Stefan number

About: Stefan number is a research topic. Over the lifetime, 482 publications have been published within this topic receiving 32056 citations.

Transient heat characteristics of water‐saturated porous media with freezing

Abstract: Analytical and experimental investigations were performed to examine the transient heat characteristics of water-saturated porous media with freezing. As a physical model, a two-dimensional vertical cavity was considered. One vertical wall was abruptly cooled below the fusion temperature, the other three walls were thermally insulated. Three different sizes of glass, and iron, alumina, and copper beads were used as the porous media. The cold energy stored in the porous media and the average thickness of the frozen layer were measured in the experiments. Comparisons of the analytical results with the experimental ones were made, and the effects of Darcy number, Stefan number, and modified Prandtl number on the transient heat characteristics were discussed. The dimensionless equations for predicting the averaged frozen layer thickness and the stored cold energy were obtained as a function of various dimensionless parameters.

Development of Instant Interface Temperature at Time τ = 0+ of Low Melting Temperature Cylindrical Solid Additive-Bath System

Abstract: A mathematical model in integral format is devised for the development of instant temperature at the interface between a low melting temperature solid cylindrical additive and the freezing layer of the bath material around the additive immediately after immersion of the additive in the bath. It indicates that this temperature is function of the phase change parameters, the Stefan number, S ta of the additive, and S tb of the bath material, the thermophysical property-ratio, γ and the melting temperature ratio, θ ab of the additive-bath system and gives a close form expression for the instant interface temperature, θ e. For given θ ab < 1 and the Stefan number, S ta, of the additive decreasing the Stefan number, S tb of the bath material (∞ ≥ S tb ≥ 0) or increasing γ (0 ≤ γ ≤ ∞) permits θ e to increase from the initial temperature of the additive to the freezing temperature of the bath material. θ e also gets increased by increasing any or both of S tb and θ ab. When the additive gets only heated after its immersion in the bath, the model of the present problem becomes exactly the same that was investigated recently validating the present problem.

Mushy Zones Evolution Under Microgravity Conditions

Abstract: High-purity pivalic acid (PVA) dendrites were observed under convection-free conditions on STS-87 as part of the United States Microgravity Payload Mission (USMP4) flown on NASA’s space shuttle Columbia in 1997. Our telemetry video data show that PVA dendrites melt without relative motion with respect to the quiescent melt phase. With a small fixed superheat above the melting point, ∆T ≡ Tm − T∞, designated in the theory by a Stefan number, dendritic fragments melt and shrink steadily. Fragmentation of the dendrites is observed at higher initial supercoolings. Individual fragments follow a squareroot time-dependence as predicted using a quasi-static conduction-limited approach [1]. Agreement between the analytic theory and experiments was found when the melting process occurs under shape-preserving conditions, where needle-like crystal fragments may be approximated as prolate spheroids with a constant C/A ratio. In microgravity experiments where C/A ratio is not constant, because of interactions in the mushy zone, a “sectorizing” approach was employed that divides the melting process into a series of steps, each approximated b ya constant average value of the C/A ratio. Sectorization allows prediction of melting kinetics using quasistatic theory. Theoretical Stefan numbers were calculated for each sector of melting independently using the initial and final axial lengths for that interval.