Non-Fourier Melting of a Semi-Infinite Solid

1977 ◽  
Vol 99 (1) ◽  
pp. 25-28 ◽  
Author(s):  
M. H. Sadd ◽  
J. E. Didlake
Keyword(s):  
Boundary Surface ◽  
Thermal Relaxation ◽  
Heat Propagation ◽  
Melting Phenomenon ◽  
Thermal Disturbance ◽  
Interface Location ◽  
Fourier Theory ◽  
Fourier Heat Conduction ◽  
Solid Liquid Interface ◽  
Solid Liquid

The melting of a semi-infinite solid subjected to a step change in temperature is solved according to a non-Fourier heat conduction law postulated by Cattaneo and Vernotte. Unlike the classical Fourier theory which predicts an infinite speed of heat propagation, the non-Fourier theory implies that the speed of a thermal disturbance is finite. The effect of this finite thermal wave speed on the melting phenomenon is determined. The problem is solved by following a similar method as used by Carslaw and Jaeger for the corresponding Fourier problem. Non-Fourier results differ from Fourier theory only for small values of time. Comparing the temperature profiles and the solid-liquid interface location for aluminum, differences between the two theories were significant only for times on the order of 10−9–10−11 s and in a region within approximately 10−4–10−5 cm from the boundary surface. However, these results are based on an approximate value of the thermal relaxation time.

Analysis of the Thermal Response in Micromachine under the Thermal Shock

2011 ◽  
Vol 464 ◽  
pp. 583-587
Author(s):  
Ying Ze Wang ◽  
Xin Nan Song
Keyword(s):  
Heat Conduction ◽  
Relaxation Times ◽  
Boundary Surface ◽  
Thermal Relaxation ◽  
Thermal Response ◽  
Heat Propagation ◽  
Hyperbolic Heat Conduction ◽  
Thermal Relaxation Times ◽  
Fourier Heat Conduction ◽  
Sudden Temperature Change

The thermal response for given micromachine with the boundary surface exposed to sudden temperature change is studied by deriving an analytical solution of the hyperbolic heat conduction equation. Using the obtained analytical expression, the temperature profiles at the outer surface and interior of the micro beam are evaluated for various thermal relaxation times. The behaviors of hyperbolic heat propagation in micro beam are analyzed and possible anomalies are discussed by comparing the thermal behaviors of Fourier heat conduction.

A Moving Boundary Problem in a Finite Domain

1990 ◽  
Vol 57 (1) ◽  
pp. 50-56 ◽  
Author(s):  
Z. Dursunkaya ◽  
S. Nair
Keyword(s):  
Temperature Distribution ◽  
Differential Equations ◽  
Moving Boundary ◽  
Moving Boundary Problem ◽  
Fourier Series Expansion ◽  
Finite Domain ◽  
Finite Region ◽  
Interface Location ◽  
Solid Liquid Interface ◽  
Solid Liquid

The heat conduction and the moving solid-liquid interface in a finite region is studied numerically. A Fourier series expansion is used in both phases for spatial temperature distribution, and the differential equations are converted to an infinite number of ordinary differential equations in time. These equations are solved iteratively for the interface location as well as for the temperature distribution. The results are compared with existing solutions for low Stefan numbers. New results are presented for higher Stefan numbers for which solutions are unavailable.

Analytical Modeling of Outward Solidification With Convective Boundary in Cylindrical Coordinates

2020 ◽  
Author(s):  
Minghan Xu ◽  
Saad Akhtar ◽  
Ahmad F. Zueter ◽  
Mahmoud A. Alzoubi ◽  
Agus P. Sasmito
Keyword(s):  
Moving Boundary ◽  
Two Phase ◽  
Convective Boundary ◽  
Interface Motion ◽  
Stefan Number ◽  
Melting Phenomenon ◽  
Approximate Analytical Solutions ◽  
Highly Nonlinear ◽  
Solid Liquid Interface ◽  
Solid Liquid

Abstract Solidification consists of three stages at macroscale: subcooling, freezing and cooling. Classical two-phase Stefan problems describe freezing (or melting) phenomenon initially not at the fusion temperature. Since these problems only define subcooling and freezing stages, an extension to characterize the cooling stage is required to complete solidification. However, the moving boundary in solid-liquid interface is highly nonlinear, and thus exact solution is restricted to certain domains and boundary conditions. It is therefore vital to develop approximate analytical solutions based on physically tangible assumptions, like a small Stefan number. This paper proposes an asymptotic solution for a Stefan-like problem subject to a convective boundary for outward solidification in a hollow cylinder. By assuming a small Stefan number, three temporal regimes and four spatial layers are considered in the asymptotic analysis. The results are compared with numerical method. Further, effects of Biot numbers are also investigated regarding interface motion and temperature profile.

scholarly journals Numerical Solution of Heat Transfer Process in PCM Storage Using Tau Method

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
B. Heydari ◽  
F. Talati
Keyword(s):  
Phase Change ◽  
Phase Change Materials ◽  
Numerical Approach ◽  
Heat Transfer Process ◽  
Liquid Interface ◽  
Tau Method ◽  
Two Dimensional ◽  
Interface Location ◽  
Solid Liquid Interface ◽  
Solid Liquid

Thermal energy storage units that utilize phase change materials have been widely employed to balance temporary temperature alternations and store energy in many engineering systems. In the present paper, an operational approach is proposed to the Tau method with standard polynomial bases to simulate the phase change problems in latent heat thermal storage systems, that is, the two-dimensional solidification process in rectangular finned storage with a constant end-wall temperature. In order to illustrate the efficiency and accuracy of the present method, the solid-liquid interface location and the temperature distribution of the fin for three test cases with different geometries are obtained and compared to simplified analytical results in the published literature. The results indicate that using a two-dimensional numerical approach can predict the solid-liquid interface location more accurately than the simplified analytical model in all cases, especially at the corners.

Numerical and Experimental Investigation of Phase Change Heat Transfer in the Presence of Rayleigh–Benard Convection

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Mohammad Parsazadeh ◽  
Xili Duan
Keyword(s):  
Nusselt Number ◽  
Phase Change ◽  
Local Heat ◽  
Liquid Interface ◽  
Interface Location ◽  
Local Heat Flux ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Abstract This research investigates the melting rate of a phase change material (PCM) in the presence of Rayleigh–Benard convection. A scaling analysis is conducted for the first time for such a problem, which is useful to identify the parameters affecting the phase change rate and to develop correlations for the solid–liquid interface location and the Nusselt number. The solid–liquid interface and flow patterns in the liquid region are analyzed for PCM in a rectangular enclosure heated from bottom. Numerical and experimental results both reveal that the number of Benard cells is proportional to the ratio of the length of the rectangular enclosure over the solid–liquid interface location (i.e.,, the liquified region aspect ratio). Their effect on the local heat flux is also analyzed as the local heat flux profile changes with the solid–liquid interface moving upward. The variations of average Nusselt number are obtained in terms of the Stefan number, Fourier number, and Rayleigh number. Eventually, the experimental and numerical data are used to develop correlations for the solid–liquid interface location and average Nusselt number for this type of melting problems.

Uncertainty Analysis of Solid-Liquid-Vapor Phase Change of a Metal Particle Subject to Nanosecond Laser Heating

2012 ◽  
Author(s):  
Hao Peng ◽  
Yuwen Zhang ◽  
P. Frank Pai
Keyword(s):  
Phase Change ◽  
Vapor Phase ◽  
Laser Heating ◽  
Metal Particles ◽  
Nanosecond Laser ◽  
Uncertain Parameters ◽  
Interface Location ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Liquid Vapor

Effects of uncertainties of various parameters, including laser fluence, diameter of metal powder articles, laser pulse width and initial temperature of metal particles, on solid-liquid-vapor phase change processes of metal particles under nanosecond laser heating are investigated in this paper. A systematic approach of simulating phase change with uncertain parameters are presented and a sample-based stochastic model are established to investigate the influence of different uncertain parameters on maximum surface temperature of metal particles, maximum solid-liquid interface location, maximum liquid-vapor interface location, maximum saturation temperature and maximum recoil pressure, and time needed to reach maximum solid-liquid interface location. The results show that the mean value and standard deviation of laser fluence have dominant effects on all output parameters.

Uncertainty Analysis of Solid-Liquid-Vapor Phase Change of a Metal Particle Subject to Nanosecond Laser Heating

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Hao Peng ◽  
Yuwen Zhang ◽  
P. Frank Pai
Keyword(s):  
Phase Change ◽  
Vapor Phase ◽  
Laser Heating ◽  
Metal Particles ◽  
Nanosecond Laser ◽  
Uncertain Parameters ◽  
Interface Location ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Liquid Vapor

The effects of the uncertainties of various parameters, including the laser fluence, diameter of metal powder particles, laser pulse width, and the initial temperature of metal particles on solid-liquid-vapor phase change processes of metal particles under nanosecond laser heating are investigated in this paper. A systematic approach of simulating the phase change with uncertain parameters is presented and a sample-based stochastic model is established in order to investigate the influence of different uncertain parameters on the maximum surface temperature of metal particles, the maximum solid-liquid interface location, maximum liquid-vapor interface location, maximum saturation temperature, and maximum recoil pressure and the time needed to reach the maximum solid-liquid interface location. The results show that the mean value and standard deviation of the laser fluence have dominant effects on all output parameters.

Atom-probe analysis of the solid-liquid interface

1995 ◽  
Vol 53 ◽  
pp. 676-677
Author(s):  
J.A. Panitz
Keyword(s):  
Molecular Level ◽  
Selective Adsorption ◽  
Electronic Devices ◽  
Atom Probe ◽  
Chemical Agent ◽  
Hostile Environment ◽  
Solid Interface ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Chemically Selective

The first few atomic layers of a solid can form a barrier between its interior and an often hostile environment. Although adsorption at the vacuum-solid interface has been studied in great detail, little is known about adsorption at the liquid-solid interface. Adsorption at a liquid-solid interface is of intrinsic interest, and is of technological importance because it provides a way to coat a surface with monolayer or multilayer structures. A pinhole free monolayer (with a reasonable dielectric constant) could lead to the development of nanoscale capacitors with unique characteristics and lithographic resists that surpass the resolution of their conventional counterparts. Chemically selective adsorption is of particular interest because it can be used to passivate a surface from external modification or change the wear and the lubrication properties of a surface to reflect new and useful properties. Immunochemical adsorption could be used to fabricate novel molecular electronic devices or to construct small, “smart”, unobtrusive sensors with the potential to detect a wide variety of preselected species at the molecular level. These might include a particular carcinogen in the environment, a specific type of explosive, a chemical agent, a virus, or even a tumor in the human body.

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