Showing papers on "Rayleigh number published in 2016"

Nanofluid convective heat transfer using semi analytical and numerical approaches: A review

Abstract: The use of additives in the base fluid like water or ethylene glycol is one of the techniques applied to augment the heat transfer. Newly an innovative nanometer sized particles have been dispersed in the base fluid in heat transfer fluids. The fluids containing the solid nanometer size particle dispersion are called ‘nanofluids’. Two main categories were discussed in detail as the single-phase modeling which the combination of nanoparticle and base fluid is considered as a single-phase mixture with steady properties and the two-phase modeling in which the nanoparticle properties and behaviors are considered separately from the base fluid properties and behaviors. Both single phase and two phase models have been presented in this paper. This paper intends to provide a brief review of researches on nanofluid flow and heat transfer via semi analytical and numerical methods. It was also found that Nusselt number is an increasing function of nanoparticle volume fraction, Rayleigh number and Reynolds number, while it is a decreasing function of Hartmann number.

Electrohydrodynamic free convection heat transfer of a nanofluid in a semi-annulus enclosure with a sinusoidal wall

Abstract: Natural convection heat transfer of a nanofluid in the presence of an electric field is investigated. The control volume finite element method (CVFEM) is utilized to simulate this problem. A Fe3O4–ethylene glycol nanofluid is used as the working fluid. The effect of the electric field on nanofluid viscosity is taken into account. Numerical investigation is conducted for several values of Rayleigh number, nanoparticle volume fraction, and the voltage supplied. The numerical results show that the voltage used can change the flow shape. The Coulomb force causes the isotherms to become denser near the bottom wall. Heat transfer rises with increase in the voltage supplied and Rayleigh number. The effect of electric field on heat transfer is more pronounced at low Rayleigh numbers due to the predomination of the conduction mechanism.

Application of Caputo-Fabrizio derivatives to MHD free convection flow of generalized Walters’-B fluid model

Abstract: The present article applies the idea of Caputo-Fabrizio time fractional derivatives to magnetohydrodynamics (MHD) free convection flow of generalized Walters’-B fluid over a static vertical plate. Free convection is caused due to combined gradients of temperature and concentration. Hence, heat and mass transfers are considered together. The fractional model of Walters’-B fluid is used in the mathematical formulation of the problem. The problem is solved via the Laplace transform method. Exact solutions for velocity, temperature and concentration are obtained. The physical quantities of interest are examined through plots for various values of fractional parameter: $\alpha$ , Walters’-B parameter $\Gamma$ , magnetic parameter M , Prandtl number Pr, Schmidt number Sc, thermal Grashof number Gr and mass Grashof number Gm. As a special case, the published results from open literature are recovered.

Conjugate heat transfer and entropy generation in a cavity filled with a nanofluid-saturated porous media and heated by a triangular solid

Abstract: Entropy generation due to conjugate natural convection–conduction heat transfer in a square domain is numerically investigated under steady-state condition. The domain composed of porous cavity heated by a triangular solid wall and saturated with a CuO–water nanofluid. Equations governing the heat transfer in the triangular solid together with the heat and nanofluid flow in the nanofluid-saturated porous medium are solved numerically using the over-successive relaxation finite-difference method. A temperature dependent thermal conductivity and modified expression for the thermal expansion of nanofluid are adopted. A new criterion for assessment of the thermal performance is proposed. The investigated parameters are the nanoparticles volume fraction φ (0–0.05), modified Rayleigh number Ra (10–1000), solid wall to base-fluid saturated porous medium thermal conductivity ratio K ro (0.44, 1, 23.8), and the triangular solid thickness D (0.1–1). The results show that both the average Nusselt number and the entropy generation are increasing functions of K ro , while they are maxima at some critical values of D . It is also found that the addition of nanoparticles increases the entropy generation. According to the new proposed criterion, the results show that the largest solid thickness ( D = 1.0) and the lower wall thermal conductivity ratio manifest better thermal performance.

Entropy Generation and Natural Convection of CuO-Water Nanofluid in C-Shaped Cavity under Magnetic Field

Abstract: This paper investigates the entropy generation and natural convection inside a C-shaped cavity filled with CuO-water nanofluid and subjected to a uniform magnetic field. The Brownian motion effect is considered in predicting the nanofluid properties. The governing equations are solved using the finite volume method with the SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm. The studied parameters are the Rayleigh number (1000 ≤ Ra ≤ 15,000), Hartman number (0 ≤ Ha ≤ 45), nanofluid volume fraction (0 ≤ φ ≤ 0.06), and the cavity aspect ratio (0.1 ≤ AR ≤ 0.7). The results have shown that the nanoparticles volume fraction enhances the natural convection but undesirably increases the entropy generation rate. It is also found that the applied magnetic field can suppress both the natural convection and the entropy generation rate, where for Ra = 1000 and φ = 0.04, the percentage reductions in total entropy generation decreases from 96.27% to 48.17% for Ha = 45 compared to zero magnetic field when the aspect ratio is increased from 0.1 to 0.7. The results of performance criterion have shown that the nanoparticles addition can be useful if a compromised magnetic field value represented by a Hartman number of 30 is applied.

Viscoplastic dimensionless numbers

Abstract: In the present paper we analyze the dimensionless numbers that concern the flow of viscoplastic materials. The Bingham material is used to conduct the main discussion but the ideas are generalized to more complex viscoplastic models at the end of the article. Although one can explore the space of solutions with a set of dimensionless numbers where only one of them takes into account the yield stress, like the Bingham number for example, we recommend that the characteristic stress should be defined as the extra-stress intensity evaluated at a characteristic (maximum) deformation rate. Such a definition includes the yield stress in every dimensionless number that is related to viscous effects like the Reynolds number, the viscosity ratio, and the Rayleigh number. This procedure was shown to be more effective on collapsing data into master curves and to provide a fairer comparison with the Newtonian case. This happens because a more representative viscous effect is taken into account, concentrating the plastic effects into a single parameter. The plastic number, the ratio of the yield stress to the maximum stress of the domain, is shown to better capture plastic effects than the usual Bingham number. The analysis of problems where a characteristic stress, but not a characteristic velocity, is provided, indicates that a more representative characteristic velocity should be defined with respect to the driving potential for the motion, i.e., the difference between the characteristic and yield stresses. This method is in contrast to the majority of the literature, where for Bingham materials, the dimensionless numbers are maintained in the same form as the original Newtonian ones, replacing the Newtonian viscosity by the viscous parameter of the Bingham model.

The Spectral Amplitude of Stellar Convection and its Scaling in the High-Rayleigh Number Regime

Abstract: Convection plays a central role in the dynamics of any stellar interior, and yet its operation remains largely hidden from direct observation. As a result, much of our understanding concerning stellar convection necessarily derives from theoretical and computational models. The Sun is, however, exceptional in that regard. The wealth of observational data afforded by its proximity provides a unique test bed for comparing convection models against observations. When such comparisons are carried out, surprising inconsistencies between those models and observations become apparent. Both photospheric and helioseismic measurements suggest that convection simulations may overestimate convective flow speeds on large spatial scales. Moreover, many solar convection simulations have difficulty reproducing the observed solar differential rotation owing to this apparent overestimation. We present a series of three-dimensional stellar convection simulations designed to examine how the amplitude and spectral distribution of convective flows are established within a star's interior. While these simulations are nonmagnetic and nonrotating in nature, they demonstrate two robust phenomena. When run with sufficiently high Rayleigh number, the integrated kinetic energy of the convection becomes effectively independent of thermal diffusion, but the spectral distribution of that kinetic energy remains sensitive to both of these quantities. A simulation that has converged to a diffusion-independent value of kinetic energy will divide that energy between spatial scales such that low-wavenumber power is overestimated and high-wavenumber power is underestimated relative to a comparable system possessing higher Rayleigh number. We discuss the implications of these results in light of the current inconsistencies between models and observations.

Vigorous convection as the explanation for Pluto’s polygonal terrain

Abstract: A parameterized convection model and observations of the puzzling polygons of the Sputnik Planum region of Pluto are used to compute the Rayleigh number of its nitrogen ice and show that it is vigorously convecting, kilometres thick and about a million years old. NASA's New Horizons spacecraft has revealed fascinating details of the surface of Pluto, including a vast ice-filled basin known as Sputnik Planum, which is central to Pluto's geological activity. Much of the surface of Sputnik Planum, consisting mostly of nitrogen ice, is divided into irregular polygons that are tens of kilometres in diameter and whose centres rise tens of metres above their sides. Two papers in this issue of Nature analyse New Horizons images of this polygonal terrain. Both conclude that it is continually being resurfaced by convection, but arrive at contrasting models for the process. Alexander Trowbridge et al. report a parameterized convection model in which the nitrogen ice is vigorously convecting, ten or more kilometres thick and about a million years old. William McKinnon et al. — from the New Horizons team — show that 'sluggish lid' convective overturn in a several-kilometre-thick layer of solid nitrogen can explain both the presence of the cells and their great width. Pluto’s surface is surprisingly young and geologically active1. One of its youngest terrains is the near-equatorial region informally named Sputnik Planum, which is a topographic basin filled by nitrogen (N2) ice mixed with minor amounts of CH4 and CO ices1. Nearly the entire surface of the region is divided into irregular polygons about 20–30 kilometres in diameter, whose centres rise tens of metres above their sides. The edges of this region exhibit bulk flow features without polygons1. Both thermal contraction and convection have been proposed to explain this terrain1, but polygons formed from thermal contraction (analogous to ice-wedges or mud-crack networks)2,3 of N2 are inconsistent with the observations on Pluto of non-brittle deformation within the N2-ice sheet. Here we report a parameterized convection model to compute the Rayleigh number of the N2 ice and show that it is vigorously convecting, making Rayleigh–Benard convection the most likely explanation for these polygons. The diameter of Sputnik Planum’s polygons and the dimensions of the ‘floating mountains’ (the hills of of water ice along the edges of the polygons) suggest that its N2 ice is about ten kilometres thick. The estimated convection velocity of 1.5 centimetres a year indicates a surface age of only around a million years.