Melting of a Free Solid in a Spherical Enclosure: Effects of Subcooling

1989 ◽  
Vol 111 (1) ◽  
pp. 32-36 ◽  
Author(s):  
Sanjay K. Roy ◽  
Subrata Sengupta
Keyword(s):  
Temperature Gradient ◽  
Moving Boundary ◽  
Solid Phase ◽  
Closed Form Solution ◽  
Melting Process ◽  
Form Solution ◽  
Solid Core ◽  
Infinite Domain ◽  
Thermal Systems ◽  
Time Step

The melting process within a spherical enclosure with the solid phase uniformly subcooled initially has been studied. The preliminary analysis of the problem is similar to a previous study where the degree of subcooling was zero. However, the heat transfer equation has been modified to include the effects of a temperature gradient in the solid core. As a result, a closed-form solution cannot be obtained. At every time step, the unsteady conduction equation has been solved numerically using a toroidal coordinate system, which has been suitably transformed to immobilize the moving boundary and to transform the infinite domain into a finite one. The temperature gradient at the surface is now used to solve the film equation numerically. The melt time, Nusselt number, and melt flux distributions have been obtained over a range of the parameters (Sb, Ste/Cp*, and 1 /Prα*) normally encountered in solar thermal systems.

Study on Contact Melting Inside an Elliptical Tube With Nonisothermal Wall

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Yuansong Zhao ◽  
Wenzhen Chen ◽  
Fengrui Sun
Keyword(s):  
Temperature Distribution ◽  
Aspect Ratio ◽  
Wall Temperature ◽  
Film Theory ◽  
Closed Form Solution ◽  
Cylindrical Tube ◽  
Melting Process ◽  
Contact Melting ◽  
Form Solution ◽  
Basic Equations

The problem of contact melting inside an elliptical tube with nonisothermal wall is investigated. A theoretical model, which the inner wall temperature of source varied with angle ϕ, is established by applying film theory. The basic equations of the melting process are solved theoretically, and a closed-form solution is obtained. Under certain cases, comparisons of results for the melting velocity with those of contact melting inside a horizontal cylindrical tube with nonisothermal wall and an elliptical tube with constant temperature are reported for the validity of the solution in this paper. Effects of aspect ratio J and inner wall temperature distribution are critically assessed. It is found that the smaller the elliptical aspect ratio J is, the greater the effect of wall temperature distribution on melting velocity, and the time to complete melting increases with the augment of coefficient c in temperature distribution.

Laminar gravitational convection of heat in dead-end channels

1981 ◽  
Vol 110 ◽  
pp. 97-113 ◽  
Author(s):  
Terry W. Sturm
Keyword(s):  
Temperature Gradient ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Gravitational Convection ◽  
Longitudinal Temperature Gradient ◽  
Dead End ◽  
Longitudinal Temperature ◽  
Surface Heat Transfer Coefficient ◽  
Energy Equations

A closed-form solution of the coupled momentum and thermal energy equations is obtained for laminar gravitational circulation of water resulting from a longitudinal temperature gradient in a dead-end channel. The temperature gradient is determined by the rate of heat loss from the water surface. The solution is shown to be dependent on a modified Rayleigh number which involves the local surface heat-transfer coefficient. An experimental study was conducted, and the results are compared with the closed-form solution.

On the Numerical Implementation of Elastoplastic Models

1984 ◽  
Vol 51 (2) ◽  
pp. 283-288 ◽  
Author(s):  
P. J. Yoder ◽  
R. G. Whirley
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Computational Efficiency ◽  
Kinematic Hardening ◽  
Closed Form Solution ◽  
Form Solution ◽  
Perturbation Solution ◽  
Numerical Implementation ◽  
Time Step ◽  
Trade Offs

A closed-form solution is given for the way stresses evolve during an elastoplastic time step under conditions of purely kinematic hardening or softening. When isotropic effects are included, the analysis becomes more difficult, so a perturbation solution is developed. These solutions are then compared with various algorithms commonly used in finite element programs in order to assess the trade-offs between accuracy and computational efficiency.

Gravity and Conduction Driven Melting in a Sphere

1986 ◽  
Vol 87 ◽  
Author(s):  
P A. Bahrami ◽  
T. G. Wang
Keyword(s):  
Phase Change ◽  
Closed Form Solution ◽  
Melting Process ◽  
Step Function ◽  
Form Solution ◽  
Film Condensation ◽  
Theoretical Point ◽  
Void Space ◽  
Free Expansion ◽  
Interface Position

AbstractThe fundamental processes of melting, the well known Stefan and Neumann problems, have been of great interest from a theoretical point of view as well as for their wide applications. The yet unmolten part of the material undergoing phase change within spherical containments is generally presumed to remain stationary, an unlikely occurrence in practice. The differing densities of the liquid and the solid may readily cause a force imbalance on the solid in gravitational and perhaps microgravitational environments, thereby moving the solid away from the center. In the present work, an approach related to the theories of lubrication and film condensation was employed and an approximate closed-form solution of melting within spheres was obtained. It was shown that a group of dimensionless parameters containing, Prandtl, Archimedes and Stefan numbers describes the melting process. Fundamental heat transfer experiments were also performed on the melting of a phase-change medium in a spherical shell. Free expansion of the medium into a void space within the sphere was permitted. A step function temperature jump on the outer shell wall was imposed and the timewise evolution of the melting process and the position of the solid-liquid interface was photographically recorded. Numerical integration of the interface position data yielded information about the melted mass and the energy of melting that support the theory.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

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