On the melting of the nanocrystalline vortex matter in high-temperature superconductors

Multilevel Monte Carlo simulations of the vortex matter in the highly-anisotropic high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_8$ were performed. We introduced low concentration of columnar defects satisfying $B_\phi\le B$. Both the electromagnetic and Josephson interactions among pancake vortices were included. The nanocrystalline, nanoliquid and homogeneous liquid phases were identified in agreement with experiments. We observed the two-step melting process and also noted an enhancement of the structure factor just prior to the melting transition. A proposed theoretical model is in agreement with our findings.Comment: 4 figure

Langevin Dynamics of the vortex matter two-stage melting transition in Bi_2Sr_2CaCu_2O8+δ_{8+\delta} in the presence of straight and of tilted columnar defects

In this paper we use London Langevin molecular dynamics simulations to investigate the vortex matter melting transition in the highly anisotropic high-temperature superconductor material Bi_2Sr_2CaCu_2O$_{8+\delta}$ in the presence of low concentration of columnar defects (CDs). We reproduce with further details our previous results obtained by using Multilevel Monte Carlo simulations that showed that the melting of the nanocrystalline vortex matter occurs in two stages: a first stage melting into nanoliquid vortex matter and a second stage delocalization transition into a homogeneous liquid. Furthermore, we report on new dynamical measurements in the presence of a current that identifies clearly the irreversibility line and the second stage delocalization transition. In addition to CDs aligned along the c-axis we also simulate the case of tilted CDs which are aligned at an angle with respect to the applied magnetic field. Results for CDs tilted by $45^{\circ}$ with respect to c-axis show that the locations of the melting and delocalization transitions are not affected by the tilt when the ratio of flux lines to CDs remains constant. On the other hand we argue that some dynamical properties and in particular the position of the irreversibility line should be affected.Comment: 13 pages, 11 figure

Unsteady Finite Amplitude Convection of Water-Copper Nanoliquid in High-Porosity Enclosures

Unicellular Rayleigh–Bénard convection of water–copper nanoliquid confined in a high-porosity enclosure is studied analytically. The modified-Buongiorno–Brinkman two-phase model is used for nanoliquid description to include the effects of Brownian motion, thermophoresis, porous medium friction, and thermophysical properties. Free–free and rigid–rigid boundaries are considered for investigation of onset of convection and heat transport. Boundary effects on onset of convection are shown to be classical in nature. Stability boundaries in the R1*–R2 plane are drawn to specify the regions in which various instabilities appear. Specifically, subcritical instabilities' region of appearance is highlighted. Square, shallow, and tall porous enclosures are considered for study, and it is found that the maximum heat transport occurs in the case of a tall enclosure and minimum in the case of a shallow enclosure. The analysis also reveals that the addition of a dilute concentration of nanoparticles in a liquid-saturated porous enclosure advances onset and thereby enhances the heat transport irrespective of the type of boundaries. The presence of porous medium serves the purpose of heat storage in the system because of its low thermal conductivity

Non-classical Rotational Inertia in a Two-dimensional Bosonic Solid Containing Grain Boundaries

We study the occurrence of non-classical rotational inertia (NCRI) arising from superfluidity along grain boundaries in a two-dimensional bosonic system. We make use of a standard mapping between the zero-temperature properties of this system and the statistical mechanics of interacting vortex lines in the mixed phase of a type-II superconductor. In the mapping, the liquid phase of the vortex system corresponds to the superfluid bosonic phase. We consider numerically obtained polycrystalline configurations of the vortex lines in which the microcrystals are separated by liquid-like grain boundary regions which widen as the vortex system temperature increases. The NCRI of the corresponding zero-temperature bosonic systems can then be numerically evaluated by solving the equations of superfluid hydrodynamics in the channels near the grain boundaries. We find that the NCRI increases very abruptly as the liquid regions in the vortex system (equivalently, superfluid regions in the bosonic system) form a connected, system-spannig structure with one or more closed loops. The implications of these results for experimentally observed supersolid phenomena are discussed.Comment: Ten pages, including figure

Oberbeck–Boussinesq free convection of water based nanoliquids in a vertical channel using Dirichlet, Neumann and Robin boundary conditions on temperature

AbstractA numerical investigation is carried out into the flow and heat transfer within a fully-developed mixed convection flow of water–alumina (Al2O3–water), water–titania (TiO2–water) and water–copperoxide (CuO–water) in a vertical channel by considering Dirichlet, Neumann and Robin boundary conditions. Actual values of thermophysical quantities are used in arriving at conclusions on the three nanoliquids. The Biot number influences on velocity and temperature distributions are opposite in regions close to the left wall and the right wall. Robin condition is seen to favour symmetry in the flow velocity whereas Dirichlet and Neumann conditions skew the flow distribution and push the point of maximum velocity to the right of the channel. A reversal of role is seen between them in their influence on the flow in the left-half and the right-half of the channel. This leads to related consequences in heat transport. Viscous dissipation is shown to aid flow and heat transport. The present findings reiterate the observation on heat transfer in other configurations that only low concentrations of nanoparticles facilitate enhanced heat transport for all three temperature conditions. Significant change was observed in Neumann condition, whereas the changes are too extreme in Dirichlet condition. It is found that Robin condition is the most stable condition. Further, it is also found that all three nanoliquids have enhanced heat transport compared to that by base liquid, with CuO–water nanoliquid shows higher enhancement in its Nusselt number, compared to Al2O3 and TiO2

Amplitude Equation and Heat Transport for Rayleigh–Bénard Convection in Newtonian Liquids with Nanoparticles

Rayleigh–Bénard convection in liquids with nanoparticles is modelled as a single phase system with liquid properties like density, viscosity, thermal expansion coefficient, heat capacity and thermal conductivity modified by the presence of the nanoparticles. Expressions for the thermophysical properties are chosen from earlier works. The tri-modal Lorenz model is derived under the assumptions of Boussinesq approximation and small-scale convective motions. Ginzburg–Landau equation is arrived at from the generalized Lorenz model. The amplitudes of convective modes required for estimating the heat transport are determined analytically. A table is prepared documenting the actual values of the thermophysical properties of water, ethylene-glycol, engine-oil and glycerine with different nanoparticles, namely copper, copper oxide, titania, silver and alumina, and Nusselt number is calculated. Enhanced thermal conductivity being the reason for the enhancement of heat transport due to the presence of the nanoparticles is shown. Detailed discussion is made on the percentage increase of heat transport in twenty Newtonian nanoliquids compared to that in Newtonian liquids without nanoparticles

A Study of Rayleigh–Bénard Convection in Hybrid Nanoliquids with Physically Realistic Boundaries

Linear and weakly nonlinear stability analyses of Rayleigh– B´enard convection in water–copper–alumina hybrid nanoliquid bounded by rigid isothermal boundaries is studied analytically. A single-phase description is used for the nanoliquid. Using a minimal Fourier series representation and an appropriate scaling a classical Lorenz model for rigid isothermal boundaries is derived. The Lorenz model is transformed to the Ginzburg–Landau model using the renormalization group method. The solution of the Ginzburg–Landau model is used to arrive at the expression of the Nusselt number. The study shows that the presence of two nanoparticles in water is to increase the coefficient of friction, advance the onset of convection and enhance the heat transfer. Further, it is shown that compared to a single nanoparticle the combined influence of two nanoparticles is more effective on heat transfer. The percentage of heat transfer enhancement in water due to Al2O3−Cu hybrid nanoparticles is almost twice that of Al2O3 nanopartcles. It is found that the hybrid nanoparticles of Al2O3−Cu intensify convection in water more than the mono nanoparticles of Al2O3 and the plots of stream function and isotherm point to this fact. The effect of the physically realistic rigid boundaries is to inhibit the onset of convection when compared with that of free boundaries

A theoretical study of enhanced heat transfer in nanoliquids with volumetric heat source

Rayleigh�Bénard convection in nanoliquids is studied in the presence of volumetric heat source. The present analytical work concerns twenty nanoliquids. Carrier liquids considered are water, ethylene glycol, engine oil and glycerine and with them five different nanoparticles considered are copper, copper oxide, silver, alumina and titania. Expression for the thermophysical properties of the nanoliquids is chosen from phenomenological laws or mixture theory. Heat source is characterized by an internal nanoliquid Rayleigh number (Formula presented.). Heat source adds to the energy of the system and hence an advanced onset is observed in this case compared to the problem with no heat source. In the case of heat sink, however, heat is drawn from the system leading to delay in onset. The individual effect of all the nanoparticles is to advance convection. Enhanced heat transport situation is observed in each of the nanoliquids with engine-oil-silver transporting maximum heat and water-titania the least. Additional Fourier modes are found not to have any profound effect on the results predicted by minimal modes. The connection between the Lorenz model and the Ginzburg�Landau model is clearly shown in the paper. © 2017 Korean Society for Computational and Applied Mathematic

A Study of Rayleigh–Bénard Convection in Hybrid Nanoliquids with Physically Realistic Boundaries

Linear and weakly nonlinear stability analyses of Rayleigh–Bénard convection in water–copper–alumina hybrid nanoliquid bounded by rigid isothermal boundaries is studied analytically. A single-phase description is used for the nanoliquid. Using a minimal Fourier series representation and an appropriate scaling a classical Lorenz model for rigid isothermal boundaries is derived. The Lorenz model is transformed to the Ginzburg–Landau model using the renormalization group method. The solution of the Ginzburg–Landau model is used to arrive at the expression of the Nusselt number. The study shows that the presence of two nanoparticles in water is to increase the coefficient of friction, advance the onset of convection and enhance the heat transfer. Further, it is shown that compared to a single nanoparticle the combined influence of two nanoparticles is more effective on heat transfer. The percentage of heat transfer enhancement in water due to Al2O3-Cu hybrid nanoparticles is almost twice that of Al2O3 nanopartcles. It is found that the hybrid nanoparticles of Al2O3-Cu intensify convection in water more than the mono nanoparticles of Al2O3 and the plots of stream function and isotherm point to this fact. The effect of the physically realistic rigid boundaries is to inhibit the onset of convection when compared with that of free boundaries