transfer characteristics of the present porous system are identified. Parametric study indicates that the average Nusselt number (Nu) generally increases with Gr and Re. The higher porosity promotes much more enhancement of convective heat transfer, but the lower porosity is desired for higher total heat transfer due to the higher value of effective thermal conductivity. Finally, the Nu correlation is established based on the numerical results.     

Inverse Boundary Design Problems in Enclosures With Non-Gray Media

In this work, the inverse analysis is applied to radiative heat transfer boundary design problems with non-gray media. The objective of the inverse problem is to find the power of the heaters on the heater surface that produces the desired output, that is, temperature and heat flux distribution over the design surface. The inverse problem is formulated as an optimization problem for minimization of an objective function, which is defined by the sum of the squared difference between estimated and desired heat flux distributions over the design surface. The non-gray optimization problem is solved using the conjugate gradient method, which is a gradient-based optimization method. The spectral line weighted-sum-of-gray-gases model (SLW) is used to account for non-gray gas radiation properties. The radiative transfer equation is solved by the discrete ordinates method combined with two models for simulation of non-gray media. Enclosures with diffuse and gray walls are considered. Radiation is assumed the dominant mode of heat transfer. Example problems including homogeneous/nonhomogeneous, isothermal/nonisothermal media are considered. The results obtained using the SLW model and the gray model are compared.     

Natural Convection Heat Transfer in an Inclined Enclosure Filled with a Water-Cuo Nanofluid

This article presents the results of a numerical study on natural convection heat transfer in an inclined enclosure filled with a water-CuO nanofluid. Two opposite walls of the enclosure are insulated and the other two walls are kept at different temperatures. The transport equations for a Newtonian fluid are solved numerically with a finite volume approach using the SIMPLE algorithm. The influence of pertinent parameters such as Rayleigh number, inclination angle, and solid volume fraction on the heat transfer characteristics of natural convection is studied. The results indicate that adding nanoparticles into pure water improves its heat transfer performance; however, there is an optimum solid volume fraction which maximises the heat transfer rate. The results also show that the inclination angle has a significant impact on the flow and temperature fields and the heat transfer performance at high Rayleigh numbers. In fact, the heat transfer rate is maximised at a specific inclination angle depending on Rayleigh number and solid volume fraction.     

平面叶栅气动设计的变域变分原理及有限元计算

采用变域变分原理,对以流函数描述的无粘流体流动的亚音速平面叶栅反设计问题进行了理论分析和有限元计算。由于变域变分能将未知形状的几何变量及控制方程结合在一个变分泛函中,使得数学描述简洁、紧凑,且几何变量及控制方程的求解能耦合地进行。采用变分有限元方法计算结果表明,该计算原理具有较高的精度,能获得较为满意的叶栅反设计的结果。     

铝翼散热管式中冷器的设计计算方法

介绍了铝翼散热管式中冷器的特点，导出了该种形式的中冷器冷却元件几何参数的计算公式；对管外流体侧的通道当量直径计算、对流换热和流通阻力准则方程的建立提出了一种新的方法，总结出一套完整的中冷器设计和校核的计算步骤，并对12V190B柴油机中冷器进行了设计计算和试验。由计算和试验结果对比可知，增压空气进、出口温差的计算误差在6％以内，进、出口压力损失的计算误差在10％以内，说明该计算方法可以满足铝翼散热管式中冷器的设计使用要求。     

几何参数变化对离心压气机性能影响的仿真研究

采用离心压气机性能仿真数学模型研究某些几何参数，如叶片顶部间隙，叶轮叶片出口角变化对压气机性能产生的影响，是当今设计高压比、宽工作范围、高效离心压气机的关键步骤。为此，首先建立了离心压气机性能仿真数学模型。为了验证数学模型的有效性，对Krain叶轮性能进行了计算。随后，对不同叶片顶部间隙，不同出口叶片角的压气机性能进行仿真研究。研究结果表明，随顶部间隙的增大，压气机效率及压比下降；后弯叶轮性能优于径向叶轮。     

铝翼散热管式中冷器的设计计算方法

介绍了铝翼散热管式中冷器的特点,导出了该种形式的中冷器冷却元件几何参数的计算公式;对管外流体侧的通道当量直径计算、对流换热和流通阻力准则方程的建立提出了一种新的方法,总结出一套完整的中冷器设计和校核的计算步骤,并对12V190B柴油机中冷器进行了设计计算和试验.由计算和试验结果对比可知,增压空气进、出口温差的计算误差在6%以内,进、出口压力损失的计算误差在10%以内,说明该计算方法可以满足铝翼散热管式中冷器的设计使用要求.     

Unsteady Mixed Convection in a Vented Enclosure Partially Filled with Two Non-Darcian Porous Layers

Mixed convection in a ventilated rectangular cavity with a horizontal strip occupied by two media of different permeability is studied by using the finite-volume method. The effect of the parameters that govern the problem, the Reynolds number (200–500), the Richardson number (0.1–10), the Darcy number (1.E–6–1.E–2), permeability ratio (0.01–100), aspect ratio of the cavity (1–1.5), and direction of flow with or against gravity, is investigated. From the numerical results, the influence of Darcy and Reynolds numbers on the fluid mechanics can be inferred. When the cold fluid flow is descending, the fluid–porous medium heat transfer increases because the hotter fluid is located in the upper zones of the cavity. As the aspect ratio (height/width) increases from 0.67 to 1.5, both the Nusselt number (7.5 < Nu < 27) and the friction coefficient increase. The friction coefficient on the walls is greater when Re = 500 and Ri = 10 in the two directions of flow. As the Darcy number increases, the velocity gradients increase near the walls, causing an increase of the friction coefficient (0 < Cf Re < 47).     

Numerical Investigation of Natural Convection in an Enclosure Filled with Porous Medium Under Magnetic Field

In this study, natural convection in an enclosure filled with a fluid-saturated porous medium in a strong magnetic field is investigated numerically. Two physical models are considered. One is heated from the bottom and cooled from the top (Model A), and the other is heated from the left side vertical wall and cooled from the opposite wall (Model B). An electric coil is set below this enclosure to generate a magnetic field. The Brinkman-Forchheimer extended Darcy model is used to solve the momentum equations, and the energy equations for the fluid and solid are solved with the local thermal nonequilibrium (LTNE) model. The linkage between velocity and pressure is handled with the SIMPLE algorithm. Computations are performed for a range of Darcy number from 10^?5 to 10^?1, Rayleigh number from 10³ to 10⁵, and magnetic force parameter γ from 0 to 100. The results show that the magnetic force has significant effect on the flow field and heat transfer in the fluid-saturated porous medium.     

An Inverse Problem Method for Overall Heat Transfer Coefficient Estimation in a Partially Filled Rotating Cylinder

The objective of this article is to study the estimation of an overall heat transfer coefficient in a partially filled rotating cylinder. Herein is an inverse analysis for estimating the overall heat transfer coefficient in an arbitrary cross-section of the aforementioned system from the temperatures measured on the shell. The material employs the finite-volume method to solve the direct problem. The hybrid effective algorithm applied here contains the local optimization algorithm to estimate the unknown parameter by minimizing the objective function. The data measured here are simulated by adding random errors to the exact solution. An investigation is made of the impact of the measurement errors on the accuracy of the inverse analysis. Two-optimization algorithms in determining the overall heat transfer coefficient are used. It is determined that the Conjugate Gradient Method is better than the Levenberg-Marquardt Method because the former produces greater accuracy for the same measurement errors. The resulting observation indicates that good agreement exists between the exact value and estimated result for both algorithms.     

Fast Identification Method of Total Normal Surface Absorptances Using Inverse Techniques

This paper proposes a simple and fast method to identify the normal absorptance of various surfaces submitted to a radiation source, using inverse techniques. The method consists of imposing during a lap of a few seconds a radiative flux on the front face of a sample whose absorptance is to be identified. The time-dependent temperature on the rear face is measured, and the procedure of inversion is implemented to give a time function of absorbed flux. Only one time–temperature function is measured using a current type K thermocouple. The normal absorptance of the front face is obtained by comparing the time heat flux function of the source and the identified absorbed heat flux function. This method can be quickly and efficiently adopted for many practical applications without the need to use optical devices, which give accurate measurement but at substantial cost. The inverse technique using a conjugate gradient method of minimization with adjoint problem is implemented to estimate the absorbed heat flux. In order to achieve good values of radiative absorptances, reliable knowledge of thermal diffusivities and adequately manufactured samples are required.     

Analysis of Conduction-Radiation Heat Transfer in a 2D Enclosure Using the Lattice Boltzmann Method

Application of the lattice Boltzmann method (LBM) recently extended by Pietro et al. [P. Asinari, S. C. Mishra, and R. Borchiellini, A Lattice Boltzmann Formulation to the Analysis of Radiative Heat Transfer Problems in a Participating Medium, Numer. Heat Transfer B, 57(2), 126–146, 2010] for calculation of volumetric radiative information is extended for the analysis of a combined mode transient conduction and radiation heat transfer in a 2D rectangular enclosure containing an absorbing, emitting and scattering medium. Unlike all previous studies, with volumetric radiative information computed using the proposed LBM, the energy equation is formulated and solved using the LBM. In the combined mode conduction–radiation problem, to assess the computational advantage of computing the radiative information too using the LBM, the same problem is also solved using the LBM–finite volume method (FVM) formulation. In this LBM–FVM formulation, the FVM is used to calculate the volumetric radiative information needed for the energy equation, and the energy equation is solved using the LBM. Comparisons are made for the effects of the extinction coefficient, the scattering albedo and the conduction–radiation parameter on the temperature distributions in the medium. Although the number of iterations for the converged solution in LBM–LBM is much more than that of the LBM–FVM, computationally, the LBM–LBM is faster than the LBM–FVM.     

Effect of Inclination on Heat Transfer and Fluid Flow in a Finned Enclosure Filled with a Dielectric Liquid

The problem of two-dimensional natural convection flow of a dielectric fluid in a square inclined enclosure with a fin placed on the hot wall is investigated numerically. The fin thickness and length are 1/10 and 1/2 of the enclosure side, respectively. The Rayleigh number is varied from 10³ to 5 × 10⁵ and the solid to fluid thermal conductivity ratio is fixed at 10³. The enclosure tilt or inclination angle is varied from 0° to 90°. The streamlines and isotherms within the enclosure are produced and the heat transfer is calculated. It is found that for 2.5 × 10⁴ ≤ Ra ≤ 2.5 × 10⁵, the average Nusselt number is maximum when γ = 0° and minimum when γ = 90°. For Ra = 5 × 10⁵, the values of enclosure tilt angle for which the average Nusselt number is maximum or minimum are completely different due to the transition to unsteady state. In this case, the maximum heat transfer is obtained for γ = 60°, while the minimum heat transfer is predicted for γ = 0°. Monomial correlations relating the average Nusselt number with the different values of the Rayleigh number from 10⁴ to 10⁵ are determined for two different angles, γ = 0° and γ = 90°.     

离心压气机叶轮的一种反问题设计方法及分析

在离心叶轮回转面上运用控制载荷方式的方法对叶片型线进行设计,并且与采用Pezier曲线构造法设计的子午面通道相结合,通过几何对应关系对叶片进行三维设计。在已设计的子午面轮廓和叶根为同一卸载式的加载规律前提下,设计了4种组合加载方式的叶轮。运用数值模拟的方法对叶轮模型的性能进行计算和分析,结果表明,设计方法可行,只要给出合适的加载规律和子午通道就可以设计出高性能的叶轮。这种设计方法可以通过调节叶片的不同组合的加载方式来达到灵活控制叶片扭曲状态和做功方式的目的。