Sanyal, D and Ramachandrarao, P and Gupta, O P (2006) A fractal description of transport phenomena in dendritic porous network. Chemical Engineering Science, 61 (2). 307 -315. ISSN 0009-2509

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Solidification of alloy is characterised by a diffuse layer, called the mushy zone, comprising liquid percolating through a network of dendrites. Thermosolutal or double diffusive convection within this mushy zone is reckoned as one of the key hydrodynamics phenomena governing the microstructure of the product and its properties. The study of the mushy zone hydrodynamics has so far been attempted by considering the mush as a saturated porous medium with permeability as a function of solid (or liquid) fraction. However, the dendritic network with its self-similar structure, with spatial periodicity in the primary, secondary and tertiary arm scales, is amenable to description under the framework of fractal sets. In this paper, we present the mushy zone as a network of continuous fractal structures. The geometric description of a dendritic network is proposed in the form of fractals using two separate measures based on area and perimeter in the transverse and longitudinal directions. The tortuosity of the fractal bed of dendrites is represented as a ratio of the fractal measure based on perimeter to the step size of the order of primary dendrite spacing. The interdendritic permeability is calculated based on fractal dimensions and shows excellent fit with experimental data performed on lead-tin alloy and previously reported in the published literature

Item Type: Article
Uncontrolled Keywords: transport processes; porous media; dendrites; fractals; phase change; permeability
Subjects: Glass
Depositing User: Mrs Chandana Patra
Date Deposited: 01 Feb 2012 07:43
Last Modified: 01 Feb 2012 07:45

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