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Showing papers by "Ephraim M Sparrow published in 1975"


Journal ArticleDOI
TL;DR: In this article, 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.
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.

385 citations


01 Jan 1975
TL;DR: In this article, 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.
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.

372 citations


Journal ArticleDOI
TL;DR: In this paper, the authors measured the transfer coefficients resulting from the impingement of a slot jet on a plane surface using naphthalene sublimation technique and found that the surface distributions of the transfer coefficient were bell-shaped, with the largest value at the stagnation point.

121 citations







Journal ArticleDOI
TL;DR: In this article, the authors measured local wall heat transfer coefficients and fluid temperature distributions in a cavity consisting of a pair of parallel disks and a cylindrical shroud, where one of the disks was rotating, whereas the other disk and the shroud were stationary.
Abstract: Local wall heat transfer coefficients and fluid temperature distributions were measured in a cavity consisting of a pair of parallel disks and a cylindrical shroud. One of the disks was rotating, whereas the other disk and the shroud were stationary. Coolant air entered the cavity through a central aperture in the rotating disk and exited through an annular gap at the rim of the rotating disk. The coolant flow rate, the disk rotational speed, and the cavity aspect ratio (disk separation distance to radius) were varied throughout the course of the experiments. The latter parameter took on values as large as two. The heat transfer results and the fluid isotherm maps suggested that the flow pattern within the cavity was markedly different depending upon whether the coolant stream or the pumping action of the rotating disk was predominant. The surface distributions of the heat transfer coefficients reversed the direction of their spatial variation over the range from no rotation to high rotation. However, the maximum values of the Nusselt number curves for no rotation were as high as the maximum values of the curves for corresponding cases with high rotation. The isotherm maps for the no-rotation cases revealed that the major portion of the cavity was filled with nearly isothermal fluid. On the other hand, in the presence of strong rotation, there were substantial fluid temperature variations throughout the cavity.

6 citations



Journal ArticleDOI
TL;DR: It was shown that two-film systems can yield reasonably high values of the unextinguished component, with minimal sensitivity of the extinguished component to off-design conditions.
Abstract: An analysis is made of reflection polarizers consisting of two transparent films on an absorbing substrate. A method is described for determining the angles of incidence at which the reflectance of either component of polarization is extinguished. It is demonstrated that polarized light can be obtained over a finite range of incidence angles. This is in contrast to a polarizer having a single transparent film, where polarization occurs only at a specific angle of incidence. At each angle of incidence in the polarizing range, any one of a number of discrete thicknesses of the films can be used to obtain polarized light; and the procedures for finding these thicknesses are described. Numerical application of the theory was made for metallic substrates that range from good to intermediate reflectors. The results serve to illustrate most of the significant characteristics of two-film polarizers. It was shown that two-film systems can yield reasonably high values of the unextinguished component, with minimal sensitivity of the extinguished component to off-design conditions.

Journal ArticleDOI
TL;DR: In this article, the Navier-Stokes and energy equations are expanded in series, with 1 √ Re as the expansion parameter, and the latter equations were solved by a difference-differential method, with Pr = 0·72 for the energy equation.