Phase-Change in Finite Slabs With Time-Dependent Convective Boundary Conditions

Volume 3 ◽  
2004 ◽  
Author(s):  
Anand P. Roday ◽  
Michael J. Kazmierczak
Keyword(s):  
Phase Change ◽  
Change Process ◽  
Initial Conditions ◽  
Convective Boundary Condition ◽  
Liquid Interface ◽  
Convective Boundary ◽  
Phase Change Process ◽  
The Right ◽  
Solid Liquid Interface ◽  
Solid Liquid

The heat balance integral method is used to solve one-dimensional phase-change problem in a finite slab with time-dependent convective boundary condition, [T∞,1(t)], applied at the left face. The temperature, T∞,1(t), decreases linearly with time; the other face of the slab is subjected to a constant convective boundary condition with T∞,2 held fixed at the ambient temperature. Two initial conditions are investigated: temperature of the solid below the melting point (subcooled), and initially at the fusion temperature (Tf). The temperature, T∞,1(t) at time t = 0 is so chosen such that convective heating takes place and the slab begins to melt (i.e., T∞,1(0)> Tf> T∞,2). Thus the solid-liquid interface proceeds forward to the right. As time continues, and T∞,1(t) decreases with time, the phase-change front slows, stops, and may even reverse direction. Hence this problem features sequential melting and freezing of the slab with partial penetration of the solid-liquid front before reversal of the phase-change process. It should, however, be noted that the study is limited to only one solid-liquid interface at any given time during the phase-change process (either melting or freezing) and that slight subcooling of the melt is allowed. The effect of varying the Biot number at the right face of the slab, for both the initial conditions, is also investigated to determine its impact on the growth/recession of the solid-liquid interface. Temperature profiles in both regions (liquid and solid) are reported in detail. The effect of a slower decay rate of T∞,1(t) on the phase-change process is also analyzed for the initial condition of the slab being at the fusion temperature.

Numerical Analysis of Aerospace Nickel-Based Single-Crystal Superalloy Weldability Part I: Crystallography-Dependent Dendrite Growth

2021 ◽  
Vol 1018 ◽  
pp. 3-12
Author(s):  
Zhi Guo Gao
Keyword(s):  
Single Crystal ◽  
Weld Pool ◽  
Dendrite Growth ◽  
Liquid Interface ◽  
Solidification Cracking ◽  
Microstructure Development ◽  
Growth Region ◽  
The Right ◽  
Solid Liquid Interface ◽  
Solid Liquid

The thermal-metallurgical modeling of microstructure development was further advanced during single-crystal superalloy weld pool solidification by coupling of heat transfer model, columnar/equiaxed transition (CET) model and multicomponent dendrite growth model on the basis criteria of minimum dendrite velocity, constitutional undercooling and marginal stability of planar front. It is clearly indicated that heat input (laser power and welding speed) and welding configuration simultaneously influence the stray grain formation, columnar/equiaxed transition and dendrite growth. For beneficial (001) and [100] welding configuration, the microstructure development along the solid/liquid interface is symmetrically distributed about the weld pool centerline throughout the weld pool. Finer columnar in [001] epitaxial dendrite growth region is kinetically favored at the bottom of the weld pool. For detrimental (001) and [110] welding configuration, the microstructure development along the solid/liquid interface is asymmetrically distributed. The dendrite trunk spacing along the solid/liquid interface from the beginning to end of solidification morphologically increases on the left side of the weld pool, while it spontaneously decreases on the right side. The vulnerable location of solidification cracking is confined in the [100] dendrite growth region on the right side of the weld pool because of increasing metallurgical contributing factors of severe stray grain formation, centerline grain boundary formation and coarse dendrite size. The mechanism of crystallography-dependent asymmetrical solidification cracking due to microstructure anomalies is proposed. It is crystallographically favorable for predominant morphology instability to deteriorate weldability. Active [100] dendrite growth region is diminished in the shallow elliptical weld pool by optimum low heat input (low laser power and high welding speed) with (001) and [100] welding configuration to essentially facilitate single-crystal solidification conditions and provide enough resistant to solidification cracking. Moreover, the theoretical predictions agree well with the experiment results. The reliable weldability maps are therefore established to determine the prerequisite for successful crack-free laser welding or cladding. The useful model is also applicable for other single-crystal superalloys with similar metallurgical properties.

scholarly journals Approximate Analytical Solution for One-Dimensional Solidification Problem of a Finite Superheating Phase Change Material Including the Effects of Wall and Thermal Contact Resistances

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Hamid El Qarnia ◽  
Fayssal El Adnani ◽  
El Khadir Lakhal
Keyword(s):  
Analytical Solution ◽  
Phase Change ◽  
Phase Change Material ◽  
Liquid Interface ◽  
Solid Shell ◽  
Interface Position ◽  
Temperature Distributions ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Change Material

This work reports an analytical solution for the solidification of a superheating phase change material (PCM) contained in a rectangular enclosure with a finite height. The analytical solution has been obtained by solving nondimensional energy equations by using the perturbation method for a small perturbation parameter: the Stefan number,ε. This analytical solution, which takes into account the effects of the superheating of PCM, finite height of the enclosure, thickness of the wall, and wall-solid shell interfacial thermal resistances, was expressed in terms of nondimensional temperature distributions of the bottom wall of the enclosure and both PCM phases, and the dimensionless solid-liquid interface position and its dimensionless speed. The developed solution was firstly compared with that existing in the literature for the case of nonsuperheating PCM. The predicted results agreed well with those published in the literature. Next, a parametric study was carried out in order to study the impacts of the dimensionless control parameters on the dimensionless temperature distributions of the wall, the solid shell, and liquid phase of the PCM, as well as the solid-liquid interface position and its dimensionless speed.

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.

Energy Storage With Solid/Liquid Phase Change in Presence of Natural Convection

2001 ◽  
Author(s):  
M. Pinelli ◽  
S. Piva
Keyword(s):  
Natural Convection ◽  
Energy Storage ◽  
Liquid Phase ◽  
Phase Change ◽  
Change Process ◽  
Solid Phase ◽  
High Energy ◽  
Heat Transfer Process ◽  
Phase Change Process ◽  
Solid Liquid

Abstract Solid/liquid phase change process has received great attention for its capability to obtain high energy storage efficiency. In order to analyse these systems, undergoing a solid/liquid phase change, in many situations the heat transfer process can be considered conduction-dominated. However, in the past years, it has been shown that natural convection in the liquid phase can significantly influence the phase change process in terms of temperature distributions, interface displacement and energy storage. In this paper, a procedure to analyse systems undergoing liquid/solid phase change in presence of natural convection in the liquid phase based on the utilisation of a commercial computer code (FLUENT), has been developed. This procedure is applied to a cylinder cavity heated from above and filled with a Phase Change Material. It was found that when the coupling with the environment, even if small, is considered, natural convection in the liquid phase occurs. The numerical results are then compared with available experimental data. The analysis shows that the agreement between numerical and experimental results is significantly improved when the results are obtained considering the presence of circulation in the liquid phase instead of considering the process only conduction-dominated. Furthermore, some interesting features of the flow field are presented and discussed.

Numerical Simulation of the Effect of the Size of Nanoparticles on the Solidification Process of Nanoparticle-Enhanced Phase Change Materials

2012 ◽  
Author(s):  
Yousef M. F. El Hasadi ◽  
J. M. Khodadadi
Keyword(s):  
Particle Size ◽  
Phase Change ◽  
Phase Change Materials ◽  
Concentration Field ◽  
Solidification Process ◽  
Liquid Interface ◽  
Constitutional Supercooling ◽  
Fluid Mixture ◽  
Solid Liquid Interface ◽  
Solid Liquid

Nanoparticle-enhanced phase change materials (NEPCM) were proposed recently as alternatives to conventional phase change materials due to their enhanced thermophysical properties. In this study, the effect of the size of the nanoparticles on the morphology of the solid-liquid interface and evolving concentration field, during solidification had been reported. The numerical method that was used is based on the one-fluid-mixture model. The model takes into account the thermal as well as the solutal convection effects. A square cavity model was used in the simulation. The NEPCM that was composed of a suspension of copper nanoparticles in water was solidified from the bottom. The nanoparticles size used were 5 nm and 2 nm. The temperature difference between the hot and cold sides was 5 degrees centigrade and the loading of the nanoparticles that have been used in the simulation was 10% by mass. The results obtained from the model were compared with those existing in the literature, and the comparison was satisfactory. The solid-liquid interface for the case of NEPCM with 5 nm particle size was almost planar throughout the solidification process. However, for the case of the NEPCM with particle size of 2 nm, the solid-liquid interface evolved from a planar stable shape to an unstable dendritic shape, as the solidification process proceeded with time. This was attributed to the constitutional supercooling effect. It has been observed that the constitutional supercooling effect is more pronounced as the particle size decreases. Furthermore, the freezing time increases as the particle size decreases.

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