Stefan number

About: Stefan number is a(n) research topic. Over the lifetime, 482 publication(s) have been published within this topic receiving 32056 citation(s).

Conduction of Heat in Solids

Abstract: This classic account describes the known exact solutions of problems of heat flow, with detailed discussion of all the most important boundary value problems.

Analysis of Multidimensional Conduction Phase Change Via the Enthalpy Model

Abstract: The basis of the enthalpy model for multidimensional phase change problems in media having a distinct phase change temperature is demonstrated, and subsequent numerical applications of the model are carried out. It is shown that the mathematical representation of the enthalpy model is equivalent to the conventional conservation equations in the solid and liquid regions and at the solid-liquid interface. The model is employed in conjunction with a fully implicit finite-difference scheme to solve for solidification in a convectively cooled square container. The implicit scheme was selected because of its ability to accommodate a wide range of the Stefan number Ste. After its accuracy had been established, the solution method was used to obtain results for the local and surface-integrated heat transfer rates, boundary temperatures, solidified fraction, and interface position, all as functions of time. The results are presented with SteFo (Fo = Fourier number) as a correlating parameter, thereby facilitating their use for all Ste values in the range investigated. At low values of the Biot number, the surface-integrated heat transfer rate was relatively constant during the entire solidification period, which is a desirable characteristic for phase change thermal energy storage.

Analysis of multidimensional conduction phase change via the enthalpy model.

Abstract: The basis of the enthalpy model for multidimensional phase change problems in media having a distinct phase change temperature is demonstrated, and subsequent numerical applications of the model are carried out. It is shown that the mathematical representation of the enthalpy model is equivalent to the conventional conservation equations in the solid and liquid regions and at the solid-liquid interface. The model is employed in conjunction with a fully implicit finite-difference scheme to solve for solidification in a convectively cooled square container. The implicit scheme was selected because of its ability to accommodate a wide range of the Stefan number Ste. After its accuracy had been established, the solution method was used to obtain results for the local and surface-integrated heat transfer rates, boundary temperatures, solidified fraction, and interface position, all as functions of time. The results are presented with SteFo (Fo = Fourier number) as a correlating parameter, thereby facilitating their use for all Ste values in the range investigated. At low values of the Biot number, the surface-integrated heat transfer rate was relatively constant during the entire solidification period, which is a desirable characteristic for phase change thermal energy storage.

Molten droplet deposition and solidification at low Weber numbers

Abstract: Low Weber number deposition of small molten droplets on cold targets is of importance in certain dropwise buildup processes, but at this time, critical elements are absent from our theoretical understanding of the deposition process, and prediction from basic principles is not possible. This paper lays down a framework for understanding low Weber number deposition in terms of similarity laws and experimentation. Based on experiments from the highly viscous limit to the inertia-dominated limit, correlations are given for the spreading velocity, spreading time scales, post-spreading oscillation amplitudes, and oscillation damping time scales. Molten droplets are arrested, and their final solid shape determined, by contact line freezing. In homologous deposition, where the drop and the target are of the same material, the spreading factor is determined principally by the Stefan number, the dimensionless parameter which measures the temperature difference between the fusion point and the target temperature. Some concluding remarks are offered on what needs to be done to accurately compute such deposition processes.

Forced convection heat transfer in microencapsulated phase change material slurries: flow in circular ducts

Abstract: The heat transfer characteristics of microencapsulated phase change material slurry flow in circular ducts are presented in this paper. The energy equation is formulated by taking into consideration both the heat absorption (or release) due to the phase change process and the conductivity enhancement induced by the motion of the particles. The heat source or heat generation function in the energy equation is derived from solutions for freezing or melting in a sphere. The correlation for the effective conductivity of the slurry is obtained based on available analytical and experimental results. The governing parameters are found to be the particle concentration, a bulk Stefan number, the duct/particle radius ratio, the particle/fluid conductivity ratio, and a modified Peclet number. For low temperature applications, it is found that the dominant parameters are the bulk Stefan number and concentration. The numerical solutions show that heat fluxes about 2–4 times higher than single phase flow may be achieved by a slurry system.