Onset of finger convection in a horizontal porous layer underlying a fluid layer

Journal Article · Sun May 01 00:00:00 EDT 1988 · Journal of Heat Transfer (Transcations of the ASME (American Society of Mechanical Engineers), Series C); (United States)

DOI:https://doi.org/10.1115/1.3250499· OSTI ID:5465428

Chen, F; Chen, C F ^[1]

---

1. Univ. of Arizona, Tucson (USA)

In the directional solidification of concentrated alloys, the frozen solid region is separated from the melt region by a mushy zone consisting of dendrites immersed in the melt. Simulataneous occurrence of temperature and solute gradients through the melt and mushy zones may be conductive to the occurrence of salt-finger convection, which may in turn cause adverse effects such as channel segregation. The authors have considered the problem of the onset of finger convection in a porous layer underlying a fluid layer using linear stability analysis. The eigenvalue problem is solved by a shooting method. As a check on the method of solution and the associated computer program, they first consider the thermal convection problem. In this process, it is discovered that at low depth ratios d (the ratio of the fluid layer depth to the porous layer depth), the marginal stability curve is bimodal. At small {cflx d}, the long-wave branch is the most unstable and the convection is dominated by the porous layer. At large {cflx d}, the short-wave branch is the most unstable and the convection is dominated by the fluid layer, with a convection pattern consisting of square cells in the fluid layer. In the salt-finger case with a given thermal Rayleigh number Ra{sub m} = 50, as the depth ratio {cflx d} is increased from zero, the critical salt Rayleigh number Ra{sub sm} = 50, as the depth ratio {cflx d} is increased from zero, the critical salt Rayleigh number Ra{sub sm} first decreases, reaches a minimum, and then increases. The system is more stable at {cflx d} > 0.2 than at {cflx d} = 0. This rather unusual behavior is again due to the fact that at small {cflx d}, convection is dominated by the porous layer and, at large {cflx d}, convection is dominated by the fluid layer. However, in the latter case, the convection pattern in the fluid layer consists of a number of high aspect ratio cells.

• OSTI ID: 5465428
• Journal Information: Journal of Heat Transfer (Transcations of the ASME (American Society of Mechanical Engineers), Series C); (United States), Vol. 110:2; ISSN 0022-1481
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
POROUS MATERIALS
CONVECTION
AMMONIUM CHLORIDES
AQUEOUS SOLUTIONS
DENDRITES
EIGENVALUES
SALINITY GRADIENTS
TEMPERATURE GRADIENTS
AMMONIUM COMPOUNDS
AMMONIUM HALIDES
CHLORIDES
CHLORINE COMPOUNDS
CRYSTALS
DISPERSIONS
ENERGY TRANSFER
HALIDES
HALOGEN COMPOUNDS
HEAT TRANSFER
MASS TRANSFER
MATERIALS
MIXTURES
SOLUTIONS
420400* - Engineering- Heat Transfer & Fluid Flow