Perturbation Solutions for Spherical Solidification of Saturated Liquids

1973 ◽  
Vol 95 (1) ◽  
pp. 42-46 ◽  
Author(s):  
R. I. Pedroso ◽  
G. A. Domoto
Keyword(s):  
Boundary Condition ◽  
Series Solution ◽  
Freezing Temperature ◽  
Perturbation Solution ◽  
Partial Sums ◽  
Regular Perturbation ◽  
Constant Wall Temperature ◽  
Temperature Boundary ◽  
Temperature Boundary Condition ◽  
Perturbation Solutions

A perturbation solution is obtained for outward and partial inward spherical solidification of a liquid initially at the freezing temperature. The constant-wall-temperature boundary condition is considered with the properties of the solidified material assumed as constants. A nonlinear transformation is applied to the sequence of partial sums in the perturbation solution to increase its range of applicability. For inward solidification it is found that the regular perturbation solution diverges for front positions close to the center. An Euler transformation and an overall energy balance are then used to obtain a modified series solution which is compared with numerical results.

A Numerical Study on Taylor Flow Heat Transfer in Square Microchannels Under Constant Wall Temperature Boundary Condition

2012 ◽  
Author(s):  
V. Talimi ◽  
Y. S. Muzychka ◽  
S. Kocabiyik
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Transfer Process ◽  
Wall Temperature ◽  
Heat Transfer Process ◽  
Constant Wall Temperature ◽  
Temperature Boundary ◽  
Slug Flows ◽  
Temperature Boundary Condition

Heat transfer in Taylor flows or slug flows has been examined exclusively by researchers. Noncircular microchannels have not been widely considered in the literature. There is a large gap in research since noncircular microchannels are common structures in microcooling processes. Square and rectangular microchannels are the most important examples. In the present study the heat transfer process in slug flows in square microchannels has been investigated numerically under constant wall temperature boundary condition. The local heat flux for the moving slugs has been converted to total microchannel heat flux using the integration methods suggested recently by the authors. This leads to microchannel wall average heat flux which is the parameter of interest in heat sink problems. Finally, effects of liquid film around bubbles on heat transfer process have been discussed.

Shear work, viscous dissipation and axial conduction effects on microchannel heat transfer with a constant wall temperature

2015 ◽  
Vol 230 (14) ◽  
pp. 2496-2507 ◽  
Author(s):  
K Ramadan ◽  
Iskander Tlili
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Wall Temperature ◽  
Slip Flow ◽  
Brinkman Number ◽  
Constant Wall Temperature ◽  
Fully Developed Flow ◽  
Boundary Shear ◽  
Temperature Boundary ◽  
Temperature Boundary Condition

Convective heat transfer in a microchannel rarefied gas flow with a constant wall temperature boundary condition is investigated numerically. The boundary shear work, viscous dissipation and axial conduction are all included in the study. An analytical solution is also derived for the fully developed flow condition including the boundary shear work. The proper thermal boundary condition considering the sliding friction at the wall is implemented. A comparative study is performed to quantify the effect of the shear work on heat transfer in the entrance – and the fully developed – regions of the microchannel for both gas cooling and heating. The results demonstrate that the effect of shear work on heat transfer is significant and it increases with increasing both the Knudsen number and Brinkman number. Neglecting the shear work in a microchannel slip flow leads to over- or under estimation of the Nusselt number considerably. For a fully developed flow in a microchannel with constant wall temperature boundary condition, the contribution of the shear work to heat transfer can be around 55% in the vicinity of the upper limit of the slip flow regime, regardless of how small the non-zero Brinkman number can be. Including the shear work is therefore crucial in the analysis of microchannel heat transfer and should not be neglected.

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.

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