Free convection heat and mass transfer during pool penetration into a melting miscible substrate

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    Abstract

    A theoretical investigation is made of the process of free convection melting of a solid slab by an overlying hot liquid pool. The solid, when molten, is lighter than and miscible with the pool material. Systematic mathematical approximations to the Boussinesq equations of motion are performed to determine the behavior of the temperature and the concentration fields in two different flow regions. These are the boundary layer region at the melting interface and the turbulent core region in the bulk pool. The dependence of the melting rate on various controlling parameters, including the Grashof number based on the pool-to-substrate density ratio, the external Stefan number based on the pool-to-substrate temperature difference, and the internal Stefan number based on the freezing-point depression, is obtained by matching the boundary layer solution and the turbulent core solution in the region of overlap. Comparison of the present theory is made with existing experiments and found to be good.

    Original languageEnglish (US)
    Pages (from-to)1061-1075
    Number of pages15
    JournalInternational Journal of Heat and Mass Transfer
    Volume30
    Issue number6
    DOIs
    StatePublished - Jan 1 1987

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    Natural convection
    free convection
    mass transfer
    Melting
    Mass transfer
    penetration
    heat transfer
    melting
    Heat transfer
    boundary layers
    Boundary layers
    Substrates
    Grashof number
    Freezing
    Equations of motion
    melting points
    Molten materials
    temperature gradients
    equations of motion
    slabs

    All Science Journal Classification (ASJC) codes

    • Condensed Matter Physics
    • Mechanical Engineering
    • Fluid Flow and Transfer Processes

    Cite this

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    title = "Free convection heat and mass transfer during pool penetration into a melting miscible substrate",
    abstract = "A theoretical investigation is made of the process of free convection melting of a solid slab by an overlying hot liquid pool. The solid, when molten, is lighter than and miscible with the pool material. Systematic mathematical approximations to the Boussinesq equations of motion are performed to determine the behavior of the temperature and the concentration fields in two different flow regions. These are the boundary layer region at the melting interface and the turbulent core region in the bulk pool. The dependence of the melting rate on various controlling parameters, including the Grashof number based on the pool-to-substrate density ratio, the external Stefan number based on the pool-to-substrate temperature difference, and the internal Stefan number based on the freezing-point depression, is obtained by matching the boundary layer solution and the turbulent core solution in the region of overlap. Comparison of the present theory is made with existing experiments and found to be good.",
    author = "Cheung, {Fan-bill B.}",
    year = "1987",
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    TY - JOUR

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    AU - Cheung, Fan-bill B.

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    N2 - A theoretical investigation is made of the process of free convection melting of a solid slab by an overlying hot liquid pool. The solid, when molten, is lighter than and miscible with the pool material. Systematic mathematical approximations to the Boussinesq equations of motion are performed to determine the behavior of the temperature and the concentration fields in two different flow regions. These are the boundary layer region at the melting interface and the turbulent core region in the bulk pool. The dependence of the melting rate on various controlling parameters, including the Grashof number based on the pool-to-substrate density ratio, the external Stefan number based on the pool-to-substrate temperature difference, and the internal Stefan number based on the freezing-point depression, is obtained by matching the boundary layer solution and the turbulent core solution in the region of overlap. Comparison of the present theory is made with existing experiments and found to be good.

    AB - A theoretical investigation is made of the process of free convection melting of a solid slab by an overlying hot liquid pool. The solid, when molten, is lighter than and miscible with the pool material. Systematic mathematical approximations to the Boussinesq equations of motion are performed to determine the behavior of the temperature and the concentration fields in two different flow regions. These are the boundary layer region at the melting interface and the turbulent core region in the bulk pool. The dependence of the melting rate on various controlling parameters, including the Grashof number based on the pool-to-substrate density ratio, the external Stefan number based on the pool-to-substrate temperature difference, and the internal Stefan number based on the freezing-point depression, is obtained by matching the boundary layer solution and the turbulent core solution in the region of overlap. Comparison of the present theory is made with existing experiments and found to be good.

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