A relation between surface temperature and time for a phase change process with a convective boundary condition

1979 ◽  
Vol 6 (3) ◽  
pp. 189-197
Author(s):  
A Solomon
Keyword(s):  
Boundary Condition ◽  
Surface Temperature ◽  
Phase Change ◽  
Change Process ◽  
Convective Boundary Condition ◽  
Convective Boundary ◽  
Phase Change Process

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.

Phase Change Process Inside a Small-radii Cylinder Subjected to Cyclic Convective Boundary Conditions: a Numerical Study

2021 ◽  
Author(s):  
Yousef Kanani ◽  
Avijit Karmakar ◽  
Sumanta Acharya
Keyword(s):  
Heat Transfer ◽  
Surface Temperature ◽  
Phase Change ◽  
Phase Change Materials ◽  
Numerical Study ◽  
Convective Boundary Condition ◽  
Freezing Process ◽  
Fourier Number ◽  
Two Phase ◽  
Convective Boundary

Abstract We numerically investigate the melting and solidi?cation behavior of phase change materials encapsulated in a small-radii cylinder subjected to a cyclic convective boundary condition (square wave). Initially, we explore the effect of the Stefan and Biot numbers on the non-dimensionalized time required (i.e. reference Fourier number Tref ) for a PCM initially held at Tcold to melt and reach the cross?ow temperature Thot. The increase in either Stefan or Biot number decreases Tref and can be predicted accurately using a correlation developed in this work. The variations of the PCM melt fraction, surface temperature, and heat transfer rate as a function of Fourier number are reported and analyzed for the above process. We further study the effect of the cyclic Fourier number on the periodic melting and freezing process. The melting or freezing front initiates at the outer periphery of the PCM and propagates towards the center. At higher frequencies, multiple two-phase interfaces are generated (propagating inward), and higher overall heat transfer is achieved as the surface temperature oscillates in the vicinity of the melting temperature, which increases the effective temperature difference driving the convective heat transfer.

Impact of surface temperature and convective boundary conditions on a Nanofluid flow over a radially stretched Riga plate

2021 ◽  
pp. 095440892110544
Author(s):  
K.V. Prasad ◽  
Hanumesh Vaidya ◽  
Fateh Mebarek-Oudina ◽  
Rajashekhar Choudhari ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Surface Temperature ◽  
Surface Concentration ◽  
Mass Transfer Process ◽  
Convective Boundary Condition ◽  
Convective Boundary Conditions ◽  
Convective Boundary ◽  
Analytical Methodology ◽  
Riga Plate

The current work provides the optimal homotopic analytical methodology for the steady circulation over a non-isothermal radially stretched Riga plate/disc unit. The attributes of the heat, along with the mass transfer process, are assessed in the existence of variable transport and magnetic features. Radial stretched Riga disc is considered along with additional realistic boundary heating conditions, namely, prescribed surface temperature as well as prescribed surface concentration, convective boundary conditions and also zero mass flux concentration on the surface area of the Riga disc. The model tracks Brownian motion as well as the thermal diffusion of nanoparticles in fluid circulation all at once. Regulating equations, which are highly coupled, are changed right into non-dimensional equations using appropriate transformations of similarity. Through assembling series solutions, the resulting framework is planned and examined. Graphic summaries are offered for the rheological qualities of various parameters in size for velocity, temperature, as well as nanoparticles. The modified Hartman number improves the velocity distribution and reduces the temperature distribution in both prescribed surface temperature and convective boundary condition cases. The effect of the chemical reaction parameter shows the reduced concentration distribution for the prescribed surface temperature case. In contrast, it is precisely the opposite in the convective boundary condition case.

scholarly journals Determination of One Unknown Thermal Coefficient through a Mushy Zone Model with a Convective Overspecified Boundary Condition

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Andrea N. Ceretani ◽  
Domingo A. Tarzia
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Mushy Zone ◽  
Phase Change ◽  
Convective Boundary Condition ◽  
Zone Model ◽  
Thermal Coefficient ◽  
Convective Boundary

A semi-infinite material under a solidification process with the Solomon-Wilson-Alexiades mushy zone model with a heat flux condition at the fixed boundary is considered. The associated free boundary problem is overspecified through a convective boundary condition with the aim of the simultaneous determination of the temperature, the two free boundaries of the mushy zone and one thermal coefficient among the latent heat by unit mass, the thermal conductivity, the mass density, the specific heat, and the two coefficients that characterize the mushy zone, when the unknown thermal coefficient is supposed to be constant. Bulk temperature and coefficients which characterize the heat flux and the heat transfer at the boundary are assumed to be determined experimentally. Explicit formulae for the unknowns are given for the resulting six phase-change problems, besides necessary and sufficient conditions on data in order to obtain them. In addition, relationship between the phase-change process solved in this paper and an analogous process overspecified by a temperature boundary condition is presented, and this second problem is solved by considering a large heat transfer coefficient at the boundary in the problem with the convective boundary condition. Formulae for the unknown thermal coefficients corresponding to both problems are summarized in two tables.

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