Showing papers on "Rayleigh number published in 2014"

Augmentation of the Heat Transfer Performance of a Sinusoidal Corrugated Enclosure by Employing Hybrid Nanofluid

Abstract: This paper numerically examines laminar natural convection in a sinusoidal corrugated enclosure with a discrete heat source on the bottom wall, filled by pure water, Al2O3/water nanofluid, and Al2O3-Cu/water hybrid nanofluid which is a new advanced nanofluid with two kinds of nanoparticle materials. The effects of Rayleigh number (103≤Ra≤106) and water, nanofluid, and hybrid nanofluid (in volume concentration of 0% ≤ ϕ ≤ 2%) as the working fluid on temperature fields and heat transfer performance of the enclosure are investigated. The finite volume discretization method is employed to solve the set of governing equations. The results indicate that for all Rayleigh numbers been studied, employing hybrid nanofluid improves the heat transfer rate compared to nanofluid and water, which results in a better cooling performance of the enclosure and lower temperature of the heated surface. The rate of this enhancement is considerably more at higher values of Ra and volume concentrations. Furthermore, by applying ...

Effect of spatially variable magnetic field on ferrofluid flow and heat transfer considering constant heat flux boundary condition

Abstract: Ferrofluid flow and heat transfer in the presence of an external variable magnetic field is studied. The inner cylinder is maintained at uniform heat flux and the outer cylinder has constant temperature. The Control Volume based Finite Element Method (CVFEM) is applied to solve the governing equations. Combined magnetohydrodynamic and ferrohydrodynamic effects have been taken into account. The effects of magnetic number, Hartmann number, Rayleigh number and nanoparticle volume fraction on hydrothermal behavior have been examined. Results show that the Nusselt number is an increasing function of Magnetic number, Rayleigh number and nanoparticle volume fraction while it is a decreasing function of the Hartmann number. Also, it can be concluded that the enhancement in heat transfer decreases with an increase in the Rayleigh number and magnetic number but it increases with an increase in the Hartmann number.

Natural convection heat transfer in a cavity with sinusoidal wall filled with CuO–water nanofluid in presence of magnetic field

Abstract: Control volume based finite element method (CVFEM) is applied to investigate flow and heat transfer of CuO–water nanofluid in presence of magnetic field. The enclosure has a sinusoidal wall under constant heat flux. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo–Kleinstreuer–Li) correlation. In this model effect of Brownian motion on the effective thermal conductivity is considered. The numerical investigations are conducted at a fixed Prandtl number equal to 6.2. Various values of non-dimensional governing parameters such as volume fraction of nanoparticles (ϕ), Rayleigh number (Ra), dimensionless amplitude of the sinusoidal wall (a) and Hartmann number (Ha) are examined. Also a correlation of Nusselt number corresponding to active parameters is presented. The results show that Nusselt number is an increasing function of nanoparticles volume fraction, dimensionless amplitude of the sinusoidal wall and Rayleigh number while it is a decreasing function of Hartmann number.

A study of natural convection heat transfer in a nanofluid filled enclosure with elliptic inner cylinder

Abstract: – The purpose of this paper is to study the effects of natural convection heat transfer in a cold outer circular enclosure containing a hot inner elliptic circular cylinder. The fluid in the enclosure is Cu-water nanofluid. The main emphasis is to find the numerical treatment for the said mathematical model. The effects of Rayleigh number, inclined angle of elliptic inner cylinder, effective of thermal conductivity and viscosity of nanofluid, volume fraction of nanoparticles on the flow and heat transfer characteristics have been examined. , – A very effective and higher order numerical scheme Control Volume-based Finite Element Method (CVFEM) is used to solve the resulting coupled equations. The numerical investigation is carried out for different governing parameters namely; the Rayleigh number, nanoparticle volume fraction and inclined angle of elliptic inner cylinder. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell-Garnetts (MG) and Brinkman models, respectively. , – The results reveal that Nusselt number increases with an increase of nanoparticle volume fraction, Rayleigh numbers and inclination angle. Also it can be found that increasing Rayleigh number leads to a decrease in heat transfer enhancement. For high Rayleigh number the minimum heat transfer enhancement ratio occurs at. , – To the best of the authors’ knowledge, no such analysis is available in the literature which can describe the natural convection heat transfer in a nanofluid filled enclosure with elliptic inner cylinder by means of CVFEM.

Magnetic field effect on nanofluid flow and heat transfer using KKL model

Abstract: In this paper, MHD effect on natural convection heat transfer in an inclined L-shape enclosure filled with nanofluid is studied. The numerical investigation is carried out using the control volume based finite element method (CVFEM). The fluid in the enclosure is a water-based nanofluid containing Al2O3 nanoparticle. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo–Kleinstreuer–Li) correlation in which effect of Brownian motion on the effective thermal conductivity is considered. The heat transfer between cold and hot regions of the enclosure cannot be well understood by using isotherm patterns so heatline visualization technique is used to find the direction and intensity of heat transfer in a domain. Effect of Hartmann number, volume fraction of nanoparticle, Rayleigh number and inclination angle on streamline, isotherm and heatline are examined. The results show that Nusselt number increases with increase of Rayleigh number and volume fraction of nanoparticle while it decreases with augment of Hartmann number and inclination angle. Enhancement in heat transfer has reverse relationship with Hartmann number and Rayleigh number.

Investigation of refrigeration efficiency for fully wet circular porous fins with variable sections by combined heat and mass transfer analysis

Abstract: Temperature distribution equation and refrigeration efficiency for fully wet circular porous fins with variable sections are introduced in this study by a new modified wet fin parameter presented by Sharqawy and Zubair. This parameter can be calculated without knowing the fin tip condition by considering the temperature and humidity ratio differences for the driving forces of heat and mass transfer, respectively. It's assumed that heat and mass convective coefficients vary with fin temperature and heat transfer through porous media is simulated using passage velocity from the Darcy's model. After presenting the governing equation, Least Square Method (LSM) and fourth order Runge-Kutta method (NUM) are applied for predicting the temperature distribution in the sample aluminum porous fins. After that, effects of porosity, Darcy number, Rayleigh number, Lewis number and etc. on fin efficiency are examined. As a main outcome, for reaching to high values of fin efficiency, rectangular fin should be used instead of convex and triangular sections.

MHD free convection in an eccentric semi-annulus filled with nanofluid

Abstract: In this study magnetohydrodynamic effect on free convection of nanofluid in an eccentric semi-annulus filled is considered. The effective thermal conductivity and viscosity of nanofluid are calculated by the Maxwell–Garnetts (MG) and Brinkman models, respectively. Lattice Boltzmann method is applied to simulate this problem. This investigation compared with other works and found to be in excellent agreement. Effects of the Hartmann number, nanoparticle volume fraction, Rayleigh numbers and position of the inner circular cylinder on flow and heat transfer characteristics are examined. Also a correlation of Nusselt number corresponding to active parameters is presented. The results show that Nusselt number has direct relationship with nanoparticle volume fraction and Rayleigh number but it has inverse relationship with Hartmann number and position of inner cylinder at high Rayleigh number. Also it can be concluded that heat transfer enhancement increases with increase of Hartmann number and decreases with augment of Raleigh number.

Heat transfer and natural convection of nanofluids in porous media

Abstract: Natural convection of a nanofluid in a square cavity filled with a porous matrix is numerically investigated using a meshless technique. The Darcy–Brinkman and the energy transport equations are used to describe the nanofluid flow and the heat transfer process in the porous medium as these are generated by heating one of the cavity walls. The role of the nanofluid properties in the cooling performance of the medium and in the relevant heat process is thoroughly investigated. Numerical results are obtained for the stream function, the temperature profile, and the Nusselt number over a wide range of dimensionless quantities (Rayleigh number between 105 and 107, Darcy number between 10−5 and 10−3). The effect of the porous medium in the cooling efficiency of the nanofluidic system is also discussed. Alternative expressions are suggested for the estimation of the effective conductivity and the thermal expansion coefficient of the nanofluid and their effects on the heat transfer problem are investigated. Excellent agreement with experimental data and trends as well as with previously published numerical results for less complicated systems was found.

Large-scale vortices in rapidly rotating Rayleigh-Bénard convection

Abstract: Using numerical simulations of rapidly rotating Boussinesq convection in a Cartesian box, we study the formation of long-lived, large-scale, depth-invariant coherent structures. These structures, which consist of concentrated cyclones, grow to the horizontal scale of the box, with velocities significantly larger than the convective motions. We vary the rotation rate, the thermal driving and the aspect ratio in order to determine the domain of existence of these large-scale vortices (LSV). We find that two conditions are required for their formation. First, the Rayleigh number, a measure of the thermal driving, must be several times its value at the linear onset of convection; this corresponds to Reynolds numbers, based on the convective velocity and the box depth, . Second, the rotational constraint on the convective structures must be strong. This requires that the local Rossby number, based on the convective velocity and the horizontal convective scale, . Simulations in which certain wavenumbers are artificially suppressed in spectral space suggest that the LSV are produced by the interactions of small-scale, depth-dependent convective motions. The presence of LSV significantly reduces the efficiency of the convective heat transport.

Inverse cascade and symmetry breaking in rapidly rotating Boussinesq convection

Abstract: In this paper, we present numerical simulations of rapidly rotating Rayleigh-Benard convection in the Boussinesq approximation with stress-free boundary conditions. At moderately low Rossby number and large Rayleigh number, we show that a large-scale depth-invariant flow is formed, reminiscent of the condensate state observed in two-dimensional flows. We show that the large-scale circulation shares many similarities with the so-called vortex, or slow-mode, of forced rotating turbulence. Our investigations show that at a fixed rotation rate the large-scale vortex is only observed for a finite range of Rayleigh numbers, as the quasi-two-dimensional nature of the flow disappears at very high Rayleigh numbers. We observe slow vortex merging events and find a non-local inverse cascade of energy in addition to the regular direct cascade associated with fast small-scale turbulent motions. Finally, we show that cyclonic structures are dominant in the small-scale turbulent flow and this symmetry breaking persists in the large-scale vortex motion.

Large-scale vortices in rapidly rotating Rayleigh-B\'enard convection

Abstract: Using numerical simulations of rapidly rotating Boussinesq convection in a Cartesian box, we study the formation of long-lived, large-scale, depth-invariant coherent structures. These structures, which consist of concentrated cyclones, grow to the horizontal size of the box, with velocities significantly larger than the convective motions. We vary the rotation rate, the thermal driving and the aspect ratio in order to determine the domain of existence of these large-scale vortices (LSV). We find that two conditions are required for their formation. First, the Rayleigh number, a meaure of the thermal driving, must be several times its value at the linear onset of convection; this corresponds to Reynolds numbers, based on the convective velocity and the box depth, $\gtrsim 100$. Second, the rotational constraint on the convective structures must be strong. This requires that the local Rossby number, based on the convective velocity and the horizontal convective scale, $\lesssim 0.15$. Simulations in which certain wavenumbers are artificially suppressed in spectral space suggest that the LSV are produced by the interactions of small-scale, depth-dependent convective motions. The presence of LSV significantly reduces the efficiency of the convective heat transport.

MHD natural convection in a nanofluid filled inclined enclosure with sinusoidal wall using CVFEM

Abstract: Magnetohydrodynamic flow in a nanofluid filled inclined enclosure is investigated numerically using the Control Volume based Finite Element Method. The cold wall of cavity is assumed to mimic a sinusoidal profile with different dimensionless amplitude, and the fluid in the enclosure is a water-based nanofluid containing Cu nanoparticles. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts and Brinkman models, respectively. Numerical simulations were performed for different governing parameters namely the Hartmann number, Rayleigh number, nanoparticle volume fraction and inclination angle of enclosure. The results show that in presence of magnetic field, velocity field retarded, and hence, convection and Nusselt number decreases. At Ra = 103, maximum value of enhancement for low Hartmann number is obtained at γ = 0°, but for higher values of Hartmann number, maximum values of E occurs at γ = 90°. Also, it can be found that for all values of Hartmann number, at Ra = 104 and 105, maximum value of E is obtained at γ = 60° and γ = 0°, respectively.