Effect of buoyancy-driven convection on steady state dendritic growth in a binary alloy

2013 ◽  
Vol 22 (11) ◽  
pp. 116805 ◽  
Author(s):  
Ming-Wen Chen ◽  
Bao Wang ◽  
Zi-Dong Wang
Keyword(s):  
Steady State ◽  
Binary Alloy ◽  
Dendritic Growth ◽  
Buoyancy Driven Convection

scholarly journals Reflections on dissipation associated with thermal convection

2013 ◽  
Vol 725 ◽  
Author(s):  
Thierry Alboussière ◽  
Yanick Ricard
Keyword(s):  
Heat Capacity ◽  
Steady State ◽  
Energy Dissipation ◽  
Thermal Convection ◽  
Constant Pressure ◽  
Reference State ◽  
Navier Stokes ◽  
Volume Integral ◽  
Anelastic Equations ◽  
Buoyancy Driven Convection

AbstractBuoyancy-driven convection is modelled using the Navier–Stokes and entropy equations. It is first shown that the coefficient of heat capacity at constant pressure, ${c}_{p} $, must in general depend explicitly on pressure (i.e. is not a function of temperature alone) in order to resolve a dissipation inconsistency. It is shown that energy dissipation in a statistically steady state is the time-averaged volume integral of $- \mathrm{D} P/ \mathrm{D} t$ and not that of $- \alpha T(\mathrm{D} P/ \mathrm{D} t)$. Secondly, in the framework of the anelastic equations derived with respect to the adiabatic reference state, we obtain a condition when the anelastic liquid approximation can be made, $\gamma - 1\ll 1$, independent of the dissipation number.

Research on Phase-Field Model of Three-Dimensional Dendritic Growth for Binary Alloy

2015 ◽  
Vol 12 (11) ◽  
pp. 4289-4296 ◽  
Author(s):  
Li Feng ◽  
Jinfang Jia ◽  
Changsheng Zhu ◽  
Yang Lu ◽  
Rongzhen Xiao ◽  
...  
Keyword(s):  
Binary Alloy ◽  
Phase Field ◽  
Dendritic Growth ◽  
Field Model ◽  
Three Dimensional ◽  
Phase Field Model

CRYSTAL GROWTH AND THE THERMODYNAMICS OF IRREVERSIBLE PROCESSES

1959 ◽  
Vol 37 (6) ◽  
pp. 739-754 ◽  
Author(s):  
J. S. Kirkaldy
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Entropy Production ◽  
Dendritic Growth ◽  
Transport Processes ◽  
Irreversible Processes ◽  
Interface Morphology ◽  
Crystal Face ◽  
Thermodynamics Of Irreversible Processes ◽  
Alloy Crystal

The principle of minimum rate of entropy production is applied to steady-state transport processes in the neighborhood of an alloy crystal face growing into its melt. The procedure gives a satisfactory rationale of observed interface morphology. It is noted that segregation, which occurs in cellular or dendritic growth of alloys, is a direct manifestation of the system's attempt to minimize entropy production by conserving free energy. The general problems of growth of pure and impure single crystals from the melt and vapor are discussed.

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