Abstract
Phase change problems play very important role in engineering sciences including casting of nuclear waste materials, vivo freezing of biological tissues, solar collectors and so forth. In present paper, we propose fractional diffusion equation model for alloy solidification. A transient heat transfer analysis is carried out to study the anomalous diffusion. Finite difference method is used to solve the fractional differential equation model. The temperature profiles, the motion of interface, and interface velocity have been evaluated for space fractional diffusion equation.
Highlights
Heat diffusion during the change of state, for example, melting and solidification, has important applications in science and technology including casting of nuclear waste materials, vivo freezing of biological tissues, and solar collectors
We propose fractional diffusion equation model for alloy solidification
We propose the governing fractional diffusion equation model for alloy solidification as follows
Summary
Heat diffusion during the change of state, for example, melting and solidification, has important applications in science and technology including casting of nuclear waste materials, vivo freezing of biological tissues, and solar collectors. Some researchers have studied simple or classic Stefan problem using fractional diffusion equation. Atkinson [11] wrote a very interesting survey paper on moving boundary problems for time and space fractional diffusion. They studied the classic Stefan problem and discussed analytical or semianalytical solution in closed form for infinite or semi-infinite region. The enthalpy formulation of space fractional diffusion model is proposed to study the alloy solidification in finite media. To study the effect of fractional order derivative α, the temperature profiles and motion of freezing interface are obtained for different values of α. The negative values for α are denoted for fractional integrals of arbitrary order
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