MHD nanofluid free convection inside the wavy triangular cavity considering periodic temperature boundary condition and velocity slip mechanisms

2021 ◽  
Vol 170 ◽  
pp. 107179
Author(s):  
Masih Shekaramiz ◽  
Shadi Fathi ◽  
Hamid Ataei Ataabadi ◽  
Hamed Kazemi-Varnamkhasti ◽  
Davood Toghraie
Keyword(s):  
Boundary Condition ◽  
Free Convection ◽  
Velocity Slip ◽  
Temperature Boundary ◽  
Periodic Temperature ◽  
Temperature Boundary Condition

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.

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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