Effect of non-planar geometry on diffusion kinetics during brazing repair process

Ghanbar, A.; Ojo, O.A.

doi:10.1080/02670836.2019.1705040

Cited by 5 publications

(2 citation statements)

References 19 publications

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“…Therefore, they present considerable limitations from the point of view of their practical application. One of the main advantages of numerical methods [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] is that they allow more realistic boundary conditions to be accepted, for which it would not be possible to obtain analytical solutions. The accuracy of these methods is generally quite high, but they require the use of computational resources as well as a certain amount of complexity.…”

Section: Introductionmentioning

confidence: 99%

On the derivation of unsteady closed-form analytical solution for the solidification of pure and eutectic materials with boundary conditions of the third kind

Ferreira,

Júnior,

Moreira

2024

Preprint

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Solidification and fusion are important processes applied in several fields of science and technology. Recently, far beyond the realms of materials science and metallurgy, many applications have risen in latent heat thermal energy storage and melting and growth of ice plates. Due to the relative difficulty in obtaining numerical solutions for moving boundary problems for a wide range of space and time scales. In this work, four closed-form solutions for the transient solidification of pure and eutectic materials are proposed for one- and three-dimensional semi-infinite slabs considering convective boundary conditions and melting superheating. The analytical results are plotted against the numerical simulation results.

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Section: Introductionmentioning

confidence: 99%

On the derivation of unsteady closed-form analytical solution for the solidification of pure and eutectic materials with boundary conditions of the third kind

Ferreira,

Júnior,

Moreira

2024

Preprint

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“…e effect of the geometrical shape of the dispersed drug particles on the drug release profile was examined for systems with different ratios of dissolution rate/diffusion rate and ratios of solubility/total drug loading value. Finally, Ghanbar and Ojo [46] have presented a new finite difference numerical model in order to investigate the importance of cylindrical and spherical solid-liquid interface geometry on the kinetics of isothermal solidification during diffusion brazing or transient liquid phase repair process. e obtained results showed that nonplanarity of the solid-liquid interface can have significant effects on the kinetics of solid-liquid phase transformation during the repair process which is crucial to the understanding and optimization of this process in nonplanar systems.…”

mentioning

confidence: 99%

On the Transient Atomic/Heat Diffusion in Cylinders and Spheres with Phase Change: A Method to Derive Closed-Form Solutions

Ferreira

Garcia

Moreira

2021

International Journal of Mathematics and Mathematical Sciences

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Analytical solutions for the transient single-phase and two-phase inward solid-state diffusion and solidification applied to the radial cylindrical and spherical geometries are proposed. Both solutions are developed from the differential equation that treats these phenomena in Cartesian coordinates, which are modified by geometric correlations and suitable changes of variables to achieve closed-form solutions. The modified differential equations are solved by using two well-known closed-form solutions based on the error function, and then equations are obtained to analyze the diffusion interface position as a function of time and position in cylinders and spheres. These exact correlations are inserted into the closed-form solutions for the slab and are used to update the roots for each radial position of the moving boundary interface. The predictions provided by the proposed analytical solutions are validated against the results of a numerical approach. Finally, a comparative study of diffusion in slabs, cylinders, and spheres is also presented for single-phase and two-phase solid-state diffusion and solidification, which shows the importance of the effects imposed by the radial cylindrical and spherical curvatures with respect to the Cartesian coordinate system in the process kinetics. The analytical model is proved to be general, as far as, a semi-infinite solution for diffusion problems with phase change exists in the form of the error function, which enables exact closed-form analytical solutions to be derived, by updating the root at each radial position the moving boundary interface.

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Closed-form solution for the inward unsteady-state solidification of cylinders and spheres: pure metals and eutectics

Ferreira

Garcia

Moreira

2022

J Therm Anal Calorim

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Effect of non-planar geometry on diffusion kinetics during brazing repair process

Cited by 5 publications

References 19 publications

On the derivation of unsteady closed-form analytical solution for the solidification of pure and eutectic materials with boundary conditions of the third kind

On the derivation of unsteady closed-form analytical solution for the solidification of pure and eutectic materials with boundary conditions of the third kind

On the Transient Atomic/Heat Diffusion in Cylinders and Spheres with Phase Change: A Method to Derive Closed-Form Solutions

Closed-form solution for the inward unsteady-state solidification of cylinders and spheres: pure metals and eutectics

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