Critical Biot Number of a Periodic Array of Rectangular Fins

We consider the heat transfer problem associated with a periodic array of rectangular fins subjected to convection heat transfer with a uniform heat transfer coefficient. Our analysis differs from the classical approach as (i) we consider two-dimensional (2D) heat conduction and (ii) the wall, to which the fins are attached, is included in the analysis

Experimental study of zeolitic diffusion by use of a concentration-dependent surface diffusion model

https://www.sciencedirect.com/science/article/pii/S2405844019358037Surface diffusivity in adsorption and ion exchange processes is probably the most important property studied expensively in the literature but some aspects, especially its dependence on solid phase concentration, is still an open subject to discussion. In this study a new concentration-dependent surface diffusion model, equipped with a flexible double selectivity equilibrium relationship is applied on the removal of Pb2+, Cr3+, Fe3+ and Cu2+ from aqueous solutions using a natural zeolite. The model incorporates the Chen-Yang surface diffusivity correlation able to deal with positive and negative dependence with surface coverage. The double selectivity equilibrium relationship successfully represents the experimental equilibrium data, which follow Langmurian isotherm type for Pb2+, sigmoidal for Cr3+ and Fe3+ and linear for Cu2+. The concentration-dependent surface diffusion model was compared with the constant diffusivity surface diffusion model and found to be moderately more accurate but considerably more useful as it provides more insights into the diffusion mechanism. The application of the model resulted in an average deviation of 8.56 ± 6.74% from the experimental data and an average solid phase diffusion coefficients between 10−9 and 10−10 cm2/s. The results showed that the diffusion of metal ions in the zeolite structure is unhindered following the surface diffusion mass transfer mechanism

Optimum interfaces that maximize the heat transfer rate between two conforming conductive media

Abstract We consider conjugate heat transfer between two conductive and conforming media, with isothermal boundary conditions on the exposed surfaces, and continuity of the temperature and the heat flux along their interface. We address the inverse problem of finding the shape of the interface such that the heat transfer rate is maximized. We formulate three isoperimetric, shape optimization problems associated with three different applications: i) the optimal shape of corrugations (surface “roughness”), ii) the optimal shape of high conductivity inserts (inverted fins) and iii) the optimal shape of high conductivity fins. As expected, the optimal geometries have the shape of an extension of the high conductivity material into the low conductivity material. For the case of corrugations and inserts, the optimum shapes are triangular for small perimeters; for large perimeters and thick slabs they are elliptical and tend to cover the whole width/period of the domain. Optimum fins are characterized by long, shallow valleys and deep, narrow protrusions of the high conductivity material. For the parameters considered in this study, the width of the protrusion is approximately one quarter of the period

Transient Powder Melting in SLM Using an Analytical Model with Phase Change and Spherical Symmetry in a Semi-Infinite Medium

In this work, we introduce an analytical expression for approximating the transient melting radius during powder melting in Selective Laser Melting (SLM) assumed with a stationary laser heat source. The purpose of this work is to evaluate the suggested analytical approach in determining the melt pool geometry during laser processing, by considering heat transfer and phase change effects. This will allow for the rendering of the first findings on the way to a quasi-real time calculation of the melt pool during laser melting, which will contribute significantly to the process design and control, especially when new powders are applied. Initially, we consider the heat transfer process associated with a point heat source, releasing a continuous and constant power (in a semi-infinite powder bed. On the point of the heat source the temperature is infinite, and the material starts to melt spherically outwards, creating an interface that separates the solid from the molten material; we assume different properties between the two phases. Unlike the cases of the cartesian and cylindrical coordinates, (in a cartesian coordinate the heat source is over a plane, i.e., W/m2, and in cylindrical along a line, i.e., W/m), where the melting process is proportional to the square root of time, in spherical coordinates the melting stops at a finite radius, i.e., a maximum radius, which depends only on the heat source, the conductivity of the solid and the difference between the far-field temperature and the melting temperature of the material. Here we should also point out that to achieve continuous melting in spherical coordinates the power of the source must increase with the square root of the time. The obtained analytical expression for the maximum melting radius and the approximate expression for its dependence on the time compare well with the numerical results obtained by a finite element analysis

Numerical calculation of mass transfer from elliptical pools in uniform flow using the boundary element method

The three-dimensional problem of advection-dispersion associated with an elliptical non-aqueous-phase liquid (NAPL) pool is addressed using the boundary element method. The boundary condition on the plane of the pool is such that over the pool the concentration is equal to the saturation concentration while a no flux boundary condition is imposed in the region not covered by the pool. The numerical results are verified by asymptotic analytical solutions obtained in the limits of diffusion-dominated and convection-dominated mass transport. For cases of practical interest an empirical expression is obtained for the Sherwood number that matches the numerical results over a wide range of the relevant parameters. Comparison with experimental results suggests that the corresponding numerical results predict a higher overall mass transfer coefficient