The inviscid stagnation-flow solidification problem

Rangel, R. H.; Bian, Xiangjuan

doi:10.1016/0017-9310(95)00260-x

Cited by 22 publications

(7 citation statements)

References 25 publications

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“…Stagnation-ow solidi cation of an inviscid uid that freezes at a common border was considered by Brattkus and Davis [24]. The problem of Stephen's solidi cation of inviscid uid in stagnation ow was solved by Rangel and Bian [25]. Freezing at the subcooled liquid stagnation point (freezing point) was investigated in the two-dimensional Cartesian coordinate system by Lambert and Rangel [26].…”

Section: Introductionmentioning

confidence: 99%

Vapor Solidification of Saturated Air in Two-Dimensional Stagnation Flow

Abbasi

Ghayeni

2018

Scientia Iranica

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This study aims to investigate the stagnation-ow solidi cation of vapor from saturated air. Saturated air with strain rate a impinges on a at plate and, thus, condensation occurs and an icy layer forms on the plate because the plate temperature is below the freezing temperature of water. The ice surface was modeled as an accelerated at plate that moves toward the impinging uid. The unsteady Navier-Stokes equations were subjected to a similarity transformation to obtain a single ordinary di erential equation for velocity distribution. Two methods of solution were used for the energy equation: a nitedi erence numerical technique and a numerical solution of a similarity equation. These two results were compared to determine the superior accuracy. First, freezing time increases as the far-eld temperature decreases from 0 C and, then, rapidly approaches zero as the fareld temperature approaches 0 C. Despite the expectation that condensation would begin at the substrate in a physical experiment, here, the size of the cell next to the substrate controls the time at which condensation begins. It was found that the maximum time before freezing began at an air temperature of about 5 C for 0.1 and 0.2 mm sizes. The ultimate frozen thickness for two saturated air temperatures was presented.

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Section: Introductionmentioning

confidence: 99%

Vapor Solidification of Saturated Air in Two-Dimensional Stagnation Flow

Abbasi

Ghayeni

2018

Scientia Iranica

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“…Concentrating upon the stagnation flow, the solidification of an inviscid fluid at an interface and the effect of its phenomena on morphological instability is investigated by Brattkus et al [12]. The Stefan problem for inviscid stagnation flow by two methods and the solidifying of super-cooled liquid stagnation inviscid flow are considered by Rangel and Lambert [13,14], respectively, in which a numerical solution to the problem using an interface tracking method is compared to analytical solutions for the instantaneous similarity and quasi-steady state. Additionally, the solidification of a viscous stagnation fiowwas investigated by Rangel and Bian [15] with the pressure consideration only along the flow and not along the boundary layer and by applying the method of instantaneous similarity, the temperature field, the solid-liquid interface location, and its growth rate that is valid for the initial stages of solidification were obtained.…”

Section: Introductionmentioning

confidence: 99%

Solidification of Two-Dimensional Viscous, Incompressible Stagnation Flow

Abbassi¹,

Rahimi

2013

Journal of Heat Transfer

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The history of the study of fluid solidiflcation in stagnation flow is limited to a few cases. Among these few studies, only some articles have considered the fluid viscosity and yet pressure variations along the thickness of the viscous layer have not been taken into account and the energy equation has been assumed to be one-dimensional. In this study the solidiflcation of stagnation flows is modeled as an accelerated flat plate moving toward an impinging fluid. The unsteady momentum equations, taking the pressure variations along viscous layer thickness into account, are reduced to ordinary differential equations by the use of proper similarity variables and are solved by using a fourth-order Runge-Kutta integrating method at each prescribed interval of time. In addition, the energy equation is numerically solved at any step for the known velocity and the problem is presented in a two-dimensional Cartesian coordinate. Comparisons of these solutions are made with existing special ranges of past solutions. The fluid temperature distribution, transient velocity component distribution, and, most important of all the rate of solidiflcation or the solidiflcation front are presented for different values of nondimensional Prandtl and Stefan numbers. The results show that an increase of the Prandtl numbers (up to ten times) or an increase of the heat diffusivity ratios (up to two times) causes a decrease of the ultimate frozen thickness by almost half, while the Stefan number has no effect on this thickness and its effect is only on the freezing time.

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“…If there is no fluid flow, then this problem becomes the well-known Stefan problem with Neumann's solution (Carslaw and Jaeger, 1959). Rangel and Bian studied this problem with an iterative numerical method (Rangel and Bian, 1995), and with a method of quasi-steady approximation (Rangel and Bian, 1996). They focused the main attention on the growth of solid and the existence of an asymptotic limit of the solid thickness.…”

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confidence: 99%

Numerical investigation of the transient heat transfer in the inviscid stagnation flow with solidification

Yoo

2000

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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The problem of transient heat transfer and growth of solid in the inviscid stagnation flow when phase change from liquid to solid occurs is considered. A fast and accurate numerical scheme is developed to determine the instantaneous temperature distribution in both solid and liquid phases and the growth rate of solid directly, without iterative calculation. The solution of the dimensionless governing equations is dependent on the three dimensionless parameters. The characteristics of the transient heat transfer and solidification process for all the parameters are elucidated.

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The inviscid stagnation-flow solidification problem

Cited by 22 publications

References 25 publications

Vapor Solidification of Saturated Air in Two-Dimensional Stagnation Flow

Vapor Solidification of Saturated Air in Two-Dimensional Stagnation Flow

Solidification of Two-Dimensional Viscous, Incompressible Stagnation Flow

Numerical investigation of the transient heat transfer in the inviscid stagnation flow with solidification

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