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Research Papers

A Numerical Study of Diffusion of Nanoparticles in a Viscous Medium During Solidification

[+] Author and Article Information
Kazi M. Rahman

Department of Mechanical and Industrial
Engineering,
Montana State University,
Bozeman, MT 59717

M. Ruhul Amin

Department of Mechanical and Industrial
Engineering,
Montana State University,
Bozeman, MT 59717
e-mail: ramin@montana.edu

Ahsan Mian

Department of Mechanical and Materials
Engineering,
Wright State University,
Dayton, OH 45435

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF THERMAL SCIENCE AND ENGINEERING APPLICATIONS. Manuscript received June 5, 2018; final manuscript received August 7, 2018; published online October 15, 2018. Assoc. Editor: Steve Q. Cai.

J. Thermal Sci. Eng. Appl 11(1), 011013 (Oct 15, 2018) (10 pages) Paper No: TSEA-18-1298; doi: 10.1115/1.4041349 History: Received June 05, 2018; Revised August 07, 2018

In the field of additive manufacturing process, laser cladding is widely considered due to its cost effectiveness, small localized heat generation, and full fusion to metals. Introducing nanoparticles with cladding metals produces metal matrix nanocomposites, which in turn improves the material characteristics of the clad layer. The governing equations that control the fluid flow are standard incompressible Navier–Stokes and heat diffusion equation, whereas the Euler–Lagrange approach has been considered for particle tracking. The mathematical formulation for solidification is adopted based on enthalpy porosity method. Liquid titanium has been considered as the initial condition where particle distribution has been assumed uniform throughout the geometry. A numerical model implemented in a commercial software based on control volume method has been developed, which allows to simulate the fluid flow during solidification as well as tracking nanoparticles during this process. A detailed parametric study has been conducted by changing the Marangoni number, convection heat transfer coefficient, constant temperature below the melting point of titanium, and insulated boundary conditions to analyze the behavior of the nanoparticle movement. The influence of increase in Marangoni number results in a higher concentration of nanoparticles in some portions of the geometry and lack of nanoparticles in rest of the geometry. The high concentration of nanoparticles decreases with a decrease in Marangoni number. Furthermore, an increase in the rate of solidification time limits the nanoparticle movement from its original position which results in different distribution patterns with respect to the solidification time.

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Figures

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Fig. 1

Computational domain in terms of dimensional parameters

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Fig. 2

Flow diagram of pressure-based segregated algorithm

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Fig. 3

Comparison of numerically obtained solidification front positions with experimental data by Wolff and Viskanta [21]

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Fig. 4

Comparison of numerically obtained particle distribution with numerical results from Akbar et al. [6]

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Fig. 5

Quantitative comparison of numerically obtained particle fraction remained in the domain with numerical results from Akbar et al. [6]

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Fig. 6

Initial particle distribution

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Fig. 7

Final particle distribution at h = 5 W/m2K: (a) Ma = 4.3 × 103, (b) Ma = 4.3 × 104, and (c) Ma = 4.3 × 105

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Fig. 8

Final particle distribution at h = 146 W/m2K: (a) Ma = 4.3 × 103, (b) Ma = 4.3 × 104, and (c) Ma = 4.3 × 105

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Fig. 9

Final particle distribution at h = 600 W/m2K: (a) Ma = 4.3 × 103, (b) Ma = 4.3 × 104, and (c) Ma = 4.3 × 105

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Fig. 10

Effect of convective heat transfer coefficient (h), Marangoni number (Ma), insulated (i) and constant temperature (c) bottom boundary on liquid fraction

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Fig. 11

Effect of Marangoni number (Ma), insulated (i) and constant temperature (c) bottom boundary condition on top wall heat flux at h = 5 W/m2K

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Fig. 12

Effect of Marangoni number (Ma), insulated (i) and constant temperature(c) bottom boundary condition on top wall heat flux at h = 146 W/m2K

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Fig. 13

Effect of Marangoni number (Ma), insulated (i) and constant temperature (c) bottom boundary condition on top wall heat flux at h = 600 W/m2K

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Fig. 14

Power law curve fit for top wall's solidification time versus h at different Marangoni number (Ma), insulated (i) and constant temperature (c) bottom wall

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Fig. 15

Linear curve fit for variation of top wall's solidification time versus total geometry's solidification time at different Ma and h

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Fig. 16

Power law curve fit for variation of top wall's solidification time versus total geometry's solidification time at different Ma and h

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