Heat transfer features of buoyancy-driven nanofluids inside rectangular enclosures differentially heated at the sidewalls

The heat transfer features of buoyancy-driven nanofluids inside rectangular enclosures differentially heated at the vertical walls, are investigated theoretically. The main idea upon which the present work is based is that nanofluids behave more like a single-phase fluid rather than 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 conventional mixing theory. The heat transfer enhancement across the differentially heated enclosure that derives from the dispersion of nano-sized solid particles into a host liquid is calculated for different operating conditions, nanoparticle diameters, combinations of suspended nanoparticles and base liquid, and cavity aspect ratios. The fundamental result obtained is the existence of an optimal particle loading for maximum heat transfer. Specifically, for any assigned combination of solid and liquid phases, the optimal volume fraction is found to increase slightly with decreasing the nanoparticle size, and to increase much more remarkably with increasing both the nanofluid average temperature and the slenderness of the enclosure.     

Effective boundary conditions for buoyancy-driven flows and heat transfer in fully open-ended two-dimensional enclosures

The present work achieves an accurate representation of the effective boundary conditions at the aperture plane of a two-dimensional open-ended structure for wide range of pertinent parameters. The presented effective boundary conditions are correlated in terms of Rayleigh number, Prandtl number, and the aspect ratio of the open-ended geometry. The numerical procedure used in this work is based on the Galerkin weighted residual method of finite-element formulation. Comprehensive comparisons between the present investigation using the effective boundary conditions for the anticipated closed-ended model and the results for the fully extended computational domain confirm successful implementation of the proposed model. Implementation of this representation reduces the main difficulties associated with specifying the open-ended boundary conditions and results in very substantial savings in CPU and memory usage. The present work plays an important role on modeling a basic and generic set of effective boundary conditions at the aperture plane for several applications of practical interest.     

Natural convective heat transfer in square enclosures heated from below

The paper deals with the results of an experimental and numerical study of free convective heat transfer in a square enclosure characterized by a discrete heater located on the lower wall and cooled from the lateral walls.The study analysed how the heat transfer develops inside the cavity at the increasing of the heat source length.The experimental data are obtained by measuring the temperature distribution in the air layer by real-time and double-exposure holographic interferometry while the commercial finite volumes code Fluent 6.0 is used for the numerical study. Convection has been studied for Rayleigh number from 10³ to 10⁶. Different convective forms are obtained depending on Ra and on the heat source length.The local Nusselt number is evaluated on the heat source surface and it shows a symmetrical form raising near the heat source borders. Graphs of the local Nusselt number on the heat source and of the average Nusselt number at several Ra are finally presented.     

Heat transfer enhancement in cubical enclosures with vertical fins

Natural convection of air in a cubical enclosure with a thick partition fitted vertically on the hot wall is numerically investigated for Rayleigh numbers of 10³–10⁶. A three dimensional convective circulation is generated, in which the cold flow sweeps the fin faces and the hot wall, with low flow blockage. The combined contributions of these faces cause heat transfer enhancements over 40% at high Rayleigh numbers and thermal conductivity ratios (R_k). These enhancements significantly exceed the ones obtained with horizontal fins. Even low R_k values cause heat transfer enhancements, except at Ra = 10⁴.     

Immersed boundary computations of shear- and buoyancy-driven flows in complex enclosures

Cartesian grids used with the immersed boundary method (IBM) offer an attractive alternative for simulating fluid flows in complex geometries. We present a ghost fluid method for incompressible flows solved with staggered grids. The primary feature is the satisfaction of local mass continuity for ghost pressure cells, rather than extrapolating the pressures from within the flow domain. The method preserves local continuity in each cell and also global continuity. As a result, no explicit mass sources or sinks are needed. We have applied the method to study shear- and buoyancy-driven flows in a number of complex cavities.     

Temperature effects on the enhanced or deteriorated buoyancy-driven heat transfer in differentially heated enclosures filled with nanofluids

ABSTRACT

A two-phase model based on the double-diffusive approach is used to perform a numerical study of natural convection in differentially heated vertical cavities filled with water-based nanofluids, 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 through 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 the literature experimental data. The pressure–velocity coupling is handled using the SIMPLE-C algorithm. Numerical simulations are executed for three different nanofluids, using the diameter and the average volume fraction of the suspended nanoparticles, as well as the cavity width, the average temperature of the nanofluid, and the temperature difference imposed across the cavity, as independent variables. It is found that the heat transfer performance of the nanofluid relative to that of the base fluid increases notably with increasing the average temperature, showing a peak at an optimal particle loading. Conversely, the other controlling parameters have moderate effects.     

Mixed convective heat transfer in rectangular enclosures driven by a continuously moving horizontal plate

The fluid flow and heat transfer induced by the combined effects of the mechanically driven lid and the buoyancy force within rectangular enclosures were investigated in this work. The fluid filled enclosures are heated and lid-driven either on the upper or on the lower horizontal wall, thermally isolated on the right vertical wall, and cooled on the other walls. The basis of the investigation was the numerical solutions of the equations for the conservation of mass, momentum, and energy transport using the finite difference method. The effects of the flow governing parameters including the Richardson and the Prandtl numbers, and the length-to-height aspect ratio, respectively, in the range 10⁻²  Ri  10², 10⁻³  Pr  10, and 1  AR  4 for a fixed Reynolds number, Re = 100, were studied. The results are presented in the form of the hydrodynamic and thermal fields, and the profiles for vertical and horizontal components of velocity, temperature, and the local heat flux. The fluid flow and energy distributions within the enclosures and heat flux on the heated wall are enhanced by the increase in the Richardson number. While an increase in the Prandtl number improves the heat flux on the heated wall, an increase in aspect ratio suppresses it. The results can be used as base line data in the design of systems in which mixed convection heat transfer in rectangular enclosures occurs.     

Experimental and numerical study of transient natural convection due to mass transfer in inclined enclosures

Both experiments and numerical work are performed to study transient natural convection flow and transport process due to mass transfer in the enclosures inclined at different angles. In the experiments, the enclosure is filled with aqueous solution containing CuSO₄ + H₂SO₄ where the flow structure can be visualized by both particle tracer and shadowgraph. Two opposed side walls of the enclosure are maintained at different concentrations which are made by passing current through the electrodes at the limiting condition. All the other side walls are made insulated and impermeable to the species transfer. Both the concentration distribution and its fluctuations are measured with non-intrusive optical method. During the experiments, the Rayleigh number ranges from 1.126 × 10⁸ to 1.157 × 10¹¹, the angles of inclination from 30 to 90 degree and the aspects ratio of the enclosure from 0.6 to 1. Comparison between the data and prediction is made and discussed at various conditions.     

Numerical research of nature convective heat transfer enhancement filled with nanofluids in rectangular enclosures

Heat transfer enhancement utilizing nanofluids in a two-dimensional enclosure is investigated for various pertinent parameters. The Khanafer's model is used to analyze heat transfer performance of nanofluids inside an enclosure taking into account the solid particle dispersion. Transport equations are model by a stream function-vorticity formulation and are solved numerically by finite-difference approach. Based upon the numerical predictions, the effects of Rayleigh number (Ra) and aspect ratio (AR) on the flow pattern and energy transport within the thermal boundary layer are presented. The diameter of the nanoparticle d_p is taken as 10 nm in nanofluids. The buoyancy parameter is 10³ ≤ Ra ≤ 10⁶ and aspect ratios (AR) of two-dimensional enclosure are 1/2, 1, 2. Results show that increasing the buoyancy parameter and volume fraction of nanofluids cause an increase in the average heat transfer coefficient. Finally, the empirical equation was built between average Nusselt number and volume fraction.     

Comparison of four insulation schemes for reduction of natural convective heat transfer in rectangular enclosures

This paper reports a comparative study of using four insulation schemes to reduce natural convective heat transfer in two-dimensional rectangular enclosures. The SIMPLER algorithm was used to solve the equations governing heat and fluid flow in the enclosures. Reduction in heat transfer was determined for a wide range of conditions and the effectiveness of the different insulation schemes was established.     

Analysis of convective momentum and wall heat transfer: application to vortex boundary layer interaction

The main topic of this paper is the analysis of momentum and heat transfer mechanisms occurring inside a disturbed boundary layer. This analysis is carried out based on a phenomenological decomposition using von Karman’s integral equations, in which appear terms that account for several contributions: the flat plate term, and the unsteady and external gradient terms.This method is applied to the interaction between a single transverse vortex and a boundary layer developing on a flat plate. Based on numerical simulations, we present a qualitative and quantitative study of the behavior of momentum and heat wall transfer described by the terms resulting from the phenomenological decomposition. Finally, the time-dependent behavior of the analogy factor is investigated.     

Numerical study of transient buoyancy-driven convective heat transfer of water-based nanofluids in a bottom-heated isosceles triangular enclosure

A numerical study of transient buoyancy-driven convective heat transfer of water-based nanofluids inside a bottom-heated horizontal isosceles triangular cylinder is presented. Nano-sized copper oxide (CuO) particles suspended in water with two different volume fractions are considered. The thermophysical properties of water in the presence of nanoparticles are predicted using existing models, in which the effects of the Brownian motion of nanoparticles are taken into account. It is shown that pitchfork bifurcation appears for relatively high Grashof numbers and the critical Grashof number is found to be 5.60 × 10⁴. The predicted development of convective flow of nanofluids is presented by means of the average Nusselt number over the bottom. Additionally, the flow development time towards a steady/quasi-steady state and the time-averaged Nusselt number are scaled with Grashof number. It is also shown that at constant Grashof numbers the time-averaged Nusselt number is lowered as more nanoparticles are added to the base liquid and will be overestimated if the Brownian motion effects are not considered.     

管内对流换热过程的热优化分析

对管内对流换热过程的温差换热和粘性摩擦引起的熵产进行了分析和优化计算 ,对换热设备和传热技术的设计和优化组织具有一定的指导意义。     

Three-dimensional bifurcations in a cubic cavity due to buoyancy-driven natural convection

Rich and complex buoyancy-driven flow field due to natural convection will be studied numerically over a wide range of Rayleigh numbers in a cubic cavity by virtue of the simulated bifurcation diagram, limit cycle, power spectrum and phase portrait. When increasing the Rayleigh number, the predicted flow is found to evolve from the conductive state to the state with the onset of convection, which is featured with the steady and symmetric laminar solution, and then to the asymmetric state (pitchfork bifurcation), which will not be discussed in this paper. As the Rayleigh number was further increased, a limit cycle branching from the fixed point of the investigated dynamical system is observed. Supercritical Hopf bifurcation is confirmed to be the birth of the orbitally stable limit cycle that separates the vortex flow into an inner unstable region (moving away from the vortex coreline) and an outer stable region (moving towards the vortex coreline). As the Rayleigh number is increased still, the investigated buoyancy-driven flow became increasingly destabilized through quasi-periodic bifurcation and then through two predicted frequency-doubling bifurcations. Thanks to the power spectrum analysis, bifurcation scenario was confirmed to have an initially single harmonic frequency, which is featured with a driving amplitude. Then an additional ultraharmonic frequency showed its presence. Prior to chaos, in the five predicted arithmetically related frequencies there exists one frequency that is incommensurate to the other two fundamental frequencies. This computational study enlightens that the investigated nonlinear system, which involves frequency-doubling bifurcations, loses its stability to a quasi-periodic bifurcation featured with the formation of a subharmonic frequency. Subsequent to the formation of three frequency-doubling bifurcations and one quasi-periodic bifurcation, an infinite number of frequencies was observed in flow conditions with the continuously increasing Rayleigh numbers. Finally, the chaotic attractor was predicted to be evolved from the strange attractor in the corresponding phase portraits.     

Heat flow visualization for natural convection in rhombic enclosures due to isothermal and non-isothermal heating at the bottom wall

Analysis has been carried out for the energy distribution and thermal mixing in steady laminar natural convective flow through the rhombic enclosures with various inclination angles, φ for various industrial applications. Simulations are carried out for various regimes of Prandtl (Pr) and Rayleigh (Ra) numbers. Dimensionless streamfunctions and heatfunctions are used to visualize the flow and energy distribution, respectively. Multiple flow circulations are observed at Pr = 0.015 and 0.7 for all φs at Ra = 10⁵. On the other hand, two asymmetric flow circulation cells are found to occupy the entire cavity for φ = 75° at higher Pr (Pr = 7.2 and 1000) and Ra (Ra = 10⁵). Heatlines are found to be parallel circular arcs connecting the cold and hot walls for the conduction dominant heat transfer at Ra = 10³. The enhanced convective heat transfer is explained with dense heatlines and convective loop of heatlines at Ra = 10⁵. Heatlines clearly demonstrate that the left wall receives heat from the bottom wall as heatlines directly connect both the walls whereas the convective heat circulation cells play lead role to distribute the heat along the right wall, especially for smaller φs. On the other hand, the heat flow is evenly distributed to both side walls at higher φs via convection as well as direct conductive transport. Significant convective heat transfer from the bottom hot wall to the left cold wall occurs for φ = 30° cavity whereas the heat transfer to the right cold wall is maximum for φ = 75° irrespective of Pr. Average Nusselt number studies also show that φ = 30° cavity gives maximum heat transfer rate from the bottom to left wall irrespective of Pr in isothermal heating case. On the other hand, enhanced thermal mixing occurs at φ = 75° for both isothermal and non-isothermal heating strategies except at Pr = 0.015 in isothermal heating case.     

Heat transfer and two-phase flow during convective boiling in a partially-heated cross-ribbed channel

Measured local heat transfer data and visual observations of the two-phase flow behavior are reported for convective boiling of saturated liquids in a cross-ribbed channel similar to geometries used in formed-plate compact heat exchangers. Experiments in this study were conducted using a special test section which permitted direct visual observation of the boiling process while simultaneously measuring the local heat transfer coefficient at several locations along the channel. One wall of the channel was heated while the opposite and lateral walls were adiabatic. Measured local heat transfer coefficients on the heated portion of the channel wall were obtained for convective boiling of methanol and n-butanol at atmospheric pressure with the channel oriented vertically and in horizontal positions with top heating, side heating and bottom heating of the channel. Vertical flows were observed to be in the churn or annular flow regimes over most of the channel length whereas the horizontal flows were either in the wavy or annular flow regime over most of the channel. Visual observations also indicated that virtually no nucleate boiling was present when the flow was in one of these three regimes. For the same coolant and flow conditions, at moderate to high qualities, the measured convective boiling heat transfer coefficients for the vertical and horizontal orientations were usually found to differ by only a small amount. However, for some orientations, partial dryout of the heated wall of the channel was sometimes observed to reduce the heat transfer coefficient. A method of correlating the heat transfer data for annular film-flow boiling in cross-ribbed channel geometries is also described.     

Heat transfer in enclosures having a fixed amount of solid material simulated with heterogeneous and homogeneous models

This work compares two different approaches for obtaining numerical solutions for laminar and turbulent natural convection within a cavity filled by a fixed amount of a solid conducting material. In the first model, a porous-continuum, homogeneous or macroscopic approach is considered based on the assumption that the solid and the fluid phases are observed as a single medium, over which volume-averaged transport equations apply. Secondly, a continuum, heterogeneous or microscopic model is considered to solve the momentum equations for the fluid phase resulting in a conjugate heat transfer problem in both the solid and the void space. In the continuum model, the solid phase is composed of square obstacles, equally spaced within the cavity. In both models, governing equations are numerically solved using the finite volume method. The average Nusselt number at the hot wall, obtained from the porous-continuum, homogeneous or macroscopic model, for several Darcy numbers, are compared with those obtained with the second approach, namely the continuum model, with different number of obstacles. When comparing the two methodologies, this study shows that the average Nusselt number calculated for each approach for the same Ra_m differs from each other and that this discrepancy increases as the Darcy number decreases, in the porous-continuum model, or the number of blocks increases, in the continuum model. Inclusion of turbulent transfer raises Nusselt for both the continuum and the porous-continuum models. A correlation is suggested to modify the macroscopic Rayleigh number in order to match the average Nusselt numbers calculated by the two models for Ra_m = const = 10⁴ and Da ranging from 1.2060 × 10⁻⁴ to 1.