• 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 $10{\leq}P_B{\leq}200\;Torr$.

• Advances in nano research
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• v.10 no.3
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• pp.221-234
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• 2021

During the previous few years, phenomenon of bioconvection along with the use of nanoparticles showed large number of applications in technological and industrial field. This paper analyzed the bioconvection phenomenon in magnetohydrodynamic boundary layer flow of a Powell-Eyring nanoliquid past a stretchable cylinder with Cattaneo-Christov heat flux. In addition, the impacts of chemical reaction and heat generation/absorption parameter are considered. By the use of appropriate transformation, the governing PDEs (nonlinear) have been transformed and formulated into nonlinear ODEs. The resulting nonlinear ODEs subjected to relevant boundary conditions are solved analytically through homotopy analysis method which is programmed in Mathematica software. Graphical and numerical results versus physical quantities like velocity, temperature, concentration and motile microorganism are investigated under the impact of physical parameters. It is noted that velocity profile enhances as the curvature parameter A and Eyring-Powell fluid parameter M increases but a decline manner for large values of buoyancy ratio parameter Nr and bio-convection Rayleigh number Rb. In the presence of Prandtl number Pr, Eyring-Powell fluid parameter M and heat absorption parameter ��, temperature profile decreases. Nano particle concentration profile increases for increasing values of magnetic parameter Ha and thermophoresis parameter Nt. The motile density profile has revealed a decrement pattern for higher values of bio-convection Lewis number Lb and bio-convection peclet number Pe. This study may find uses in bio-nano coolant systems, advance nanomechanical bio-convection energy conversion equipment's, etc.

• 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 $10{\le}{\Delta}T{\le}50K$.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.16 no.5
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• pp.203-209
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• 2006

For $P_B=50,\;{\Delta}T=10K$, Ar=5, Pr=2.36, Le=0.015, Pe=1.26, Cv=1.11, the intensity of solutal convection (solutal Grashof number $Grs=3.44x10^4$) is greater than that of thermal convection (thermal Grashof number $Grt=1.81x10^3$) by one order of magnitude, which is based on the solutally buoyancy-driven convection due to the disparity in the molecular weights of the component A($Hg_2Cl_2$) and B(He). With increasing the partial pressure of component B from 10 up to 200 Torr, the rate is decreased exponentially. The convective transport decreases with lower g level and is changed to the diffusive mode at 0.1 $g_0$. In other words, for regions in which the g level is 0.1 $g_0$ or less, the diffusion-driven convection results in a parabolic velocity profile and a recirculating cell is not likely to occur. Therefore a gravitational acceleration level of less than 0.1 $g_0$ can be adequate to ensure purely diffusive transport.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.19 no.1
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• pp.39-47
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• 2009

The effects of thermo-solutal convection on mercurous chloride system of ${Hg_2}{Cl_2}$, and Ne during physical vapor transport are numerically investigated for further understanding and insight into essence of transport phenomena, For $10\;K{\le}{\Delta}T{\le}30\;K$, the growth rate slowly increases and, then is decreased gradually until ${\Delta}T$=50 K, The occurrence of this critical point near at ${\Delta}T$=30 K is likely to be due to the effects of thermo-physical properties stronger than the temperature gradient corresponding to driving force for thermal convection. For the range of $10\;Torr{\le}P_B{\le}300\;Torr$, the rate is second order-exponentially decayed with partial pressures of component B, $P_B$. For the range of $5{\le}M_B{\le}200$, the rate is second order-exponentially decayed with a function of molecular weight of component B, $M_B$. Like the case of a partial pressure of component B, the effects of a molecular weight arc: reflected through the binary diffusivity coefficients, which are intimately related with suppressing the convection flow inside the growth enclosure, i,e., transition from convection to diffusion-dominant flow mode as the molecular weight of B increases. The convective mode is near at a ground level, i,e., on earth (1 $g_0$), and the convection is switched to the diffusion mode for $0.1\;g_0{\le}g{\le}10^{-2}g_0$, whereas the diffusion region ranges from $10^{-2}g_0$ up to $10^{-5}g_0$.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.14 no.4
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• pp.160-168
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• 2004

We investigate the effects of solutal convection on the crystal growth rate in a horizontal configuration for diffusive-convection conditions and purely diffusion conditions achievable in a low gravity environment for a nonlinear thermal gradient. It is concluded that the solutally-driven convection due to the disparity in the molecular weights of the component A $(Hg_2Br_2)$ and B (CO) is stronger than thermally-driven convection for both the nonlinear and the linear thermal profiles, corresponding to $Gr_t= 8.5{\times}10^3,\; Gr_s = 1.05{\times}10^5$. For both solutal and thermal convection processes, the growth rates for the linear thermal profile (conducting walls) are greater than for the nonlinear case. With the temperature humps, there are found to be observed in undersaturation for diffusive-convection processes ranging from $D_{AB}$ = 0.087 to 0.87. For the vertical configurations, the diffusion mode is so much dominated that the growth rate and interfacial distribution is nearly regardless of the gravitational accelerations. Also, the diffusion mode is predominant over the convection for the gravity levels less than 0.1 $g_0$ for the horizontally oriented configuration.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.20 no.3
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• pp.125-132
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• 2010

For typical governing dimensionless parameters of Ar = 5, Pr = 1.16, Le = 0.14, Pe = 3.57, Cv = 1.02, $Gr_s=2.65{\times}10^6$, the effects of thermo physical properties such as a molecular weight, a binary diffusivity coefficient, a partial pressure of component B on solutally buoyancy-driven convection (solutal Grashof number $Gr_s=2.65{\times}10^6$) are theoretically investigated for further understanding and insight into an essence of solutal convection occurring in the vapor phase during the physical vapor transport of a $Hg_2Cl_2-N_2$ system. The solutally buoyancy-driven convection is significantly affected by any significant disparity in the molecular weight of the crystal components and the impurity gas of nitrogen. The solutal convection in a vertical orientation is found to be more suppressed than a tenth reduction of gravitational accelerations in a horizontal orientation. For crystal growth parameters under consideration, the greater uniformity in the growth rate is obtained for either solutal convection mode in a vertical orientation or thermal convection mode in horizontal geometry. The growth rate is also found to be 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.256-263
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• 2007

For $P_B=50Torr,\;P_T=5401Torr,\;T_S=450^{\circ}C,\;{\Delta}T=20K$, Ar=5, Pr=3.34, Le=0.01, Pe=4.16, Cv=1.05, adiabatic and linear thermal profiles at walls, the intensity of solutal convection (solutal Grashof number $Grs=7.86{\times}10^6$) is greater than that of thermal convection (thermal Grashof number $Grt=4.83{\times}10^5$) by one order of magnitude, which is based on the solutally buoyancy-driven convection due to the disparity in the molecular weights of the component A ($Hg_2Cl_2$) and B (He). With increasing the partial pressure of component B from 20 up to 800 Torr, the rate is decreased exponentially. It is also interesting that as the partial pressure of component B is increased by a factor of 2, the rate is approximately reduced by a half. For systems under consideration, the rate increases linearly and directly with the dimensionless Peclet number which reflects the intensity of condensation and sublimation at the crystal and source region. The convective transport decreases with lower g level and is changed to the diffusive mode at $0.1g_0$. In other words, for regions in which the g level is $0.1g_0$ or less, the diffusion-driven convection results in a parabolic velocity profile and a recirculating cell is not likely to occur. Therefore a gravitational acceleration level of less than $0.1g_0$ can be adequate to ensure purely diffusive transport.

• 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.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.23 no.1
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• pp.20-26
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• 2013

Special attention in the role of convection in vapor crystal growth has been paid since some single crystals under microgravity environments less than 1 $g_0$ exhibits a diffusive-convection mode and much uniformity in front of the crystal regions than a normal gravity acceleration of 1 $g_0$. The total molar fluxes show asymmetrical patterns in interfacial distribution, which indicates the occurrence of either one single or more than one convective cell. As the gravitational level decreases form 1 $g_0$ down to $1.0{\times}10^{-4}\;g_0$, the intensity of convection, indicative of the maximum molar fluxes, is reduced significantly for ${\Delta}T=30K$ and 90 K. The total molar fluxes decay first order exponentially with the partial pressure of component B, PB (Torr) for 20 Torr ${\leq}PB{\leq}$ 300 Torr, and two gravity accelerations of $g_y=1\;g_0$ and 0.1 $g_0$.