Radiative equilibrium in a rectangular enclosure bounded by gray walls

Two-dimensional temperature and heat flux distributions are calculated for an absorbing-emitting gray medium at radiative equilibrium in a rectangular enclosure. The bounding walls are gray and diffuse with arbitrary surface temperature distributions, and heat generation may take place inside the medium. As a first approximation, the problem is solved for optically thick systems (differential approximation). These results are subsequently improved by the introduction of a number of geometrical parameters to yield good accuracy for all optical thicknesses. As examples, two cases are discussed in detail: (1) uniform heat generation in a black enclosure and (2) an enclosure with one gray surface at constant temperature. Comparison with some numerical solutions generated by Hottel's zonal method shows excellent agreement.     

多维梯度折射率介质内辐射传递的扩散近似

推导多维梯度折射率介质内稳态辐射传递的扩散近似方程.使用有限元法对扩散近似进行离散和求解,利用两个二维半透明介质的稳态辐射传递问题验证该扩散近似的精度及适用性.算例考虑介质为均匀折射率及梯度折射率两种情况.利用扩散近似分别求解辐射平衡时的边界热流、介质内温度场分布,并与辐射传递方程的求解结果进行对比分析.结果表明:介质折射率变化、散射特性、光学厚度及散射反照率均直接影响扩散近似的精度;在光学厚及强散射条件下,该扩散近似可以作为一种快速算法应用于梯度折射率介质稳态辐射传递的求解.     

Upshot of Chemical Species and Nonlinear Thermal Radiation on Oldroyd-B Nanofluid Flow Past a Bi-directional Stretched Surface with Heat Generation/Absorption in a Porous Media

A three-dimensional mathematical model is developed to examine the flow of nonlinear thermal radiation Oldroyd-B nanofluid past a bidirectional linearly stretched surface in a porous medium. The flow is induced by temperature dependent thermal conductivity, chemical reaction and convective heat and mass conditions. Novel characteristics of Brownian motion and thermophoresis are accompanied by magnetohydrodynamic and heat generation/absorption.Self-similar transformations are employed to convert the system of nonlinear partial differential equations to a system of ordinary differential equations with high nonlinearity and are solved by strong analytic technique named as Homotopy Analysis method(HAM). Effects of varied arising parameters on involved distributions are reflected through graphical illustrations. From this study, it is perceived that strong magnetic field hinders the fluid's motion and leads to rise in temperature that eventually lowers heat transfer rate from the surface. Further, decrease in heat transfer rate is also observed for enhanced values of thermal radiation parameter. To validate our results, a comparison with already published paper in limiting case is also given and results are found in excellent oncurrence; hence reliable results are being presented.     

Upshot of Chemical Species and Nonlinear Thermal Radiation on Oldroyd-B Nanofluid Flow Past a Bi-directional Stretched Surface with Heat Generation/Absorption ina Porous Media

A three-dimensional mathematical model is developed to examine the flow of nonlinear thermal radiation Oldroyd-B nanofluid past a bidirectional linearly stretched surface in a porous medium. The flow is induced by temperature dependent thermal conductivity, chemical reaction and convective heat and mass conditions. Novel characteristics of Brownian motion and thermophoresis are accompanied by magnetohydrodynamic and heat generation/absorption. Self-similar transformations are employed to convert the system of nonlinear partial differential equations to a system of ordinary differential equations with high nonlinearity and are solved by strong analytic technique named as Homotopy Analysis method (HAM). Effects of varied arising parameters on involved distributions are reflected through graphical illustrations. From this study, it is perceived that strong magnetic field hinders the fluid's motion and leads to rise in temperature that eventually lowers heat transfer rate from the surface. Further, decrease in heat transfer rate is also observed for enhanced values of thermal radiation parameter. To validate our results, a comparison with already published paper in limiting case is also given and results are found in excellent oncurrence; hence reliable results are being presented.     

Non-Fourier heat conduction with radiation in an absorbing, emitting, and isotropically scattering medium

This article numerically analyses the combined conductive and radiative heat transfer in an absorbing, emitting, and isotropically scattering medium. The non-Fourier heat conduction equation, which includes the time lag between heat flux and the temperature gradient, is used to model the conductive heat transfer in the medium. It predicts that a temperature disturbance will propagate as a wave at finite speed. The radiative heat transfer is solved using the P₃ approximation method. In addition, the MacCormack's explicit predictor-corrector scheme is used to solve the non-Fourier problem. The effects of radiation including single scattering albedo, conduction-to-radiation parameter, and optical thickness of the medium on the transient and steady state temperature distributions are investigated in detail. Analysis results indicate that the internal radiation in the medium significantly influences the wave nature. The thermal wave nature in the combined non-Fourier heat conduction with radiation is more obvious for large values of conduction-to-radiation parameter, small values of optical thickness and higher scattering medium. The results from non-Fourier-effect equation are also compared to those obtained from the Fourier equation. Non-Fourier effect becomes insignificant as either time increases or the effect of radiation increases.     

Tomographic reconstruction of damage images in hollow cylinders using Lamb waves

Lamb wave tomography (LWT) is a potential and efficient technique for non-destructive tomographic reconstruction of damage images in structural components or materials. A two-stage inverse algorithm proposed by the authors for quickly reconstructing the damage images was applied to hollow cylinders. An aluminum hollow cylinder with an internal surface pit and a Carbon Fiber Reinforced Plastic (CFRP) laminated hollow cylinder with an artificial internal surface damage were used to validate the proposed method. The results show that the present method is capable of successfully reconstructing the images of the above damages in a larger inspection area with much less experimental data compared to some conventional ultrasonic tomography techniques.     

Calculation of the thermal effect of an electron probe on a sample of GaN

Stationary temperature fields due to the interaction of an electron probe with a GaN sample are examined. In order to calculate the density of generated heat, the process of electron energy loss is modeled by the Monte Carlo method. The heat generation region is assumed to have the shape of a half-ellipsoid. In the case of uniform heat generation in the ellipsoid, an analytical solution to the heat conduction problem is found and expressed in terms of elementary functions. It is shown that the maximum heating temperature and the temperature field distribution depend only slightly on the shape of the heat generation region. An approximation of the density of heat sources by a uniform distribution over a hemisphere of radius equal to the ultimate range of electrons leads to a considerably underestimated maximum heating temperature. An expression is derived for determining the characteristic size of the heat generation region in GaN; this expression allows one to calculate the maximum heat temperature with an accuracy of 3% in a wide range of electron beam energies.     

A parametric study of radiative transfer with anisotropic scattering in a one-dimensional system

Radiative heat transfer in an absorbing, emitting, anistropically-scattering, one-dimensional medium is analyzed. Unlike many of the existing works, the present analysis does not require a known temperature distribution within the medium. Assuming a model of linear anistropic scattering, the transfer equation and the energy equation are solved simultaneously by utilizing a recently developed successive approximation technique. Closed-form approximate solutions and accurate higher-order results are both presented. Calculations show that the relative importance of the anistropic scattering effect generally decreases with decreasing wall emissivity and decreasing optical thickness. For radiative equilibrium without internal heat generation, it is demonstrated that the anistropic-scattering heat-transfer results can be approximated quite adequately by the isotropic-scattering result with the introduction of the concept of an effective optical thickness. For media with internal heat generation, an interesting effect of the scattering albedo is observed. It is established that, in the limit of a large scattering albedo, the temperature of the medium approaches a constant value that is independent of anistropic-scattering effects and wall emissivity. The exact limiting expressions for the temperature and apparent emissivity of an isothermal slab are found.     

Heat Transfer Evaluation Method in Complex Rotating Environments Employing IR Thermography and CFD

This article presents a measuring method for determination of convective heat transfer in rotating environments. The method is used to obtain temperature and Nusselt number distributions on optically accessible objects inside real operating environments, without the need for implementation of complex surface heat flux measurements. Temperature maps of the observed surfaces are acquired non-intrusively by infrared (IR) thermography, whereas heat flux data is computed numerically by computational fluid dynamics (CFD) tools. The method was employed on a rotating hollow blade, heated internally by secondary air flow. Experimental and numerical results for the observed blade side are compared in terms of surface temperature 2D distributions. Temperature distributions are further statistically evaluated and show good agreement, which is the basic precondition for combining experimental and numerical data by the method. Results are presented in terms of combined experimental-numerical Nusselt number shown as two-dimensional distribution on the blade pressure side.     

Heat generation in a torsional spring subjected to sinusoidal oscillations

The effect of thermomechanical coupling in a viscoelastic hollow cylinder subjected to sinusoidal shear stresses or shear displacements has been studied. The problem is a simple model of torsional springs made of rubberlike materials. The material is assumed to be thermorheologically simple. A non-linear boundary value problem is formulated for the almost steady mechanical oscillation coupled with a slowly varying temperature distribution. The wave motion is analyzed by the well-known WKB approximation. Corresponding temperature distributions are calculated numerically by iterative procedures. Although the applied stress and applied displacement are small, significant temperature rises are found. Different stress and temperature distributions are compared for various frequencies.     

Unsteady MHD Non-Darcian Flow over a Vertical Stretching Plate Embedded in a Porous Medium with Thermal Non-Equilibrium Model

An analysis is performed to study the influence of local thermal non-equilibrium (LTNE) on unsteady MHD laminar boundary layer flow of viscous, incompressible fluid over a vertical stretching plate embedded in a sparsely packed porous medium in the presence of heat generation/absorption. The flow in the porous medium is governed by Brinkman-Forchheimer extended Darcy model. A uniform heat source or sink is presented in the solid phase. By applying similarity analysis, the governing partial differential equations are transformed into a set of time dependent non-linear coupled ordinary differential equations and they are solved numerically by Runge-Kutta Fehlberg method along with shooting technique. The obtained results are displayed graphically to illustrate the influence of different physical parameters on the velocity, temperature profile and heat transfer rate for both fluid and solid phases. Moreover, the numerical results obtained in this study are compared with the existing literature in the case of LTE and found that they are in good agreement.     

A high average power rotating hollow cylinder Nd : glass laser

The rotating hollow cylinder glass laser is one of the approaches for the generation of high average output powers scaling to kilowatt levels from solid-state laser materials. An analytical solution of the heat conduction equation is presented for a thin wall, infinitely long glass medium, with boundary conditions given by Newton's law of cooling. The theoretical result is applied to predict thermal effects of this geometry which ultimately limit the laser performance, and the design of such a laser. A flashlamp pumped rotating Nd-doped phosphate glass hollow cylinder laser has been demonstrated. An average power output of 300 W has been achieved at 3.8% slope efficiency and 2.6% overall efficiency. Our investigation shows that the development of a kilowatt average power rotating cylinder laser is feasible.     

An integral equation for radiation transport in an infinite cylinder with Fresnel reflection

We formulate an integral equation for radiation transport in an infinitely long cylinder. Scattering is included and sources arise from incidence on the surface and from an internal volume source. Internal reflection at the surface follows the Fresnel law. For the special case of no scattering and no axial variation of the source, we obtain an exact solution which we have compared numerically with some results of Tian and Chiu [Radiative absorption in an infinitely long hollow cylinder with Fresnel surfaces. JQSRT 2006;98:249]. We have also obtained closed form analytical solutions for no scattering with a line source along the cylinder axis and also that for the case of a spatially constant volume source. The general case when there is variation in the axial direction is also presented and the special case of a radially uniform plane source at the origin is explored in some detail. The axial solution is compared with an approximate areal average method introduced by Larsen [A one-dimensional model for three dimensional transport in a pipe. Transp Theory Stat Phys 1984;13:599; Larsen EW, Malvagi F, Pomraning GC. One dimensional models for neutral particle transport in ducts. Nucl Sci Eng 1986;93:13] in another context.     

Radiative equilibrium of a gray medium in a rectangular enclosure

Radiative equilibrium temperature distributions are calculated for an absorbing-emitting gray medium enclosed by rectangular walls of different temperatures. A “modified differential approximation” is used to obtain an approximate solution, which compares favorably with direct numerical computations carried out using a zonal method.     

Simulation study of a hot metal cylinder cooling by gas-liquid flow

A mathematical model was developed for conjugate heat transfer in a heterogeneous system “solid body ? gas-liquid medium” with account for vapor generation at the surface of hot metal cylinder with cooling by a longitudinal water flow. Results are presented for numerical parametric calculations for influence of thermophysical and hydrodynamic characteristics on the pattern of vapor generation at the cooled cylinder surface.     

Radiative absorption in an infinitely long hollow cylinder with Fresnel surfaces

Radiation absorption in an infinitely long hollow cylinder with Fresnel surfaces is studied using the ray tracing method. It is found that the inner boundary can be modeled as a total reflective surface for the infinitely long hollow cylinder. Radiative absorption of hollow cylinders with Fresnel surfaces is compared to diffusive surfaces predicted by the finite volume method. Effects of refractive index, optical thickness and hole size on radiative absorption are studied. Abrupt changes in radiative absorption near τ_r/τ_Ro=1/n are observed for hollow cylinders with Fresnel surfaces. It is because the Fresnel relation predicts a critical angle at . This trend is not observed in diffusive surfaces. Refractive index and optical thickness are two competing factors that govern the radiative absorption. Higher refractive index drives higher absorption close to the inner surface, while higher optical thickness yields higher absorption near the outer surface. The results of this study can also serve as benchmark solutions for modeling radiative heat transfer in hollow cylinders with Fresnel surfaces. It is also found that the directional or hemispherical emittance can be calculated without solving the radiative transfer equation in the media when the temperature variation in the media is small.     

Two analytic methods applied to radiative transfer in the linear-anisotropic scattering medium with graded index and diffuse gray boundaries

The curved ray-tracing method is extended to radiative transfer in the graded index medium with diffuse gray boundary conditions instead of black boundary conditions and the pseudo-source adding method is extended to the case of the linear-anisotropic scattering medium with graded index from non-scattering medium. Furthermore, the equivalence of the two methods is verified by formulation derivation. As exact analytical solutions, both the methods have high accuracy and fast computational speed. The predicted temperature distributions and dimensionless radiative heat flux at radiative equilibrium are determined by the proposed methods, and the numerical results are compared with the data in references. The results show that the present methods have a good accuracy. Influences of various combinations of refractive index and boundary emissivities on the temperature distributions and dimensionless radiative heat flux are also investigated.     

Entropy production in the flow over a swirling stretchable cylinder

In the present work, the entropy generation due to the heat transfer and fluid friction irreversibility is investigated numerically for a three-dimensional flow induced by rotating and stretching motion of a cylinder. The isothermal boundary conditions are taken into account for the heat transfer analysis. The similarity transformations are utilized to convert the governing partial differential equations to ordinary differential equations. Resulting nonlinear differential equations are solved using a numerical scheme. Expressions for the entropy generation number, the Nusselt number and the Bejan number are obtained and discussed through graphs for various physical parameters. An analysis has been made to compare the heat transfer irreversibility with fluid friction irreversibility using the expression of the Bejan number. It is found that the surface is a durable source of irreversibility and the curvature of cylinder is to enhance the fluid friction irreversibility.     

Transient conductive and radiative transfer in a planar layer with Arrhenius heat generation

Transient conductive and radiative energy transfer in a gray absorbing-emitting planar medium bounded by black walls is studied. The temperature distribution is uniform when the medium starts releasing energy according to the Arrhenius equation. The Crank-Nicolson method is used in the radiative-dominant case with good accuracy. Time-dependent temperature and heat flux distributions are calculated until steady-state is reached. Confirmation of the solution technique is made by comparison with previous investigations. The dimensionless activation energy required for ignition varies from 4.1 for pure conduction to 7.5 for pure radiation.     

离子推力器空心阴极热特性模拟分析

对离子推力器空心阴极进行了热分析。利用ANSYS有限元软件对阴极罩开启/闭合状态下的空心阴极热启动过程和达到稳态工作时温度场分布进行了模拟,结果表明稳态工作时空心阴极内部能量主要损耗在热阻丝和阴极顶部分,并且阴极罩及热屏是降低空心阴极温度损耗提高其热效率的关键部件,采用阴极罩及热屏后使得空心阴极的总体温度值提升了2.3%~13.2%,其中发射体温度提升2.3%~4.2%,热实验得出的实验数据与模拟结果基本一致,研究结果对空心阴极的优化设计提供参考。