• Journal of the Korean Crystal Growth and Crystal Technology
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• v.20 no.3
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• pp.117-124
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• 2010

For Ar=5, Pr=1.18, Le=0.15, Pe=2.89, Cv=1.06, $P_B$=20 Torr, the effects of impurity $(N_2)$ on thermally and solutally buoyancy-driven convection ($Gr_t=3.46{\times}10^4$ and $Gr_s=6.02{\times}10^5$, respectively) are theoretically investigated for further understanding and insight into an essence of thermo-solutal convection occurring in the vapor phase during the physical vapor transport. For $10K{\leq}{\Delta}T{\leq}50K$, the crystal growth rates are intimately related and linearly proportional to a temperature difference between the source and crystal region which is a driving force for thermally buoyancy-driven convection. Moreover, both the dimensionless Peclet number (Pe) and dimensional maximum velocity magnitudes are directly and linearly proportional to ${\Delta}T$. The growth rate is second order-exponentially decayed for $2{\leq}Ar{\leq}5$. This is related to a finding that the effects of side walls tend to stabilize the thermo-solutal convection in the growth reactor. Finally, the growth rate is found to be first order exponentially decayed for $10{\leq}P_B{\leq}200$ Torr.

• Solar Energy
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• v.2 no.1
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• pp.9-16
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• 1982

The problem of transient laminar natural convection in compressible fluid in a rectangular enclosure is considered. The upper and lower boundaries of the enclosure are thermally insulating and the side boundaries are maintained at fixed temperatures. The fluid is considered to be a perfect gas with constant viscosity and thermal conductivity and the formulation differs from the boussinesq simplification in that the effects of variable density are completely retained. The motions are restricted to two dimensions. For incompressible fluid, the natural convection is driven mainly by buoyancy force. But the solutions show that for compressible fluid, the natural convection is driven by pressure and buoyancy forces and the thermally induced motion is acoustic in nature.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.16 no.4
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• pp.149-156
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• 2006

For an aspect ratio (transport length-to-width) of 5, Pr = 2.89, Le = 0.018, Pe = 2.29, Cv = 1.11, $P_B$=40 Torr, solutally buoyancy-driven convection $(Gr_s=3.03{\times}10^5)$ due to the disparity in the molecular weights of the component A $(Hg_2Cl_2)$ and B (He) is stronger than thermally buoyancy-driven convection $(Cr_t=1.66{\times}10^4)$. The crystal growth rate is decreased exponentially for $2.5\;{\leq}\;Ar\;{\leq}\;5$, with (1) the linear temperature profile and a fixed temperature difference, (2) the imposed thermal profile, a fixed crystal region and varied temperature difference. This is related to the finding that the effects of side walls tend to stabilize convection in the growth reactor. But, with the imposed thermal profile, a fixed source region and varied temperature difference, the rate is increased far $2\;{\leq}\;Ar\;{\leq}\;3$, and remains nearly unchanged for $3\;{\leq}\;Ar\;{\leq}\;5$.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.18 no.6
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• pp.225-231
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• 2008

For an aspect ratio (transport length-to-width) of 5, Pr=1.13, Le=1.91, Pe=4.3, Cv=1.01, $P_B=20\;Torr$, the effects of addition of inert gas Ne on thermally buoyancy-driven convection ($Gr=2.44{\times}10^3$) are numerically investigated for further understanding and insight into essence of transport phenomena in two dimensional horizontal enclosures. For $10K{\leq}{\Delta}T{\leq}50\;K$, the crystal growth rate increases from 10 K up to 20 K, and then is slowly decreased until ${\Delat}T=50\;K$, which is likely to be due to the effects of thermo-physical properties stronger than the temperature gradient corresponding to driving force for thermal convection. The dimensional maximum velocity gratitude reflecting the intensity of thermal convection is directly and linearly proportional to the temperature difference between the source and crystal regions. The rate is first order-exponentially decreased for $2{\leq}Ar{\leq}5$. This is related to the finding that the effects of side walls tend to stabilize convection in the growth reactor. In addition, the rate is first order exponentially decayed for $10{\leq}P_B{\leq}200\;Torr$.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.17 no.6
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• pp.231-237
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• 2007

For an aspect ratio (transport length-to-width) of 5, Pr=3.34, Le=0.078, Pe=4.16, Cv=1.01, $P_B=50$ Torr, only thermally buoyancy-driven convection ($Gr=4.83{\times}10^5$) is considered in this study in spite of the disparity in the molecular weights of the component A ($Hg_2Cl_2$) and B which would cause thermally and/or solutally buoyancy-driven convection. The crystal growth rate and the maximum velocity vector magnitude are decreased exponentially for $3{\le}Ar{\le}5$, for (1) adiabatic walls and (2) the linear temperature profile, with a fixed source temperature. This is related to the finding that the effects of side walls tend to stabilize convection in the growth reactor. The rate for the linear temperature profiles walls is slightly greater than for the adiabatic walls far varied temperature differences and aspect ratios. With the imposed thermal profile, a fixed source region, both the rate and the maximum velocity vector magnitude increase linearly with increasing the temperature difference for $10{\le}{\Delta}T{\le}50K$.