Showing papers on "Stefan number published in 1991"

Freeze coating of a moving substrate with a binary alloy

Abstract: A theoretical model is presented for the problem of the deposition of a coaling layer on a flat moving substrate. The coating material is a binary alloy. Upon solidification, three distinct regions exist above the substrate: the solid region, the mixed phase region or mushy zone, and the liquid melt region. The model accounts for convection in the melt, conduction in the mixed phase region, conduction in the solid part of the coating, and conduction in the substrate. The convection in the melt is induced by the combined action of the substrate velocity and the coating deposition velocity. The numerical solution of the model determines the effect of the main parameters of the problem on the solid coating thickness and the size of the mushy zone. These parameters are exemplified by the Prandtl number, the inverse Stefan number, the ratio of the melt deposition velocity to the substrate velocity, and the ratios of material properties in the two phases (solid and liquid) and the substrate. The effect...

Heat and fluid flow processes during the coating of a moving surface

Abstract: In this paper, a theoretical study is presented for the problem of coating a flat moving surface with a small Prandtl number melt, exemplified by a liquid metal or a liquid crystal. From the heat and fluid flow standpoint, the process is modeled as one of forced convection in the melt (induced by both the motion of the surface and the velocity of the melt as it is deposited on the surface) coupled with conduction in the solidifying coating layer. The effect of the main parameters of the problem, such as the ratio of the melt deposition velocity to the surface velocity, the Stefan number, the Prandtl number, and the ratios of the main properties of the solid and liquid phases on the thickness of the resulting coating layer and the heat transfer to the moving surface, are determined. An important assumption adopted in this study is that the moving surface is isothermal. The parametric domain of validity of this assumption is defined.

Freezing around a vertical cylinder immersed in porous media incorporating the natural convection effect

Abstract: The present paper analyses the freezing heat transfer on a cold cylinder immersed in a superheated liquid-saturated porous medium. The main emphasis of this paper is to clarify the effect of natural convection in the liquid phase on the freezing process. A mathematical model was developed, based on several reasonable assumptions for fluid flow in a liquid phase. The governing equations were numerically solved. Numerical results were reported for the thickness distribution of the frozen layer and the heat transfer coefficients at the cold wall and interface. The influences of various parameters such as Rayleigh number, liquid superheat, Stefan number and the dimensionless radius of a cylinder were demonstrated.

An Experimental Study of Laminar Film Condensation With Stefan Number Greater Than Unity

Abstract: Experimental laminar condensation heat transfer data is reported for fluids with Stefan number up to 3.5. The fluid is a member of a family of fluorinated fluids developed in the last decade which have been extensively used in the electronics industry for soldering, cooling, and testing applications. Experiments were performed by suddenly immersing cold copper spheres in the saturated vapor of this fluid, and heat transfer rates were calculated using the quasi-steady temperature response of the spheres. In these experiments, the difference between saturation and wall temperature varied from 0.5{degree}C to 190{degree}C. Over this range of temperature difference, the condensate properties vary significantly. For example, viscosity of the condense varies by a factor of over 50. Corrections for the temperature dependent properties of the condensate therefore were incorporated in calculating the Nusselt number based on the average heat transfer coefficient. The results are discussed in light of past experimental data theory for Stefan number less than 1. To the knowledge of the authors, this is the first reported study of condensation heat transfer for Stefan number greater that unity. 24 refs., 7 figs., 2 tabs.

Numerical Analysis of Two-Dimensional Transient Freezing in a Spheroidal Capsule

Abstract: Faghri et al. proposed an algebraic coordinate transformation that transforms an irregular solution domain onto a rectangle. In the present work, this method is extended to axisymmetric problems by mapping an irregular cross section of the solidified zone onto concentric spheres. The calculations are performed for the Stefan number in the range of 0.03 to 0.36, and for several values of the dimensionless geometric parameter characterizing the spheroidal capsule. The results are presented in form of the solid-liquid interface shapes and the ratios of the solidification zone volume to the capsule volume.