Wax diffusivity under given thermal gradient: a mathematical model

ABSTRACTMathematical model of thermomigration of liquid inclusions through a crystal under stationary and non-stationary thermal conditions is presented. It is assumed that the mass-transfer is provided by diffusion only, the crystallization and dissolution processes are carried out in accordance with the diffuse interface mechanism for atomic-rough (non-singular) interfaces and screw-dislocation or two-dimension nucleation mechanisms for singular interfaces.The package of computer programs based on this model enables simulation of the evolution of the cross-sectional shape of cylindrical liquid inclusions. It is possible to simulate the cases of various inclusion sizes, various relationship between the interface and volume mass-transfer restrictions, various liquid phase composition, thermal gradient under stationary and non-stationary thermal conditions as well. The main results of the simulation are presented.

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High Temperature Thermal Gradient Interaction Chromatography (HT-TGIC) for Blends of Ethylene/1-Octene Copolymers: A Mathematical Model

Macromolecular Symposia ◽

10.1002/masy.201400124 ◽

2015 ◽

Vol 354 (1) ◽

pp. 361-366 ◽

Cited By ~ 3

Author(s):

Nantiya Inwong ◽

Siripon Anantawaraskul ◽

João B. P. Soares ◽

Abdulaal Z. Al-Khazaal

Keyword(s):

Mathematical Model ◽

High Temperature ◽

Thermal Gradient

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Development of a mathematical model for propagation of ultrasonic waves in thick-walled cylinders in the presence of a thermal gradient - Case of axial scanning

Ultrasonics ◽

10.1016/j.ultras.2021.106628 ◽

2021 ◽

pp. 106628

Author(s):

R. Shabani ◽

F. Honarvar

Keyword(s):

Mathematical Model ◽

Thermal Gradient ◽

Ultrasonic Waves ◽

Axial Scanning

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Mathematical Model and Simulation of a Thermal Diffusion Column

Journal of Heat Transfer ◽

10.1115/1.1560150 ◽

2003 ◽

Vol 125 (2) ◽

pp. 266-273 ◽

Cited By ~ 4

Author(s):

Juan E. Vela´squez ◽

Farid Chejne ◽

Alan F. J. Hill

Keyword(s):

Mathematical Model ◽

Temperature Gradient ◽

Thermal Diffusion ◽

Thermal Gradient ◽

Gas Mixture ◽

Two Dimensional ◽

Model And Simulation ◽

Total Reflux ◽

Diffusion Column ◽

Composition Profiles

A two-dimensional mathematical model, in stationary state was developed for the separation of species in a thermal diffusion column working with total reflux. The model was applied to a gas mixture of CO2 and N2. The existence of convective currents along the column was verified, the separation of species due to the temperature gradient was predicted and the effect of the thermal gradient and of the operation pressures on the composition profiles was analyzed.

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Development of a Mathematical Model for Propagation of Ultrasonic Waves in Thick-Walled Cylinders in the Presence of a Thermal Gradient – Case of Circumferential Scanning

SSRN Electronic Journal ◽

10.2139/ssrn.3971799 ◽

2021 ◽

Author(s):

Ramin Shabani ◽

Farhang Honarvar

Keyword(s):

Mathematical Model ◽

Thermal Gradient ◽

Ultrasonic Waves

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Fission Gas Bubbles in Fractured UO2

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100101177 ◽

1968 ◽

Vol 26 ◽

pp. 286-287

Author(s):

O. M. Katz

Keyword(s):

Electron Microscopy ◽

Thermal Gradient ◽

Gas Bubbles ◽

Inert Gas ◽

Thermal Gradients ◽

Fission Gas ◽

Beam Heating ◽

Limited Application ◽

Bubble Characteristics ◽

Electron Beam Heating

The swelling of irradiated UO2 has been attributed to the migration and agglomeration of fission gas bubbles in a thermal gradient. High temperatures and thermal gradients obtained by electron beam heating simulate reactor behavior and lead to the postulation of swelling mechanisms. Although electron microscopy studies have been reported on UO2, two experimental procedures have limited application of the results: irradiation was achieved either with a stream of inert gas ions without fission or at depletions less than 2 x 1020 fissions/cm3 (∼3/4 at % burnup). This study was not limited either of these conditions and reports on the bubble characteristics observed by transmission and fractographic electron microscopy in high density (96% theoretical) UO2 irradiated between 3.5 and 31.3 x 1020 fissions/cm3 at temperatures below l600°F. Preliminary results from replicas of the as-polished and etched surfaces of these samples were published.

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