Papers by Keyword: Integral Method

Abstract: This paper deals with the study of the heat and mass transfer characteristics of natural convection from a horizontalsurface embedded in a radiating fluid saturated porous medium. Similarity solutions for buoyancy induced heat and masstransfer from a horizontal surface, where the wall temperature and concentration are a power function of distance fromthe origin, are obtained by using an integral approach of Von Karman type. The effects of the governing parameters suchas buoyancy ratio, Lewis number, radiation parameter and the power-law exponent on local Nusselt and local Sherwoodnumbers have been investigated both numerically and graphically.

Abstract: In the present study, an integral method of Von Karman type has been used to analyse the phenomenon of natural convection heat and mass transfer near a vertical surface embedded in a fluidsaturated porous medium considering the viscous dissipation and radiation effects. The buoyancy effect is due to the variation of temperature and concentration across the boundary layer. The effects of the governing parameters e.g. buoyancy ratio (N), Lewis number (Le), Eckert number (Ec) and radiation parameter (R) on local Nusselt number, local Sherwood number, velocity profile, temperature profile and concentration profile have been investigated. The results obtained in the present analysis have been compared with the published results available in the literature and they have been found in precise agreement.

Abstract: There is a strong need for reliable residual stress measurements. On the one hand, residual stresses can be beneficial, when they are adapted to external loads. On the other hand, they can be detrimental, when they are unknown. Thus, their occurrence can lead to an uneconomical oversizing of components or in their failure, as well. Apart from diffraction methods, mechanical methods are well recognized in order to determine unknown residual stress states. Depending on the applied method, specific boundary conditions have to be taken into account. In the case of mechanical methods like the hole-drilling and the ring-core method, the characteristics of the geometry of the component should be in accordance with an ideal and thick plate. The reason behind is the need for a calibration data set to transform strains into stresses. The calibration is usually carried out numerically. For the sake of simplicity, the geometry of the component is an ideal thick plate and the hole is introduced in its center. However, in most cases, this is not identical with the geometry of the component under investigation. Hence, an application tool was designed that enables the parametric design of a Finite Element Model, the determination of calibration coefficients, the evaluation of the experiment and the visualization of the results for geometries of practical importance. So far, the application tool can represent plates variable in their geometries and in positioning of the point of measurement. The option for other geometries are also possible e.g. a turbine blade.

Abstract: The ring-core method allows the determination of residual stresses at high depth from the surface. The numerical calculation integral method, commonly used for the hole-drilling, can also be applied to the ring-core. The integral method coefficients were obtained for several depth steps after axial-symmetric FE simulations with harmonic load. These coefficients were then validated with a 3D finite element model. Finally, an application was reported, showing the performance of the Tikhonov regularization on experimental data.

Abstract: To improve the surface behavior of metal structures, like wear-and heat resistance or hardness, often thermally sprayed ceramic coatings are applied. A modern technology to realize dense layers is the High Velocity Oxygen Fuel (HVOF) technique. The deposition process and necessary pretreatments can cause high residual stresses within the coating and the substrate. While tensile stresses in the brittle coating may cause cracks, compressive stress states can even improve the materials behavior. To guarantee high product quality, it is necessary to know exactly the occurring residual stresses in the metal-ceramic hybrid system. A very common measurement technique is the incremental hole drilling (IHD) method. To determine the residual stresses out of IHD measurements the differential method (DM) or integral method (IM) can be used. To investigate the influence of interfacial layers, nonlinear stresses, cracking, anisotropy, variation of coating thickness and calculation formalisms several FEM models have been build, while case sensitive calibration was used for the coated systems.

Abstract: The incremental hole-drilling method is the method of choice to determine residual stress depth distributions with limited costs and minor destruction of the investigated component. With a spatial resolution of commonly two millimeters in diameter and one millimeter in depth especially the effects of frequently used surface treatments like e.g. shot peening or deep rolling can be reliably detected if the in depth residual stress gradients are relatively smooth. Nevertheless up to now the quantitative accuracy of the method is poor for residual stress analyses close to the materials surface up to depths of approximately 0.2 mm and in the case of steep in-depth residual stress gradients or oscillating residual stress depth distributions. In this paper, residual stress depth distributions of a broad range introduced by mechanical surface-treatments in flat specimens were analyzed with the hole-drilling method and compared with the results measured by X-ray diffraction as the reference. It comes out, that arbitrary residual stress depth distributions can be successfully determined with a modified differential evaluation formalism. For this purpose, often neglected well known weak points of the hole-drilling method were considered and improved, e.g. hole geometry, numerical calibration and data conditioning. Especially, the proposed strategy of data conditioning results in an almost user-independent evaluation formalism.

Abstract: Integral analysis of heat transfer of a laminar falling liquid film along a vertical heated plate with specified heat flux boundary condition was investigated. The temperature distribution of liquid film was obtained by utilizing an integral analysis method, which was compared with numerical solution and other researcher’s results. In this analysis a new concept of thermal changing point was put forward. It’s found that the Nusselt number has a characteristic relationship with thermal changing point, which is obtained by calculation. When the film flow distance is less than thermal changing point, the Nusselt number decreases rapidly. When the film flow distance is greater than or equal to thermal changing point, the Nusselt number reaches to a fixed value. A larger Peclet number or lower initial temperature generally leads to a larger Nusselt number in entrance region, whereas the wall heat flux is found to have no influence on the Nusselt number.

Abstract: The carbon diffusion in steel, where the carbon diffusivity varies with the carbon content, was solved with the integral methods under the third boundary condition. The variation of carbon diffusivity in steel with the carbon content was described with two different functions, linear dependence and exponential dependence. The integral approximation for both cases was improved with the numerical computation to more accurately predict the carbon profiles. The integral solution is more accurate than the formulation based on the assumption of a constant diffusivity or those based on the assumption of a constant diffusivity and/or constant carbon content at part surface. It is also more easily used in practice than the numerical method to describe the carburising process and predict the carbon content at steel surface and carbon profiles in treated layer.