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Analysis of Formability of Glassy Alloys by Surface Heating Under Convective Conditions

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TMS 2018 147th Annual Meeting & Exhibition Supplemental Proceedings (TMS 2018)

Part of the book series: The Minerals, Metals & Materials Series ((MMMS))

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Abstract

Modification of surface films by focussed energy sources with convective boundary conditions is idealised. The problem is approached by linearizing a coupled set of heat and mass transfer equation. The nonlinearity of the coupled problem introduces many complexities and exact solutions are not available in the general case. This work uses certain transformations not published earlier to obtain tractable solutions and stability benchmarks in terms of macroscopic parameters like the Stefan, Biot and Fourier numbers. Linear ODE’s are obtained from the coupled mass and heat transfer equations, which are analysed easily. Evaluation of the properties of the thermal boundary layer and attenuation with imposed fluctuating heat source shows that a regime exists for glass formation. Data from various alloy systems show that glass formability is related to the derived boundary layer thickness and certain non dimensional parameters.

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Abbreviations

a:

initial size

c:

concentration

cp:

specific heat

D:

differential operator, Diffusion coefficient

Fo:

Fourier number

Bi:

Biot number

Ste:

Stefan number

h:

heat transfer coeff.

a:

boundary length

g:

temperature concentration gradient

K:

thermal conductivity

k:

thermal diffusivity

L:

latent heat

m:

mass

q:

source strength

r:

radial variable

s:

interfacial position s = 2λ √α12τ

T:

temperature

t:

time

z:

axial coordinate

α, κ:

diffusivity (subscript m for the mass component)

δ:

Characteristic length

ε:

porosity

η:

similarity variable

θm:

non dim temperature

μ:

small perturbation parameter (not to be confused with chemical potential) τ non-dimensional time

θ:

non-dimensional temperature

ρ:

Density

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Author information

Authors and Affiliations

  1. Adarsha Institute of Technology, Off Intl Airport Road, Kundana, Bangalore, 562110, India

    Rahul Basu

Authors
  1. Rahul Basu
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Corresponding author

Correspondence to Rahul Basu .

Editor information

Editors and Affiliations

  1. Pittsburgh, Pennsylvania, USA

    The Minerals, Metals & Materials Society

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Basu, R. (2018). Analysis of Formability of Glassy Alloys by Surface Heating Under Convective Conditions. In: & Materials Society, T. (eds) TMS 2018 147th Annual Meeting & Exhibition Supplemental Proceedings. TMS 2018. The Minerals, Metals & Materials Series. Springer, Cham. https://doi.org/10.1007/978-3-319-72526-0_56

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