Numerical evaluation of heat transfer enhancement due to annular electroconvection induced by injection in a dielectric liquid

Two-dimensional numerical simulations are carried out to evaluate the enhancement of natural convection heat transfer in a dielectric liquid resulting from injection induced annular electro-convection. The liquid is confined between two concentric horizontal cylinders and subjected to the simultaneous actions of a direct current electric field and a thermal gradient. A unipolar injection from the inner cylinder introduces free space charges into the liquid. Numerical results are presented for the configuration of inner to outer diameter ratio of 0.5 and silicon oil as the working medium. It is found that the charge injection may induce a strong radial fluid motion, which consequently augments the heat transfer rate. Due to the linear stability nature of electro-convection, there exists a threshold value of the electric driving parameter, above which the electrical enhancement becomes manifest. In addition, when the electric driving parameter is sufficiently high, the flow is fully dominated by the Coulomb force, and thus heat transfer becomes independent of the thermal driving parameter.Ministerio de Ciencia y Tecnología FIS2011-25161Junta de Andalucía P10-FQM-5735Junta de Andalucía P09-FQM-458

Charge injection enhanced natural convection heat transfer in horizontal concentric annuli filled with a dielectric liquid

The natural convection heat transfer in a highly insulating liquid contained between two horizontal concentric cylinders is shown by two-dimensional numerical simulations to be noticeably enhanced by imposing a direct current electric field. This augmentation of heat transfer is due to the radial flow motion induced by unipolar injection of ions. It is found that there exists a threshold of the electric driving parameter T, above which the heat transfer enhancement due to the electric effect becomes significant. For relatively small T values, the mean Nusselt numbers are closely related to the flow pattern and Rayleigh number Ra. In addition, for sufficiently high T values, the flow is fully dominated by the Coulomb force, and thus the heat transfer rate no long depends on Ra.Ministerio de Ciencia y Tecnología FIS2011-25161Junta de Andalucía P10-FQM-5735Junta de Andalucía P09-FQM-458

Finite amplitude electroconvection induced by strong unipolar injection between two coaxial cylinders

We perform a theoretical and numerical study of the Coulomb-driven electroconvection flow of a dielectric liquid between two coaxial cylinders. The specific case where the inner to outer diameter ratio is 0.5 is analyzed. A strong unipolar injection of ions either from the inner or outer cylinder is considered to introduce free charger carriers into the system. A finite volume method is used to solve all governing equations including Navier-Stokes equations and a simplified set of Maxwell’s equations. The flow is characterized by a subcritical bifurcation in the finite amplitude regime. A linear stability criterion and a nonlinear one that correspond to the onset and stop of the flow motion, respectively, are linked with a hysteresis loop. In addition, we also explore the behavior of the system for higher values of the stability parameter. For inner injection, we observe a transition between the patterns made of 7 and 8 pairs of cells, before an oscillatory regime is attained. Such a transition leads to a second finite amplitude stability criterion. A simple modal analysis reveals that the competition of different modes is at the origin of this behavior. The charge density as well as velocity field distributions are provided to help understanding the bifurcation behavior.Ministerio de ciencia y tecnología FIS2011-25161Junta de Andalucía P10-FQM-5735Junta de Andalucía P09-FQM-458

Mathematical modelling of entropy generation in magnetized micropolar flow between co-rotating cylinders with internal heat generation

The present study investigates analytically the entropy generation in magnetized micropolar fluid flow in between two vertical concentric rotating cylinders of infinite length. The surface of the inner cylinder is heated while the surface of the outer cylinder is cooled. Internal heat generation (which arises in energy systems) is incorporated. The Eringen thermo-micropolar fluid model is used to simulate the micro-structural rheological flow characteristics in the annulus region. The flow is subjected to a constant, static, axial magnetic field. The surface of the inner cylinder is prescribed to be isothermal (constant temperature wall condition), whereas the surface of the outer cylinder was exposed to convection cooling. The conservation equations are normalized and closed-form solutions are obtained for the velocity, microrotation and temperature. These are thereafter utilized to derive the expressions for entropy generation number, Bejan number and total entropy generation rate. The effects of relevant thermo-physical parameters on the flow, heat and entropy generation rate are displayed graphically and interpreted at length. It is observed that the external magnetic force enhances the entropy production rate is minimum at the center point of the channel and maximum in the proximity of the inner cylinder. This causes more wear and tear at the surface of the inner cylinder. Greater Hartmann number also elevates microrotation values in the entire annulus region. The study is relevant to optimization of chemical engineering processes, nuclear engineering cooling systems and propulsion systems utilizing non-Newtonian fluids and magnetohydrodynamics

Buoyancy-induced convection of water-based nanofluids in differentially-heated horizontal Semi-Annuli

A two-phase model based on the double-diffusive approach is used to perform a numerical study on natural convection of water-based nanofluids in differentially- heated horizontal semi-annuli, assuming that Brownian diffusion and thermophoresis are the only slip mechanisms by which the solid phase can develop a significant relative velocity with respect to the liquid phase. The system of the governing equations of continuity, momentum, and energy for the nanofluid, and continuity for the nanoparticles, is solved by the way of a computational code which incorporates three empirical correlations for the evaluation of the effective thermal conductivity, the effective dynamic viscosity, and the thermophoretic diffusion coefficient, all based on a wide number of literature experimental data. The pressure-velocity coupling is handled through the SIMPLE-C algorithm. Numerical simulations are executed for three different nanofluids, using the diameter and the average volume fraction of the suspended nanoparticles, the cavity size, the average temperature, and the temperature difference imposed across the cavity, as independent variables. It is found that the impact of the nanoparticle dispersion into the base liquid increases remarkably with increasing the average temperature, whereas, by contrast, the other controlling parameters have moderate effects. Moreover, at temperatures of the order of room temperature or just higher, the heat transfer performance of the nanofluid is significantly affected by the choice of the solid phase material

Bejan flow visualization of free convection in a Jeffrey fluid from a semi-infinite vertical cylinder : influence of Deborah and Prandtl numbers

This article studies the pattern of heat lines in free convection non-Newtonian flow from a semi-infinite vertical cylinder via Bejan’s heat function concept. The viscoelastic Jeffrey fluid model is employed. The time-dependent, coupled, non-linear conservation equations for momentum and energy (heat) are solved computationally with the unconditionally stable finite difference Crank-Nicolson method. Extensive graphical results are presented for the influence of Deborah number (viscoelastic parameter) and Prandtl number (with ranges 0 - 0.8 and 0.68 - 7.2, respectively) on thermal and flow characteristics including time histories of overall skin friction and heat transfer rate. Lower values of Deborah number indicate that the material acts in a more fluid-like manner whereas the higher values of Deborah number correspond to the material showing characteristics more associated with a solid. The solutions indicate that the time taken for the flow-field variables to achieve the steady-state is increased with higher values of Deborah number. Boundary flow visualization is presented using heat lines, isotherms and streamlines. It is observed that as Deborah number increases the intensity of heat lines increases and they tend to deviate from the hot cylindrical wall. Furthermore, the flow field variables for the Newtonian fluid case exhibit a significantly different pattern from that of Jeffrey fluid

Buoyancy-induced convection of water-based nanofluids in differentially-heated horizontal Semi-Annuli

A two-phase model based on the double-diffusive approach is used to perform a numerical study on natural convection of water-based nanofluids in differentially- heated horizontal semi-annuli, assuming that Brownian diffusion and thermophoresis are the only slip mechanisms by which the solid phase can develop a significant relative velocity with respect to the liquid phase. The system of the governing equations of continuity, momentum, and energy for the nanofluid, and continuity for the nanoparticles, is solved by the way of a computational code which incorporates three empirical correlations for the evaluation of the effective thermal conductivity, the effective dynamic viscosity, and the thermophoretic diffusion coefficient, all based on a wide number of literature experimental data. The pressure-velocity coupling is handled through the SIMPLE-C algorithm. Numerical simulations are executed for three different nanofluids, using the diameter and the average volume fraction of the suspended nanoparticles, the cavity size, the average temperature, and the temperature difference imposed across the cavity, as independent variables. It is found that the impact of the nanoparticle dispersion into the base liquid increases remarkably with increasing the average temperature, whereas, by contrast, the other controlling parameters have moderate effects. Moreover, at temperatures of the order of room temperature or just higher, the heat transfer performance of the nanofluid is significantly affected by the choice of the solid phase material

Steady streaming confined between three-dimensional wavy surfaces

We present a theoretical and numerical study of three-dimensional pulsatile confined flow between two rigid horizontal surfaces separated by an average gap h, and having three-dimensional wavy shapes with arbitrary amplitude σ h where σ ∼ O(1), but long-wavelength variations λ, with h/λ 1. We are interested in pulsating flows with moderate inertial effect arising from the Reynolds stress due to the cavity non-parallelism. We analyse the inertial steady-streaming and the second harmonic flows in a lubrication approximation. The dependence of the three-dimensional velocity field in the transverse direction is analytically obtained for arbitrary Womersley numbers and possibly overlapping Stokes layers. The horizontal dependence of the flow is solved numerically by computing the first two pressure fields of an asymptotic expansion in the small inertial limit. We study the variations of the flow structure with the amplitude, the channel’s wavelength and the Womersley number for various families of three-dimensional channels. The steady-streaming flow field in the horizontal plane exhibits a quadrupolar vortex, the size of which is adjusted to the cavity wavelength. When increasing the wall amplitude, the wavelengths characterizing the channel or the Womersley number, we find higher-order harmonic flow structures, the origin of which can either be inertially driven or geometrically induced. When some of the channel symmetries are broken, a steady-streaming current appears which has a quadratic dependence on the pressure drop, the amplitude of which is linked to the Womersley number

Forced convection to laminar flow of liquid egg yolk in circular and annular ducts

The steady-state heat transfer in laminar flow of liquid egg yolk - an important pseudoplastic fluid food - in circular and concentric annular ducts was experimentally investigated. The average convection heat transfer coefficients, determined by measuring temperatures before and after heating sections with constant temperatures at the tube wall, were used to obtain simple new empirical expressions to estimate the Nusselt numbers for fully established flows at the thermal entrance of the considered geometries. The comparisons with existing correlations for Newtonian and non-Newtonian fluids resulted in excellent agreement. The main contribution of this work is to supply practical and easily applicable correlations, which are, especially for the case of annulus, rather scarce and extensively required in the design of heat transfer operations dealing with similar shear-thinning products. In addition, the experimental results may support existing theoretical analyses.(CNPq) National Council for Scientific and Technological Development(FAPESP) São Paulo Research Foundatio