Heat and Mass Transfer

, Volume 53, Issue 3, pp 825–848 | Cite as

Heat transfer and fluid flow analysis of self-healing in metallic materials

  • J. Martínez Lucci
  • R. S. AmanoEmail author
  • P. K. Rohatgi


This paper explores imparting self-healing characteristics to metal matrices similar to what are observed in biological systems and are being developed for polymeric materials. To impart self-healing properties to metal matrices, a liquid healing method was investigated; the met hod consists of a container filled with low melting alloy acting as a healing agent, embedded into a high melting metal matrix. When the matrix is cracked; self-healing is achieved by melting the healing agent allowing the liquid metal to flow into the crack. Upon cooling, solidification of the healing agent occurs and seals the crack. The objective of this research is to investigate the fluid flow and heat transfer to impart self-healing property to metal matrices. In this study, a dimensionless healing factor, which may help predict the possibility of healing is proposed. The healing factor is defined as the ratio of the viscous forces and the contact area of liquid metal and solid which prevent flow, and volume expansion, density, and velocity of the liquid metal, gravity, crack size and orientation which promote flow. The factor incorporates the parameters that control self-healing mechanism. It was observed that for lower values of the healing factor, the liquid flows, and for higher values of healing factor, the liquid remains in the container and healing does not occur. To validate and identify the critical range of the healing factor, experiments and simulations were performed for selected combinations of healing agents and metal matrices. The simulations were performed for three-dimensional models and a commercial software 3D Ansys-Fluent was used. Three experimental methods of synthesis of self-healing composites were used. The first method consisted of creating a hole in the matrices, and liquid healing agent was poured into the hole. The second method consisted of micro tubes containing the healing agent, and the third method consisted of incorporating micro balloons containing the healing agent in the matrix. The observed critical range of the healing factor is between 407 and 495; only for healing factor values below 407 healing was observed in the matrices.


Contact Angle Liquid Metal Shape Memory Alloy Healing Agent Mushy Zone 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols


Mushy zone


Specific heat (kJ/kg K)


Coefficient of thermal expansion


Crack characteristic length (m)




External force (N)


Gravity (m/s2)


Heat transfer coefficient (w/m2 K)


Enthalpy (kJ/kg)


Self-healing predicting factor


Healing factor


Momentum flux


Latent heat (kJ/kg)


Thermal conductivity (w/m K)


Pressure (Pa)


Heat flux (kJ/m2)


Radius of the curvature (m)


Gas constant (kJ/kg K)


Total thermal resistance




Time (s)


Temperature (K)


Healing temperature (K)

\(\overrightarrow {{v_{p} }}\)

Pull velocity (m/s)


Bulk velocity (m/s)


Volume of fraction


Amount of work (j)

x, y, z

Coordinate system

Greek alphabet


Thermal diffusivity (m2/s)


Liquid fraction


Interfacial tension (N/m)

\(\Delta H_{f}\)

Latent heat of fusion (KJ)


Contact angle


Free mean path


Dynamic viscosity (kg/m s)


Density (kg/m3)


Interface tension


Electrical conductivity (S/m)


Kinematic viscosity (m2/s)


Liquid healing agent


i, j

Term index


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • J. Martínez Lucci
    • 2
  • R. S. Amano
    • 1
    Email author
  • P. K. Rohatgi
    • 1
  1. 1.University of Wisconsin-MilwaukeeMadridSpain
  2. 2.Universidad Europea de MadridMadridSpain

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