Abstract
Phase change phenomena involving internal heat generation are of central interest in various applications, including freeze drying, preservation of biological tissues, microwave/Joule heating processes, materials processing using lasers, and nuclear power generation systems. In this work, mathematical models are developed to study the solidification processes driven by convective cooling effects on the exterior surface of phase change materials (PCM) in different geometric configurations, where both the solid and the liquid phases are subject to volumetric heating. By invoking a quasi-steady assumption and performing a simplified unified analysis, new semi-analytical approximate solutions for this unique Stefan problem in planar, cylindrical, spherical, and semi-infinite geometries of the PCM are obtained and studied. The interface evolution depends on the characteristic dimensionless parameters, such as the Biot number, Bi, internal heat generation parameter, Q, Stefan number, St, and the thermal conductivity ratio, κ. The effects of all the dimensionless parameters, viz., Bi, Q, St, and κ are systematically investigated for each geometrical configuration of the PCM. In particular, the results show the significant role of the Biot number on the transient evolution as well as the steady-state thickness of the solidifying front in the presence of an inhibiting internal heat generation. In addition, a simple and unified condition relating the dimensionless internal heating rate (Q) and the external convective cooling rate (Bi) for the onset of remelting for the special case of κ = 1 applicable for all the above geometries of the PCM is deduced.
Published Version
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