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Nanolayer Surface Phase Change in Self-Healing Materials

  • Rahul BasuEmail author
Conference paper
Part of the The Minerals, Metals & Materials Series book series (MMMS)

Abstract

The phase change problem in a semi-infinite medium where temperature and concentration are coupled is solved for variable diffusivity. An integral technique is used to solve for concentration and temperature penetration lengths and velocity of change. Surface conditions are held constant whereas diffusivity is allowed to vary slowly corresponding to phase change in the matrix. An analytic solution for variable properties under these conditions is obtained using the Kirchhoff transformation. Penetration lengths are analytically evaluated. A perturbation analysis allows the boundary layer lengths to be estimated, whence the two parameters can be compared. Dimensions obtained by the simulation show that nanomaterial thicknesses are attainable in the boundary layers. Application to phase change concepts relating to self-healing materials is illustrated for porous surface layers.

Keywords

Self-healing Self-healing materials Composite materials Surface layers Porous materials 

Nomenclature

a, b

Parameters in the Kirchhoff transformation

c

Concentration

cp

Specific heat

B

Constant

D

Diffusion coefficient

L, H

Latent heat

s, l

Solid, liquid

n

Power exponent in the approximate scheme

Ste

Stefan number = latent heat/sensible heat

Ti, To

Initial, final temperature

U, V

Transformed temperature, concentration in the Kirchhoff representation

1, 2

Labels for the interacting phases

λ

Eigenvalue for interface velocity

μ

Diffusivity variation for concentration

τ

Time

θ

Temperature (nondim)

θm

Fusion temperature

η

Similarity parameter

ε

Recombination or dissolution, small perturbation parameter

Δ

Penetration length (thermal slope is zero)

Δ1

Penetration length (concentration slope is zero)

δm

Thermo-gradient parameter

ζ

Position of the moving phase boundary

λ (τ)

Phase change eigenvalue

α

Thermal diffusivity

αm

Diffusivity of permeating phase

αij

Normalized diffusivity αi/αj

β(τ)

Penetration length for thermal Δ = 2β t0.5

β1(t)

Penetration length for concentration Δ1 = 2β1 t0.5

β0

Separation constant

γ

Temperature-dependent constant for variable diffusivity

П

3.14159

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Copyright information

© The Minerals, Metals & Materials Society 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringAdarsha Institute of TechnologyBangaloreIndia

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