scholarly journals A Mathematical Model for Single Crystal Cylindrical Tube Growth by the Edge-Defined Film-Fed Growth (EFG) Technique

10.5772/47988 ◽  
2012 ◽  
Author(s):  
Loredana Tanasie ◽  
Stefan Balint
Keyword(s):  
Mathematical Model ◽  
Single Crystal ◽  
Cylindrical Tube ◽  
Tube Growth

Physical–mathematical model of Lorentz factor for the integrated intensity of single crystal diffraction

2014 ◽  
Vol 94 ◽  
pp. 234-239
Author(s):  
Florina Violeta Anghelina ◽  
Ileana Nicoleta Popescu ◽  
Vasile Bratu ◽  
Constantin C. Anghelina ◽  
Carmen Otilia Rusanescu
Keyword(s):  
Mathematical Model ◽  
Single Crystal ◽  
Lorentz Factor ◽  
Single Crystal Diffraction ◽  
Integrated Intensity

Mathematical model for corundum single crystal growth by Verneuil method

1983 ◽  
Vol 61 (3) ◽  
pp. 629-636 ◽  
Author(s):  
Radosa̵w Grzymkowski ◽  
Bohdan Mochnacki ◽  
Józef Suchy
Keyword(s):  
Mathematical Model ◽  
Crystal Growth ◽  
Single Crystal ◽  
Single Crystal Growth

scholarly journals A Mathematical Model for the Flow of a Casson Fluid due to Metachronal Beating of Cilia in a Tube

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
A. M. Siddiqui ◽  
A. A. Farooq ◽  
M. A. Rana
Keyword(s):  
Mathematical Model ◽  
Flow Rate ◽  
Volume Flow Rate ◽  
Pressure Rise ◽  
Cylindrical Tube ◽  
Casson Fluid ◽  
Volume Flow ◽  
System Of Nonlinear Equations ◽  
Dimensional System ◽  
Axial Pressure Gradient

A mathematical model is developed to study the transport mechanism of a Casson fluid flow inspired by the metachronal coordination between the beating cilia in a cylindrical tube. A two-dimensional system of nonlinear equations governing the flow problem is formulated by using axisymmetric cylindrical coordinates and then simplified by employing the long wavelength and low Reynolds number assumptions. Exact solutions are derived for the velocity components, the axial pressure gradient, and the stream function. However, the expressions for the pressure rise and the volume flow rate are evaluated numerically. The features of the flow characteristics such as pumping and trapping are illustrated and discussed with the help of graphs. It is observed that the volume flow rate is influenced significantly by the width of plug flow regionHpas well as the cilia length parameterε. The analysis is also applied and compared with the estimated value of the volume flow rate of epididymal fluid in the ductus efferentes of the human male reproductive tract.

Melt menisci during single-crystal tube growth by the Stepanov method

2009 ◽  
Vol 54 (7) ◽  
pp. 1273-1279 ◽  
Author(s):  
A. V. Zhdanov ◽  
M. V. Yudin
Keyword(s):  
Single Crystal ◽  
Tube Growth ◽  
Stepanov Method

scholarly journals Enhanced Thermoelectric Cooling through Introduction of Material Anisotropy in Transverse Thermoelectric Composites

Materials ◽  
2019 ◽  
Vol 12 (13) ◽  
pp. 2049
Author(s):  
Bosen Qian ◽  
Fei Ren ◽  
Yao Zhao ◽  
Fan Wu ◽  
Tiantian Wang
Keyword(s):  
Mathematical Model ◽  
Single Crystal ◽  
Material Properties ◽  
Cooling Capacity ◽  
Thermoelectric Performance ◽  
Cooling Power ◽  
Material Anisotropy ◽  
Element Analysis ◽  
The Mathematical Model ◽  
Component Phase

Transverse thermoelectric materials can achieve appreciable cooling power with minimal space requirement. Among all types of material candidates for transverse thermoelectric applications, composite materials have the best cooling performance. In this study, anisotropic material properties were applied to the component phase of transverse thermoelectric composites. A mathematical model was established for predicting the performance of fibrous transverse thermoelectric composites with anisotropic components. The mathematical model was then validated by finite element analysis. The thermoelectric performance of three types of composites are presented, each with the same set of component materials. For each type of component, both anisotropic single-crystal and isotropic polycrystal material properties were applied. The results showed that the cooling capacity of the system was improved by introducing material anisotropy in the component phase of composite. The results also indicated that the orientation of the anisotropic component’s property axis, the anisotropic characteristic of a material, will significantly influence the thermoelectric performance of the composite. For a composite material consisting of Copper fiber and Bi2Te3 matrix, the maximum cooling capacity can vary as much as 50% at 300 K depending on the property axis alignment of Bi2Te3 in the composite. The composite with Copper and anisotropic SnSe single crystal had a 51% improvement in the maximum cooling capacity compared to the composite made of Copper and isotropic SnSe polycrystals.

UNSTEADY RESPONSE OF BLOOD FLOW THROUGH A COUPLE OF IRREGULAR ARTERIAL CONSTRICTIONS TO BODY ACCELERATION

2008 ◽  
Vol 08 (03) ◽  
pp. 395-420 ◽  
Author(s):  
NORZIEHA MUSTAPHA ◽  
SANTABRATA CHAKRAVARTY ◽  
PRASHANTA K. MANDAL ◽  
NORSARAHAIDA AMIN
Keyword(s):  
Mathematical Model ◽  
Blood Flow ◽  
Finite Difference ◽  
Stokes Equations ◽  
Computational Study ◽  
Cylindrical Tube ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Body Acceleration ◽  
Flow Through

A two-dimensional (2D) nonlinear mathematical model to study the response of the pulsatile flow of blood through a couple of irregular stenoses influenced by externally imposed periodic body acceleration is developed. The model is 2D and axisymmetric with an outline of the stenosis obtained from the three-dimensional (3D) casting of a mildly stenosed artery. The combined influence of an asymmetric shape and surface irregularities of the constrictions is explored in a computational study of blood flow through arterial stenoses with 48% areal occlusion. The arterial wall is treated as an elastic (moving wall) cylindrical tube having a couple of stenoses in its lumen, while the streaming blood is considered to be Newtonian. Solutions of the time-dependent nonlinear Navier–Stokes equations in the cylindrical coordinate system are obtained using a finite difference method based on the nonuniform and nonstaggered grids. The finite difference approximation helps to estimate the effects of body acceleration on the doubly constricted flow phenomena through several graphical representations quantitatively in order to validate the applicability of the present, improved mathematical model.

Simulation of Single Crystal Nickel-Based Superalloys Creep on Finite Element Method

2012 ◽  
Vol 433-440 ◽  
pp. 2029-2033
Author(s):  
Shu Zhang ◽  
Lei Meng
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Numerical Calculation ◽  
Stress Distribution ◽  
Stress Field ◽  
Single Crystal ◽  
Microstructure Evolution ◽  
The Finite Element Method ◽  
Element Method

Based on finite element Method a dynamic mathematical model is established, and the simulation of stress distribution around the defects of single crystal nickel-based superalloysis also established with ANSYS. After the change of stress field with time is analyzed, the result is compared with that achieved through numerical calculation and experimental analysis. The comparison shows that the finite element method is effective to study the stress distribution and can provide basis for creep features and microstructure evolution.

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