Laminar natural convection characteristics in an enclosure with heated hexagonal block for non-Newtonian power law fluids

This work illustrates the steady state, two dimensional natural convective flow and heat transfer features in square enclosure containing heated hexagonal block maintained either at constant wall temperature(CWT) or uniform heat flux(UHF) thermal conditions. Governing equations(mass, momentum and energy) are solved by using finite volume method(FVM) with 3rd order accurate QUICK discretization scheme and SIMPLE algorithm for range of field pertinent parameters such as, Grashof number(10~3≤ Gr ≤ 10~6), Prandtl number(1 ≤ Pr ≤ 100) and power law index(0.5 ≤ n ≤ 1.5). The analysis of momentum and heat transfer characteristics are delineated by evolution of streamlines, isotherms, variation of average Nusselt number value and Colburn factor for natural convection(j_(nH)). A remarkable change is observed on fluid flow and thermal distribution pattern in cavity for both thermal conditions. Nusselt number shows linear variation with Grashof and Prandtl numbers; while rate of heat transfer by convection decreases for power law index value. Higher heat transfer rate can be achieved by using uniform heat flux condition. A Nusselt number correlation is developed for possible utilization in engineering/scientific design purpose.     

End wall effects on thermal stratification and heat transfer in a vertical enclosure with offset partitions

End wall effects on thermal stratification and heat transfer in a vertical enclosure with offset partitions has been studied by numerically solving the governing differential equations. Two limiting end wall conditions are investigated — adiabatic end walls and perfectly conducting end walls. Two offset partition positions and three partition heights are considered. It is observed that with adiabatic end walls, the heat transfer from the vertical hot and cold walls is always greater. The effect of end wall conditions is most significant when the top partition is offset toward the cold wall and the bottom partition toward the hot wall. In this position strong thermal stratification in the core is observed. When the direction of offset is reversed, i.e., top partition is moved closer to the hot wall and the bottom partition closer to the cold wall, strong stratification effects are noted in the partition-near side wall region. Adiabatic end wall conditions promote these stratification effects.     

Numerical simulation of natural convection in a square enclosure filled with nanofluid using the two-phase Lattice Boltzmann method

Considering interaction forces (gravity and buoyancy force, drag force, interaction potential force, and Brownian force) between nanoparticles and a base fluid, a two-phase Lattice Boltzmann model for natural convection of nanofluid is developed in this work. It is applied to investigate the natural convection in a square enclosure (the left wall is kept at a high constant temperature (T_H), and the top wall is kept at a low constant temperature (T_C)) filled with Al₂O₃/H₂O nanofluid. This model is validated by comparing numerical results with published results, and a satisfactory agreement is shown between them. The effects of different nanoparticle fractions and Rayleigh numbers on natural convection heat transfer of nanofluid are investigated. It is found that the average Nusselt number of the enclosure increases with increasing nanoparticle volume fraction and increases more rapidly at a high Rayleigh number. Also, the effects of forces on nanoparticle volume fraction distribution in the square enclosure are studied in this paper. It is found that the driving force of the temperature difference has the biggest effect on nanoparticle volume fraction distribution. In addition, the effects of interaction forces on flow and heat transfer are investigated. It is found that Brownian force, interaction potential force, and gravity-buoyancy force have positive effects on the enhancement of natural convective heat transfer, while drag force has a negative effect.     

Effect of blockage on heat transfer from a cylinder to power law liquids

The influence of planar confining walls on the steady forced convection heat transfer from a cylinder to power-law fluids has been investigated numerically by solving the field equations using FLUENT (version 6.2). Extensive results highlighting the effects of the Reynolds number (1?Re?40), power-law index (0.2?n?1.8), Prandtl number (1?Pr?100) and the blockage ratio (β=4 and 1.6) on the average Nusselt number have been presented. For a fixed value of the blockage ratio, the heat transfer is enhanced with the increasing degree of shear-thinning behaviour of the fluid, while an opposite trend was observed in shear-thickening fluids. Due to the modifications of the flow and temperature fields close to the cylinder, the closely placed walls (i.e., decreasing value of the blockage ratio) further enhance the rate of heat transfer as the fluid behaviour changes from Newtonian to shear-thickening fluids (n>1), the opposite influence is seen with the decreasing value of the flow behaviour index (n) in shear-thinning (n<1) fluids. Finally, the functional dependence of the present numerical results on the relevant dimensionless parameters has been presented in the form of closure relationships for their easy use in a new application.     

以最佳温度均匀度和最小熵产为目标的航天器热循环试验系统运行参数优化

以数值模拟的方法研究了不同运行参数下航天器热循环试验箱内温度均匀度与熵产的变化规律。结果表明,在4.3×10³≤Re≤8.6×10⁵、4.62×10¹³≤Gr≤1.38×10¹⁴范围内,由于强浮升力的作用,壁面附近出现回流区,温度由上往下降低,中轴线附近气体加速下沉,温度由上往下升高。箱内量纲1温度标准偏差随Reynolds数增大而增大,随Grashof数变化不明显;混合对流过程中流动熵产远小于传热熵产,熵产数值随Reynolds数、Grashof数的增大而增大。提出了壁面Nusselt数、试验箱内量纲1平均温度、量纲1温度标准偏差及量纲1传热熵产随Reynolds数、Grashof数变化的关联式。     

Simulation of forced convection in a channel with nanofluid by the lattice Boltzmann method

This paper presents a numerical study of the thermal performance of fins mounted on the bottom wall of a horizontal channel and cooled with either pure water or an Al₂O₃-water nanofluid. The bottom wall of the channel is heated at a constant temperature and cooled by mixed convection of laminar flow at a relatively low temperature. The results of the numerical simulation indicate that the heat transfer rate of fins is significantly affected by the Reynolds number (Re) and the thermal conductivity of the fins. The influence of the solid volume fraction on the increase of heat transfer is more noticeable at higher values of the Re.     

Free Heat and Mass Transfer in a Porous Enclosure with Side Vents

Free heat and mass transfer during drying in a porous enclosure with free vents has been investigated numerically. Enclosed moist air interacts with the surrounding air through freely vented ports situated on both sides perpendicular to the heated wall. Air, heat, and moisture transport structures are visualized respectively by streamlines, heat lines, and mass lines. Effects of thermal Rayleigh number, Darcy number, vent location, and enclosure inclination on the convective heat/moisture transfer rate and volume flow rate across this enclosure are discussed. For each case, partially enclosed fluid flow undergoes different phases, increasing with buoyancy ratio; that is, heat transfer–driven flow, heat- and moisture-aided flow, and moisture transfer–dominated flow. Numerical results demonstrate that the convective heat and moisture transport patterns and transport rates greatly depend on thermal Rayleigh number, properties of porous medium, and enclosure inclination. Practices for enhancing heat and moisture transfer have been suggested for drying processes.     

NATURAL CONVECTION OF A BINARY MIXTURE IN A VERTICAL CLOSED ANNULUS

This article reports an analytical and numerical study of natural convection of a binary mixture within a vertical closed annulus. Neumann boundary conditions for temperature are applied to the vertical walls of the enclosure, while the short walls are insulated. The solutal buoyancy forces are assumed to be induced either by the imposition of constant fluxes of mass on the vertical walls (double-diffusive convection, a = 0) or by temperature gradients (Soret effect, a = 1). The governing parameters for the problem are the thermal Rayleigh number R_T, Prandtl number Pr, Lewis number Le, buoyancy ratio ?, aspect ratio A, constant a, and curvature parameter η. An analytical solution, based on the assumption of parallel flow over a large portion of enclosure, is derived. Numerical confirmation of the analytical results is also presented.     

双周期温度边界下多孔介质方腔内自然对流传热数值模拟

采用局部非热平衡模型及方腔左右两侧壁面温度正弦波变化边界条件,数值分析了具有内热源多孔介质方腔内的稳态非达西自然对流传热。探讨了不同温度波动参数N及波动相位差τ对方腔内自然对流传热的影响。结果表明:方腔两侧壁面出现了周期性分布的温度场,随着N值的增加,方腔内流场及温度场分布逐渐趋向于壁面均一温度边界情况。壁面局部Nu沿着高度方向呈现周期性分布。相对于均一温度的边界条件而言,正弦波温度边界条件在一定程度上强化了多孔介质方腔内的整体传热过程,随着N值的增加,方腔处于温度波动边界时的散热值Q逐渐趋向于均一温度边界时的情况。     

AN APPROXIMATE ANALYSIS FOR THERMAL CONVECTION WITH APPLICATION TO VERTICAL ANNULUS

An approximate analysis based upon the matching of boundary layer solutions for the hot and cold walls through an approximate core temperature, is presented for the free convective heat transfer in an enclosure of complex geometry filled with either a Newtonian fluid or a saturated porous medium. The method has been applied to obtain the heat transfer rates for a vertical porous annulus, and is observed to make reasonably accurate predictions regarding the effects of the governing parameters.     

NUMERICAL STUDY OF FORCED CONVECTION IN A PACKED CHANNEL WITH ASYMMETRIC HEATING

Numerical solution based on the control volume method is presented for the study of heat transfer for forced convective flow in a channel filled with a fluid saturated porous media. The solution of the conservative differential equations governing the flow is performed using the SZMPLE algorithm. The wall effects on the variation of porosity and thermal dispersion have been considered. In calculating the thermal dispersive conductivity, a general expression has been obtained taking into account the flow geometry and flow Reynolds number. The expression appears to serve well in the present investigation and also in reproducing the results of previous studies. The analysis includes predictions of temperature profiles and heat flux for the constant wall temperature condition at the wall and have been compared with available experimental data.     

CFD modelling of flow and heat transfer in the Taylor flow regime

Transport phenomena in the Taylor flow regime for gas–liquid flows in microchannels have received significant attention in recent years. Whilst the hydrodynamics and mass transfer rate in the Taylor flow regime have been studied extensively using experimental and numerical techniques, studies of heat transfer in Taylor flow have been neglected. In this work, the flow and heat transfer in this regime is studied using the volume of fluid (VOF) and level-set techniques to capture the gas–liquid interface, as implemented in the ANSYS Fluent and TransAT codes, respectively. The results obtained from the two different codes are found to match very closely. Fully-developed flow and heat transfer are studied using the VOF method for a Reynolds number (Re) of 280, Capillary number (Ca) of 0.006 and homogeneous void fraction (β) of 0.51 for constant wall heat flux (H) and constant wall temperature (T) boundary conditions. The Nusselt numbers obtained for both cases are 2.5 times higher than those for liquid-only flow. The effects of the mixture velocity and the homogeneous void fraction on flow and heat transfer are also studied.     

NATURAL CONVECTION OF A BINARY MIXTURE IN A VERTICAL CLOSED ANNULUS

This article reports an analytical and numerical study of natural convection of a binary mixture within a vertical closed annulus. Neumann boundary conditions for temperature are applied to the vertical walls of the enclosure, while the short walls are insulated. The solutal buoyancy forces are assumed to be induced either by the imposition of constant fluxes of mass on the vertical walls (double-diffusive convection, a = 0) or by temperature gradients (Soret effect, a = 1). The governing parameters for the problem are the thermal Rayleigh number R_T, Prandtl number Pr, Lewis number Le, buoyancy ratio ϕ, aspect ratio A, constant a, and curvature parameter η. An analytical solution, based on the assumption of parallel flow over a large portion of enclosure, is derived. Numerical confirmation of the analytical results is also presented.     

Natural convection and flow simulation in differentially heated isosceles triangular enclosures filled with porous medium

A finite element analysis is performed to investigate the effects of uniform and non-uniform heating of bottom wall on natural convection flows within isosceles triangular enclosures filled with porous medium. The detailed analysis is carried out in two cases depending on various thermal boundary conditions:

(I)

two inclined walls are maintained at constant cold temperature while the bottom wall is uniformly heated;

(II)

two inclined walls are maintained at constant cold temperature while the bottom wall is non-uniformly heated.

The present numerical procedure adopted in this investigation yields consistent performance over a wide range of parameters of Darcy number, Da (10^-5?Da?10^-3), Rayleigh number, Ra (10³?Ra?10⁶) and Prandtl number, Pr (0.026?Pr?1000) in all the cases mentioned above. Numerical results are presented in terms of stream functions, temperature profiles and Nusselt numbers. It is observed that at small Darcy numbers, the heat transfer is primarily due to conduction irrespective of Pr. As the Darcy number increases, there is a change from conduction dominant regime to convection dominant regime. Flow circulations are also found to be strong functions of Pr at large Da (Da=10^-3) and multiple circulation cells occur at small Pr with Ra=10⁶. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case, but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. As average Nusselt number is same on both the inclined walls, the average Nusselt number for bottom wall is times that of the inclined wall which is well matched in two cases considered for verifying the thermal equilibrium of the system. The correlations are proposed for average Nusselt number as functions of Ra for various Darcy and Prandtl numbers.     

Effect of Blockage on Heat Transfer Phenomena of Spheroid Particles at Moderate Reynolds and Prandtl Numbers

Effects of the confining wall or blockage on the heat transfer phenomena of spheroid particles were numerically investigated. The heated spheroid particles were maintained at constant temperature and allowed to sediment in cylindrical tubes filled with Newtonian liquids. In this flow configuration, the heat transfer took place from the heated spheroid particles to the surrounding Newtonian liquid. The governing conservation equations of the mass, momentum, and energy together with appropriate boundary conditions were numerically solved using commercial software based on computational fluid dynamics. A simple correlation for the average Nusselt number of the confined spheroid particles was developed which can be applied in new applications.     

Forced convection in cross flow of power law fluids over a tube bank

The forced convective heat transfer characteristics for incompressible power-law fluids past a bundle of circular cylinders have been investigated numerically. The cylinder-to-cylinder hydrodynamic interactions have been approximated via a simple cell model. The momentum and energy equations have been solved using a finite difference based numerical method for a range of physical and kinematic conditions. The role of the two commonly used thermal boundary conditions, namely, constant temperature or constant heat flux, on heat transfer characteristics has also been studied. Extensive numerical results elucidating the effect of shear-thinning viscosity on the values of Nusselt number have been obtained for Peclet numbers ranging from 1 to 5000, Reynolds number in the range 1-500, flow behaviour index 1?n?0.5 and three values of voidages, namely, 0.4, 0.5 and 0.6, typical of tubular heat exchangers and tube banks. Under all conditions, varying levels of enhancement in Nusselt number are observed due to shear-thinning behaviour. The surface averaged Nusselt number shows strong dependence on the values of voidage, power-law index, Reynolds and Peclet numbers. The paper is concluded by presenting comparisons with the scant experimental results available in the literature.     

Computation of wall to suspension heat transfer in vertical pipes

In this article, turbulent gas-solid flow in a vertical pipe is investigated for predicting the heat transfer from the heated wall to the suspension. The Eulerian-Eulerian model is used, incorporating a four-way coupling; i.e., considering inter-particle collisions as well as particle-wall collisions. Both the phases are simulated based on Reynolds averaged Navier-Stokes equations (RANS) with a two-equation k ? ? turbulence model for the gas phase and a granular temperature equation for the solid phase. The closure of the granular temperature (kinetic energy associated with the random motion of the particles) equation is done by the use of kinetic theory of granular flows. The main objective of the study is to investigate the variations of two-phase heat-transfer coefficient and Nusselt number with flow parameters like flow Reynolds number, particulate loading, and particle size. In comparison to single-phase flow, heat transfer is found to be significantly increased with the increase in Reynolds number and particulate loading. This happens because of the presence of the solid particles in a gas flow, which bring changes to the heat-transfer characteristics of the gas phase. Heat transfer increased by adding solid particles for particulate loading in the range of 1 to 20 and particle size in the range of 30 to 50 µm.     

缩放管内插双扭带复合强化传热的数值模拟(英文)

The paper presents a 3D numerical simulation of turbulent heat transfer and flow characteristics in converging-diverging tubes(CDs) and converging-diverging tubes equipped with twin counter-swirling twisted tapes(CDTs).The effects of Reynolds number(Re 10000-20000),pitch length(P 11.25,22.5 mm),rib height(e 0.5,0.8,1.1 mm),pitch ratio(δ1:8,5:4,8︰1),gap distance between twin twisted tapes(b 0.5,4.5,8.5 mm) and tape number(n 2,3,4,5,6) on Nusselt number(Nu),friction factor(f) and thermal enhancement factor(η) are investigated under uniform heat flux conditions,using water as working fluid.In order to illustrate the heat transfer and fluid flow mechanisms,flow structures in CDs and CDTs are presented.The obtained results reveal that all geometric parameters have important effects on the thermal performance of CD and CDT,and both CD and CDT show better thermal performance than plain tube at the constant pumping power.It is also found that the increases in the Nusselt number and friction factor for CDT are,respectively,up to 6.3%-35.7% and 1.75-5.3 times of the corresponding bare CD.All CDTs have good thermal performance with η greater than 1 which indicates that the compound heat transfer technique of CDT is commendable for the maximum enhanced heat transfer rate.     

恒壁温时污垢对管内对流换热过程热力学性能影响的分析

基于热力学第一、二定律 ,在恒壁温工况下分析了污垢对管内对流换热过程热力学性能的影响 ;提出了反映污垢对管内对流换热过程热力学性能影响的指标———单位传热量的熵增率 ;讨论了管内流体Reynolds数(无污垢时 )和量纲为 1的入口换热温差等参数对单位传热量熵增率的影响 .研究结果表明 ,该指标不仅能反映污垢对管内传热过程的影响 ,而且能反映污垢对管内流动过程的影响 ,而由污垢层导热所引起的熵产在管内传热过程总的熵产中占有重要的地位     

Investigations of heat transfer and pressure drop between parallel channels with pseudoplastic and dilatant fluids

Central to the problem of heat exchangers design is the prediction of pressure drop and heat transfer in the noncircular exchanger duct passages such as parallel channels. Numerical solutions for laminar fully developed flow are presented for the pressure drop (friction factor times Reynolds number) and heat transfer (Nusselt numbers) with thermal boundary conditions [constant heat flux (CHF) and constant wall temperature (CWT) ] for a pseudoplastic and dilatant non‐Newtonian fluid flowing between infinite parallel channels. A shear rate parameter could be used for the prediction of the shear rate range for a specified set of operating conditions that has Newtonian behavior at low shear rates, power law behavior at high shear rates, and a transition region in between. Numerical results of the Nusselt number [constant heat flux (CHF) and constant wall temperature (CWT) ] and the product of the friction factor and Reynolds number for the Newtonian region were compared with the literature values showing agreement within 0.36% in the Newtonian region. For pseudoplastic and dilatant non‐Newtonian fluids, the modified power law model is recommended to use because the fluid properties have big discrepancies between the power law model and the actual values in low and medium range of shear rates. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 3601–3608, 2003