Solidification Analysis of Density-Graded Closed-Cell Metallic Foam Under Constant Temperature Boundary Condition

2016 ◽  
Author(s):  
W. B. Wang ◽  
X. H. Yang ◽  
Q. C. Zhang ◽  
T. J. Lu
Keyword(s):  
Boundary Condition ◽  
Constant Temperature ◽  
Solidification Front ◽  
Metallic Foam ◽  
Metallic Foams ◽  
Closed Cell ◽  
Temperature Boundary ◽  
Solidification Speed ◽  
Temperature Boundary Condition ◽  
Real Density

In the industrial fabrication processes of density-graded closed-cell metallic foams, it is of great importance to control the solidification immediately after foams are formed so as to obtain the final products with well distributed density-graded pores and less defects. This paper presented an analytical work aiming to predict the solidification front of density-graded metallic foam under constant temperature boundary condition. Numerical simulations based on ideal density-graded circular pores demonstrated good agreement with the analytical solutions. The 2D porous morphology of a real density-graded aluminum foam was further reconstructed with microCT, on the basis of which the propagation of solidification front inside this real density-graded foam was numerically investigated. An equivalent shape factor for this real foam was calculated to provide an insight for the influence of different pore shapes on solidification. Compared with other pores, the solidification speed of elliptical pores (a common pore shape in real foams) is moderate, i.e., slower than circular pores but quicker than triangular pores for same porosity.

scholarly journals An integral relationship for a fractional one-phase Stefan problem

2018 ◽  
Vol 21 (4) ◽  
pp. 901-918 ◽  
Author(s):  
Sabrina Roscani ◽  
Domingo Tarzia
Keyword(s):  
Boundary Condition ◽  
Stefan Problem ◽  
One Dimensional ◽  
Similarity Type ◽  
Integral Relationship ◽  
Temperature Boundary ◽  
Liouville Derivative ◽  
The One ◽  
Stefan Condition ◽  
Temperature Boundary Condition

Abstract A one-dimensional fractional one-phase Stefan problem with a temperature boundary condition at the fixed face is considered by using the Riemann–Liouville derivative. This formulation is more convenient than the one given in Roscani and Santillan (Fract. Calc. Appl. Anal., 16, No 4 (2013), 802–815) and Tarzia and Ceretani (Fract. Calc. Appl. Anal., 20, No 2 (2017), 399–421), because it allows us to work with Green’s identities (which does not apply when Caputo derivatives are considered). As a main result, an integral relationship between the temperature and the free boundary is obtained which is equivalent to the fractional Stefan condition. Moreover, an exact solution of similarity type expressed in terms of Wright functions is also given.

Mesoscopic investigation of layered graded metallic foams under dynamic compaction

2018 ◽  
Vol 21 (14) ◽  
pp. 2081-2098 ◽  
Author(s):  
Jinhua Zhang ◽  
Yadong Zhang ◽  
Junyu Fan ◽  
Qin Fang ◽  
Yuan Long
Keyword(s):  
Impact Loading ◽  
Dynamic Properties ◽  
Three Dimensional ◽  
Metallic Foam ◽  
Layer By Layer ◽  
Metallic Foams ◽  
Mesoscopic Model ◽  
Layer Arrangement ◽  
Computed Tomography Images ◽  
Closed Cell

This article is aimed to reveal the dynamic response of layered graded metallic foam under impact loading using a three-dimensional mesoscopic model. First, a mesoscopic model for closed-cell metallic foam is proposed based on the X-ray computed tomography images. Second, a numerical analysis approach is presented and validated with test data. Third, it studies the dynamic behavior of the layered graded metallic foam under impact loading numerically. The metallic foam specimen is composed layer by layer. The porosity, which is a fraction of the voids volume over the total volume, is different with each other for the layers. Simulations are conducted to the specimen with increasing and decreasing porosity arrangement. Results show that the layer arrangement is critical to the dynamic properties. The mesoscopic deformation of cell walls and the energy absorption capability are also affected significantly. This article gives insights into the mechanical properties and mesoscopic deformation of layered graded metallic foam.

Thermoplastic Fusion Bonding of Polymer-Based Micro Devices Using a Pressure Cooker

2009 ◽  
Author(s):  
Taehyun Park ◽  
Thomas J. Zimmerman ◽  
Daniel Park ◽  
Brooks Lowrey ◽  
Michael C. Murphy
Keyword(s):  
Boundary Condition ◽  
Pressure Distribution ◽  
Water Vapor Pressure ◽  
Critical Parameters ◽  
Precise Control ◽  
Fusion Bonding ◽  
Temperature Boundary ◽  
Temperature And Pressure ◽  
Temperature Boundary Condition ◽  
Polymer Container

A novel method of thermoplastic fusion bonding (TPFB), or thermal bonding, for polymer fluidic devices was demonstrated. A pressure cooker was used in a simple sealing and packaging process with precise control of the critical parameters. Polymer devices were enclosed in a vacuum-sealed polymer container. This produced an even pressure distribution and a precise temperature boundary condition over the whole surface of the device. Deformation indicators were integrated on the devices to provide a rapid means of checking deformation and pressure distribution with the naked eye. Temperature, pressure, and time are the fundamental parameters of TPFB. The temperature and pressure are dominated by the material and contact area of the device. The temperature and pressure can be manipulated by controlling the water vapor pressure. The boiling solution guarantees an accurate, constant temperature boundary condition. Time can be eliminated as a variable by choosing a sufficient time to achieve good bonding, since there was no apparent damage to the microstructures after one hour. This new method of TPFB was demonstrated for sealing and packaging a PMMA (polymethylmethacrylate) microfluidic device. Good results were obtained using the vacuum sealed polymer container in the pressure cooker. This method is also suitable for scaling up for mass production.

scholarly journals ABOUT THE EXACT SOLUTION IN TWO PHASE-STEFAN PROBLEM

2007 ◽  
Vol 6 (2) ◽  
pp. 70 ◽  
Author(s):  
A. C. Boucíguez ◽  
R. F. Lozano ◽  
M. A. Lara
Keyword(s):  
Boundary Condition ◽  
Exact Solution ◽  
Stefan Problem ◽  
Two Phase ◽  
Flux Boundary Condition ◽  
Temperature Boundary ◽  
Infinite Slab ◽  
Heat Flux Boundary Condition ◽  
The Relationship ◽  
Temperature Boundary Condition

Two cases of the two - phase Stefan problem in a semi - infinite slab are presented here: one has heat flux boundary condition proportional to t−½ and the other has constant temperature boundary condition. In these two cases the exact solution exists, the relationship between the two boundary conditions is presented here, and the equivalence between the two problems is shown.

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