Rayleigh-Bénard convection heat transfer in nanoparticle suspensions

Natural convection heat transfer of nanofluids in horizontal enclosures heated from below is investigated theoretically. The main idea upon which the present work is based is that nanofluids behave more like a single-phase fluid rather than like a conventional solid-liquid mixture, which implies that all the convective heat transfer correlations available for single-phase flows can be extended to nanoparticle suspensions, provided that the thermophysical properties appearing in them are the nanofluid effective properties calculated at the reference temperature. In this connection, two empirical equations, based on a wide variety of experimental data reported in the literature, are developed for the evaluation of the nanofluid effective thermal conductivity and dynamic viscosity, whereas the other effective properties are evaluated by the traditional mixing theory. The heat transfer enhancement that derives from the dispersion of nano-sized solid particles into the base liquid is calculated for different operating conditions, nanoparticle diameters, and combinations of solid and liquid phases. One of the fundamental results is the existence of an optimal particle loading for maximum heat transfer across the bottom-heated enclosure. In particular, for any assigned combination of suspended nanoparticles and base liquid, it is found that the optimal volume fraction increases as the nanofluid average temperature increases, and may either increase or decrease with increasing the nanoparticle size according as the flow is laminar or turbulent. Moreover, the optimal volume fraction has a peak at a definite value of the Rayleigh number of the base fluid, that depends on both the average temperature of the nanofluid and the diameter of the suspended nanoparticles.     

Conjugate heat transfer in square enclosures

Building elements represented by square vertical enclosures encircled with finite walls or with centered solid body, could maintain the equivalent fluid volumes through the volume ratio scale. Present work aims to investigate the fluid flow and heat transfer in these two building elements. Complete two-dimensional numerical simulation of the conjugate heat conduction and natural convection occurring in both enclosures is carried out. An analytical expression for the minimum size of the inserted body at which the body begins to suppress the natural convection flow is proposed and validated by the numerical results. The fluid flow and heat transfer characteristics are analyzed through the streamlines, heatlines, and total heat transfer rates across both enclosures. Results reveal that heat transfer rates across both enclosures are complex functions of the volume ratio scale, Rayleigh number, and the relative thermal conductivity.     

Experimental study of air natural convection on metallic foam-sintered plate

The natural convection on metallic foam-sintered plate at different inclination angles was experimentally studied. Seven copper foam samples with different pore densities (10–40 pore per inch), porosities (0.90–0.95), and aspect ratios (the ratio of foam thickness to sample length, 0.1–0.5) were measured at inclination angles of 0° (vertical orientation), 15°, 30°, 45°, 60°, 75°, 90° (horizontal orientation). The heat conduction and natural convection inside the foam both contributed to the total heat transfer. Although, the form and viscous drag, which are influenced by permeability and viscous friction in the thermal boundary layer respectively, tend to suppress the natural convection, the heat transfer was finally enhanced by the foam sintered surface due to large surface area extension. Optimum inclination range 60–75° corresponding to maximum average Nu number was found in the heat flux range of 600–1800 W/m². The sintered foam surface with lower porosity and pore density was recommended for heat transfer enhancement. Particularly, the sample with porosity 0.9, pore density of 10 PPI, aspect ratio of 0.5 offered the highest average Nu number among the studied samples. An empirical correlation for modified Nusselt number at isoflux boundary condition considering the foam morphology parameter and inclination angle was proposed within deviation ±15% between the correlation and the experimental data.     

Natural convection in a square cavity with a heat generating body: Entropy consideration

Conjugate heat transfer in a cavity is an important consideration with regard to cooling of micro-electronic equipment. In the present study, a heat transfer analysis of conditions taking place in a square cavity with a heat source, located in it, is carried out. The natural convection accompanying conduction heat transfer in the heat generating solid body is examined. Air or water are considered as the fluid in the cavity while steel substrate is considered as the heat generating solid body. The location of the solid is changed in the cavity to examine the cooling conditions. The entropy analysis of the system is carried out to determine the irreversibility ratio for each location of the solid body in the cavity. It is found that the heat transfer from the solid body surfaces increases where the surfaces facing the inlet and the exit of the cavity. The entropy generated attains the maximum value for air when the solid body is located at the center of the cavity; in which case, the irreversibility ratio reduces to a minimum value. Received on 26 May 1999     

Combined natural convection heat and mass transfer in an enclosure having finite thickness walls

Unsteady three-dimensional conjugate heat and mass transfer in an enclosure having finite thickness heat-conducting walls has been analyzed numerically. The governing unsteady, three-dimensional flow, energy and contaminant transport equations for the gas cavity and unsteady heat conduction equation for solid walls, written in dimensionless terms of the vector potential functions, the vorticity vector, the temperature and the concentration, have been solved using an iterative implicit finite-difference method. Main attention was paid to the effects of the Rayleigh number, buoyancy ratio and the dimensionless time on the flow structure and heat and mass transfer regimes. It should be noted that the dominant cause of the oscillations in the dimensionless time dependences of the average Nusselt number on the heat source surface and the average Sherwood number on the contaminant source surface at Ra>5?10⁵ is the mutual influence of the analyzed object geometry and the thermo-diffusivity impact on the flow. The change in the buoyancy ratio can lead to the essential modifications of the flow, temperature and concentration fields owing to the significant influence of the concentration gradient.     

Transport through baffles in bottom heated top cooled enclosures: parametric studies

This paper presents parametric studies on the heat transfer and fluid exchange through single-hole baffles located at the median height in bottom heated top cooled enclosures. Results indicate that when the baffle area-opening ratio is smaller than 2%, the heat transfer in the enclosure is dominated by the transport through the baffle opening. Even with such small baffle openings, increasing the enclosure aspect ratio still enhances the transport across the baffle. The characteristic length scale of flow in the enclosure is a combination of baffle opening diameter and the chamber height. The Nusselt number that characterize the heat transfer through the baffle-hole is linearly correlated with the Rayleigh number based on baffle opening diameter and the temperature difference between the bulk temperatures in the two chambers, while no effects of Prandtl numbers are observed. The mechanism of transport across the baffle opening varies from conduction dominated, combined conduction and convection, and convection dominated regimes as Rayleigh number increases.     

Heat transfer in open cell polyurethane foam insulation

This paper study systematic investigates the combined conductive and non-gray radiative heat transfer of open cell polyurethane (PU) foam in the pressure range between 760 and 0.02 Torr. Direct transmission measurements are also taken using Fourier transform infrared (FTIR) spectrometer. In doing so, experimental results are obtained for the spectral extinction coefficient from 2.5 to 25 μm. In addition, the P-3 approximation method along with the box model is employed to calculate the non-gray radiative heat flux. The diffusion approximation method is also applied to calculated the radiative conductivity. Also tested herein are three samples with different cell sizes ranging from 330 to 147 μm. According to those results, the spectral extinction coefficient increases with a decrease of cell size, leading to a decrease of thermal conductivity. Moreover, evacuating the gases in the foam cells can reduce the thermal conductivity of the PU foam by as much as 75%. Furthermore, radiative heat transfer accounts for about 4% of total heat transfer at 760 Torr and increases to 20% at 0.02 Torr. Received on 20 April 1998     

Vibration analysis of foam plates based on cell volume distribution

In this paper, vibration analysis of irregular-closed-cell foam plates is per-formed. A cell volume distribution coefficient is introduced to modify the original Gibson-Ashby equations of effective Young’s modulus of foam materials. A Burr distribution is imported to describe the cell volume distribution situation. Three Burr distribution pa-rameters are obtained and related to the cell volume range and the diversity. Based on the plate theory and the effective modulus theory, the natural frequency of foam plates is calculated with the change of the cell volume distribution parameters. The relationship between the frequencies and the cell volumes are derived. The scale factor of the average cell size is introduced and proved to be an important factor to the performance of the foam plate. The result is shown by the existing theory of size effects. It is determined that the cell volume distribution has an impact on the natural frequency of the plate structure based on the cell volume range, the diversity, and the average size, and the impact can lead to optimization of the synthesis procedure.     

Effects of magnetic field on nanofluid forced convection in a partially heated microchannel

This paper numerically examines the laminar forced convection of a water–Al₂O₃ nanofluid flowing through a horizontal microchannel. The middle section of the microchannel is heated with a constant and uniform heat flux. The middle section is also influenced by a transverse magnetic field with a uniform strength. The effects of pertinent parameters such as the Reynolds number (0≤Re≤1000), the solid volume fraction (0≤?≤0.04) and the Hartmann number (0≤Ha≤100) on the flow and temperature fields and the heat transfer performance of the microchannel are examined against numerical predictions. The results show that the microchannel performs better heat transfers at higher values of the Reynolds and Hartmann numbers. For all values of the Reynolds and Hartmann numbers considered in this study, the average Nusselt number on the middle section surface of the microchannel increases as the solid volume fraction increases. The rate of this increase is considerably more at higher values of the Reynolds number and at lower values of the Hartmann number.     

Heat Transfer and Particle Behaviours in Dispersed Two-Phase Flow with Different Heat Conductivities for Liquid and Solid

Liquid-solid two-phase flow with heat transfer is directly simulated, to investigate the effects of the ratios of heat conductivities (solid to liquid) and bulk solid volume fraction from dense to dilute situations. The interaction between fluid and particles is solved by our original immersed solid approach on a rectangular grid system. A discrete element method with a soft-sphere collision model is applied for particle-particle and particle-wall interactions. Governing equation of temperature is time-updated with an implicit treatment for the diffusion term, which enables robust simulation with particles of very high/low ratios of heat conductivities (from 1/1000 to 1000) to the fluid. The local heat flux at the fluid-solid interface is modelled by a new flux decomposition technique, and incorporated into the implicit scheme of the temperature. The method is applied to a 2-D particulate flow in a natural convection in a square domain at a relatively low Rayleigh number. In the dense condition, for the cases with high ratios of heat conductivity, the heat transfer is promoted by strong convection, while the particles of low ratios of heat conductivity tend to hinder the development of the temperature rise in the flow field, causing a weak convection and low Nusselt number. Under a condition of relatively low solid volume fraction, fixed particles only depress the heat convection as the number of particles and heat conductivity ratio increase. For the cases with freely-moving particles, on the other hand, heat conductivity of particles has a stronger influence on the heat transfer of the system than the number of particles. The above simulation results highlight the effect of temperature distributions within the particles and liquid.     

Heat transfer characteristics of multi-walled carbon nanotubes suspension in a developing channel flow

The present study experimentally investigates the effect of multi wall carbon nanotubes (MWCNT) suspensions on the convective heat transfer coefficients. The MWCNT suspensions used in this study were prepared by dispersing MWCNTs in deionized water 0.25 wt% arab gum solution. The heat transfer characteristics were measured for thermally developing laminar flow in a finite length horizontal circular pipe under isothermal wall conditions. The study was conducted over a range of Reynolds number of 300–2,300, based on 0.8 mm tube diameter. Results indicate enhancements of the convective heat transfer coefficient as a function of Reynolds number and volume fractions. An average enhancement of heat transfer coefficient of 50 % was observed over the base fluid. An overall increase of pumping force varying from 20 to 30 % over the flowing range is observed. The results suggest an optimum MWCNT volume fraction point of 0.1 % which gives the best heat transfer enhancement.     

Computer simulation of Cu: AlOOH/water in a microchannel heat sink using a porous media technique and solved by numerical analysis AGM and FEM

Extensive improvements in small-scale thermal systems in electronic circuits, automotive industries, and microcomputers conduct the study of microsystems as essential. Flow and thermic field characteristics of the coherent nanofluid-guided microchannel heat sink are described in this perusal. The porous media approximate was used to search the heat distribution in the expanded sheet and Cu: γ - AlOOH/water. A hybrid blend of Boehme copper and aluminum nanoparticles is evaluated to have a cooling effect on the microchannel heat sink. By using Akbari Ganji and finite element methods, linear and non-linear differential equations as well as simple dimensionless equations have been analyzed. The purpose of this study is to investigate the fluid and thermal parameters of copper hybrid solution added to water, such as Nusselt number and Darcy number so that we can reach the best cooling of the fluid. Also, by installing a piece of fin on the wall of the heat sink, the coefficient of conductive heat transfer and displacement heat transfer with the surrounding air fluid increases, and the efficiency of the system increases. The overall results show that expanding values on the NP (series heat transfer fluid system maximizes performance with temperatures) volume division of copper, as well as boehmite alumina particles, lead to a decrease within the stream velocity of the Cu: AlOOH/water. Increasing the volume fraction of nanoparticles in the hybrid mixture decreases the temperature of the solid surface and the hybrid nanofluid. The Brownian movement improves as the volume percentage of nanoparticles in the hybrid mixture grows, spreading the heat across the environment. As a result, heat transmission rates rise. As the Darcy number increases, the thermal field for solid sections and Cu: AlOOH/water improves.     

Packing properties of binary mixtures in disordered sphere systems

Mixtures of binary spheres are numerically simulated using a relaxation algorithm to investigate the effects of volume fraction and size ratio. A complete profile of the packing properties of binary spheres is given. The density curve with respect to the volume fraction has a triangular shape with a peak at 70% large spheres. The density of the mixture increases with the size ratio, but the growth becomes slow in the case of a large size disparity. The volume fraction and size ratio effects are reflected in the height and movement, respectively, of specific peaks in the radial distribution functions. The structure of the mixture is further analyzed in terms of contact types, and the mean coordination number is demonstrated to be primarily affected by “large–small” contacts. A novel method for estimating the average relative excluded volume for binary spheres by weighting the percentages of contact types is proposed and extended to polydisperse packings of certain size distributions. The method can be applied to explain the density trends of polydisperse mixtures in disordered sphere systems.     

Packing properties of binary mixtures in disordered sphere systems

Mixtures of binary spheres are numerically simulated using a relaxation algorithm to investigate the effects of volume fraction and size ratio, A complete profile of the packing properties of binary spheres is given. The density curve with respect to the volume fraction has a triangular shape with a peak at 70% large spheres. The density of the mixture increases with the size ratio, but the growth becomes slow in the case of a large size disparity, The volume fraction and size ratio effects are reflected in the height and movement, respectively, of specific peaks in the radial distribution functions. The structure of the mixture is further analyzed in terms of contact types, and the mean coordination number is demonstrated to be primarily affected by ＂large-small＂ contacts. A novel method for estimating the average relative excluded volume for binary spheres by weighting the percentages of contact types is proposed and extended to polydisperse packings of certain size distributions. The method can be applied to explain the density trends of polydisperse mixtures in disordered sphere systems,     

Experimental study of enhanced heat transfer by addition of CuO nanoparticle

An energy storage system has been designed to study the thermal characteristics of paraffin wax with an embedded nano size copper oxide (CuO) particle. This paper presents studies conducted on phase transition times, heat fraction as well as heat transfer characteristics of paraffin wax as phase change material (PCM) embedded with CuO nanoparticles. 40?nm mean size CuO particles of 2, 5 and 10% by weight were dispersed in PCM for this study. Experiments were performed on a heat exchanger with 1.5–10?l/min of heat transfer fluid (HTF) flow. Time-based variations of the temperature distributions are revealed from the results of observations of melting and solidification curves. The results strongly suggested that the thermal conductivity enhances 6, 6.7 and 7.8% in liquid state and in dynamic viscosity it enhances by 5, 14 and 30% with increasing mass fraction of the CNEPs. The thermal conductivity ratio of the composites can be augmented by a factor up to 1.3. The heat transfer coefficient during solidification increased about 78% for the maximum flow rate. The analysis of experimental results reveals that the addition of copper oxide nanoparticles to the paraffin wax enhances both the conduction and natural convection very effectively in composites and in paraffin wax. The paraffin wax-based composites have great potential for energy storage applications like industrial waste heat recovery, solar thermal applications and solar based dynamic space power generation with optimal fraction of copper oxide nanoparticles.     

Metal Foam Heat Exchangers for Heat Transfer Augmentation from a Cylinder in Cross-Flow

A numerical study has been conducted to examine the heat transfer from a metal foam-wrapped solid cylinder in cross-flow. Effects of the key parameters including the free stream velocity and characteristics of metal foam such as porosity, permeability, and form drag coefficient on heat and fluid flow are examined. Being a determining factor in pressure drop and heat transfer increment, the porous layer thickness is changed systematically to observe that there is an optimum layer thickness beyond which the heat transfer does not improve while the pressure drop continues to increase. This has been verified by the application of Bejan’s Intersection of Asymptotes method. Results have been compared to those of a finned-tube heat exchanger to observe much higher heat transfer rate with reasonable excess pressure drop leading to a higher area goodness factor for metal foam-wrapped cylinder.     

Natural Convection Heat Transfer in 2D and 3D Trapezoidal Enclosures Filled with Nanofluid

The purpose of the present study is to investigate the heat transfer performance due to free convection of nanofluids with variable properties inside 2D and 3D channels with trapezoidal cross sections. The governing equations are solved numerically using the finite volume method and the SIMPLER algorithm. In this study, the effect of the nanoparticle volume fraction, Rayleigh number, side wall angles of the trapezoidal section, and axial slope of the 3D channel are examined. The presented results include the average Nusselt number, flow circulation streamlines, and isothermal contours. The heat transfer rate (i.e., Nusselt number) is seen to increase in both 2D and 3D channels with an increase in the Rayleigh number. In 2D trapezoidal enclosures, the Nusselt number decreases with an increase in the nanoparticle volume fraction from zero to 2% and increases if the nanoparticle volume fraction is greater than 2%. In 3D channels, an increase in the axial slope of the channel leads to an increase in the Nusselt number.     

Effect of temperature gradient within a solid particle on the rotation and oscillation modes in solid-dispersed two-phase flows

Liquid–solid two-phase flow with heat transfer is simulated, and the effect of temperature gradient within a solid particle on the particle behaviour and heat transfer is studied. The interaction between fluid and particles is considered with our original immersed solid approach on a rectangular grid system. The local heat flux at the fluid–solid interface is described with an anisotropic heat conductivity matrix, and the governing equation of temperature is time-updated with an implicit treatment for the diffusion term. The method is applied to a 2-D natural convection flow of a relatively low Rayleigh number including multiple particles. Heat transfer and particle behaviours are studied for different solid heat conductivities (ratio to the fluid conductivity ranging between 10⁻³ and 10³) and solid volume fractions. Under a condition of relatively low heat conductivity ratio, the particles show a simple circulating flow. By increasing the heat conductivity ratio, a transition of the particulate flow is observed to oscillation mode around the domain centre due to the buoyancy force as a restitution force. The oscillation period is found to vary with the heat conductivity ratio, and it is related to the time scales for the heat transfer via fluid and solid.     

Numerical simulation of glass fogging and defogging

A numerical procedure for the prediction of fogging and defogging phenomena is presented. The simulation involves the solution of an air flow field along a cold solid surface, the evaluation of the unsteady conduction through the solid itself, and a model for the heat and mass transfer within the thin water layer on the fogged surface. A suite of routines for the unsteady simulation of the water layer evolution is coupled with an equal order finite element Navier Stokes solver and a finite volume conduction code. The procedure is fully independent of the numerical details of the solid and fluid domain solvers. Two different coupling approaches may be followed: A loose one, where the Navier Stokes solution is used only for a steady state estimate of the heat transfer coefficient, or a close one, where the Navier Stokes, conduction and water layer codes are iterated simultaneously. The latter is required for the problem of natural convection, where temperature (and thus the energy balance of the water layer) and flow field are coupled. The water layer is modelled as a collection of closely packed tiny droplets, leaving a portion of dry area among them. The effect of the contact angle is taken into account, and physical assumptions allow to define the local ratio between wet and dry surface for both the fogging and defogging process. As a case study, a comparison with experimental data for a complete fogging and defogging cycle of a glass lens in natural convection is presented.     

Numerical Study of Heat Transfer in a Rectangular Channel with Porous Covering Obstacles

A numerical study is performed to analyze steady laminar forced convection in a channel in which discrete heat sources covered with porous material are placed on the bottom wall. Hydrodynamic and heat transfer results are reported. The flow in the porous medium is modeled using the Darcy–Brinkman–Forchheimer model. A computer program based on control volume method with appropriate averaging for diffusion coefficient is developed to solve the coupling between solid, fluid, and porous region. The effects of parameters such as Reynolds number, Prandtl number, inertia coefficient, and thermal conductivity ratio are considered. The results reveal that the porous cover with high thermal conductivity enhances the heat transfer from the solid blocks significantly and decreases the maximum temperature on the heated solid blocks. The mean Nusselt number increases with increase of Reynolds number and Prandtl number, and decrease of inertia coefficient. The pressure drop along the channel increases rapidly with the increase of Reynolds number.