2002年热传递研究回顾

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"Heat transfer—a review of 2002 literature" 这篇文献综述详细回顾了2002年在传热领域的主要研究进展，涉及了广泛的应用，包括化学工程、一般制造业、能源设备（如通用动力系统、换热器和高性能燃气轮机）等。作者团队由多个知名大学的热力学实验室专家组成，他们对这一领域的研究成果进行了全面梳理。 1. **引言** 文章开头通常会介绍传热研究的重要性，概述过去一年该领域的主要关注点和发展趋势，为读者提供背景信息。 2. **导热** - **接触导热/接触电阻**：讨论了材料间的接触如何影响热量传递，以及接触电阻对热流的影响。 - **微尺度/纳米尺度热传输，非傅里叶效应和激光/脉冲加热**：探讨了在微纳米尺度下，热量传递的新特性，包括非经典热传导现象以及利用激光或脉冲加热技术进行的研究。 - **复杂几何形状中的热传导，复合材料/层状介质和鳍片**：研究了在不规则形状和特殊结构中热传导的规律，以及复合材料和鳍片设计对热管理的影响。 - **分析/数值方法和建模/仿真技术**：介绍了新的理论分析工具和计算模拟方法，这些工具对于理解和预测热传递过程至关重要。 - **实验研究**：提到了一系列实验研究，这些研究通过实测数据验证理论模型并推动了传热科学的发展。 - **热应力与热机械问题**：分析了热载荷引起的应力及其对材料结构稳定性的影响。 - **其他应用**：涵盖了传热研究在其他领域，如材料科学、生物医学工程等的应用。 3. **边界层与外部流动** - **外部效应**：讨论了外部环境条件，如流体动力学特性，对边界层形成和热交换的影响。 - **几何效应**：研究了不同几何形状如何改变流动和传热特性，例如曲率、粗糙度等对流体动力学和热传输的微妙影响。 - **压缩性和高流速问题**：在高速流动和高压条件下，传热和流动行为的变化，特别是在航空航天和涡轮机械中的应用。这篇综述为研究人员、工程师和设计师提供了2002年传热研究的全面概览，帮助他们了解最新的理论发展、实验技术和工程应用，为进一步的研究和技术创新提供了基础。

transport of heat and mass have been focal points but

with little comparison to experiment. Structured media,

such as that produced by staggered parallel ﬁber arrays

for ﬁltering, were similarly treated numerically with bulk

and Brownian transport of suspended particles [365].

Flow and heat transfer in hydrothermal systems with

discrete cracks were show to depend on Peclet number,

permeability, and presence of cracks [366]. Mixed con-

vection in vertical channel ﬂow was analyzed in terms

of permeability variations under the assumption of neg-

ligible Brinkman and Forcheimer eﬀects [367]. Aiding

mixed convection in an anisotropic channel with oblique

principal axes was analyzed for the full range of possible

ﬂows to elucidate eﬀects of permeability variations [368].

Measurements of interstitial convective heat transfer

and frictional drag for duct ﬂow through metal foams

showed that friction factor and volumetric heat transfer

coeﬃcient increase with lower foam porosity at a ﬁxed

Reynolds number [369]. Forced convection in channels

ﬁlled with metallic ﬁbers was numerically analyzed and

found to be inﬂuenced by stagnant thermal conductivity,

Darcy number and ﬁber thickness [370].

Research was reported on the validity of the thermal

equilibrium assumption [321]. Laminar forced convec-

tion in structured porous media, including combined

free and porous zone ﬂows, revealed some interesting

ﬂow patterns and possible existence of recirculating ﬂow

[371–373]. Measurements of heat transfer to a packed

bed comprising mono-sized glass spheres and either

water or a water–glycerin solution were interpreted in

terms measured temperature proﬁles [374]. For three-

dimensional ﬂow, a combined time and space discretiza-

tion method was developed [375].

Fluidized bed ﬂow and heat transfer were investi-

gated experimentally for both two- and three-phase

beds. Heat transfer measurements from a heated vibrat-

ing cylinder in a bed of glass particles displayed diﬀerent

regimes depending on bed operating parameters [376].

Experiments on heat transfer to wall surfaces and to a

variety of immersed bodies were correlated for wide

range of Archimedes number under slugging ﬂow

[377]. In other experiments, bubble and slug lengths were

determined by decomposition of non-invasive power

spectral density measurements [378]. The addition of

angled deﬂectors to the ﬁn region of a membrane

water–wall heat exchanger surface in a circulating ﬂuid-

ized bed was shown to produce a signiﬁcant increase in

heat transfer rates [379].

Experiments on two- and three-phase ﬂuidized beds

showed that heat transfer coeﬃcients exhibit a maxi-

mum depending on gas and liquid velocities [380]. Heat

transfer coeﬃcients to large spheres in a ﬂuidized sand

bed were measured for a range of gas velocities and

interpreted with a model that does not depend on bubble

fraction [381]. Analysis of high temperature circulating

ﬂuidized beds showed that thermal radiation can ac-

count for up to sixty percent of total heat transfer rate,

depending on particle and gas convection rates [382].

For the particulate ﬂuid beds, analysis showed that the

heat transfer coeﬃcient increases to a maximum and

then decreases as bed void fraction increases [383].

6.4. Porous layers and enclosures

The onset of thermal convection in layers heated

from below was analyzed to determine the inﬂuences

of a magnetic ﬁeld, gravity variation, rotation, internal

heat sources, thermal radiation, and vertical through

ﬂow [384–386]. Heat transfer characteristics at the onset

of chaos in bottom-heated cavities were obtained via a

generalized integral transform technique [387]. The

onset of convection in Darcy–Brinkman ﬂow was deter-

mined via an asymptotic analysis of the singular pertur-

bation problem in the limit of small Darcy number [388].

A two-temperature model was also employed for the

same ﬂow model to show that thermal non-equilibrium

can raise the critical Rayleigh number above LapwoodÕs

value [389].

A two-equation model including viscous and inertial

eﬀects was used to determine non-equilibrium eﬀects on

overall Nusselt numbers for natural convection in a

square enclosure [390,391]. A non-equilibrium model

was shown to better represent non-Darcy natural con-

vection in high porosity metal foams heated from below

than one in which local thermal equilibrium is assumed

[392].

Numerical solutions for transient three-dimensional

Darcy natural convection in vertical cavities were ob-

tained to show the succession of stable solutions [393].

Non-Darcy eﬀects were similarly analyzed for the verti-

cal annulus, and heat transfer rate decreased with de-

creased Darcy number [394]. For the spherical annular

sector, natural convection exhibits multi-cellular ﬂows

for small aspect ratio [395]. Convection in a tilted frac-

ture in an otherwise impermeable domain was analyzed

to predict the eﬀects of convection on the overall tem-

perature distribution [396].

Natural convection in a vertical cavity comprising

two layers of diﬀerent permeability was shown to exhibit

a wide range of penetrative ﬂows depending on Rayleigh

number and the permeability ratio [397]. Transient con-

vection with heat generation was numerically analyzed

for two-dimensional ﬂow in a rectangular cavity with

air as the ﬂuid phase [398]. A parallel study for a cylin-

drical cavity revealed the eﬀects of aspect ratio and

anisotropy on heat transfer coeﬃcients [399].

For cavities with an oscillating lid, permeability has a

signiﬁcant eﬀect on ﬂow structure and a resonant fre-

quency was noted for a particular Darcy number [400].

Flow and heat transfer in a partially ﬁlled rectangular

cavity with heating from the sides shows the existence

of a quasi-parallel solution with a linear vertical temper-

834 R.J. Goldstein et al. / International Journal of Heat and Mass Transfer 48 (2005) 819–927

ature distribution [401]. Natural convection in a super-

posed ﬂuid and porous layer shows that the Marangoni

eﬀect enhances ﬂow in the ﬂuid layer, which results in a

reduction of buoyancy driven convection in the porous

sub-layer [402]. Mixed convective eﬀects were numeri-

cally analyzed for two-dimensional cavities to obtain

ﬂow structure and overall heat transfer rates [403,404].

Double diﬀusive convection in an anisotropic med-

ium with opposing buoyancy temperature and solute

gradients found to exhibit multiple solutions and oscil-

lating ﬂow [405]. Oscillatory solutions were also found

for the case heat and mass ﬂuxes were opposed

[406,407]. Doubly diﬀusive non-Darcian ﬂow driven by

the upper surface exhibited the eﬀects of varying Lewis

and Richardson numbers [408]. Double diﬀusive natural

convection in a stratiﬁed square cavity was found to be

markedly aﬀected by unequal species and thermal diﬀu-

sion coeﬃcients [409]. Double diﬀusive convection dri-

ven by cross gradients in a stably stratiﬁed enclosure

showed little diﬀerence in heat and mast transfer rates

between the two- and three-dimensional numerical solu-

tions [410]. A numerical solution was reported for dou-

ble diﬀusive convection with parallel transverse

temperature and concentration gradients in the presence

of heat generation or absorption [411,412].

Combined conduction, convection and thermal radi-

ation in a semi-transparent porous sphere were com-

puted via a modiﬁed discrete ordinate method [413].

6.5. Coupled heat and mass transfer

Theoretical work was reported on an unconditionally

stable numerical method for the general case where

material properties vary with moisture content [414]

and on the kinetics of moisture and heat transfer in cap-

illary media and in aerosols [415]. A conjugate gradient

inverse method was developed to determine unknown

time-dependent Biot numbers and transport based on

interior measurements of temperature and moisture

[416], and a multi-level time scheme was developed for

numerically solving the non-linear Luikov system [417].

A review of several pore-network models for comput-

ing eﬀective transport properties and transport rates in

capillary media has identiﬁed several open problems

for further research [418]. An analytic solution based

on a quasi-steady approach results in a constant speed

for the drying front, which is corroborated by experi-

ments [419]. LuikovÕs equations for capillary media were

solved with the aid of measured temperature and mois-

ture content [420] for both the direct and inverse prob-

lems [421]. A ﬁlm ﬂow model was developed based on

a network of capillary porous tubes for free water ﬂow

prior to the onset of the hygroscopic regime [422].A

more general numerical study of multistage drying re-

gimes determined that total drying time is mainly depen-

dent on the relative humidity of the drying medium

[423]. A novel heater was developed and characterized

for rapid vaporization of sub-cooled liquid in a capillary

medium [424].

Vacuum drying in randomly packed particles was

measured at constant heat input to qualitatively deter-

mine internal controlling factors on drying rates [425].

Microwave drying of capillary media was similarly

investigated to determine the inﬂuence of irradiation

time, particle size, and initial moisture content on inter-

nal temperature and moisture distributions [426,427].

Drying of bed particles and immersed samples in ﬂuid-

ized beds was investigated via experiments and semi-

empirical modeling [428–430]. Temperature, moisture

content, and pore pressure were measured for the drying

of concrete to determine the rate of vapor penetration

[431], and mass diﬀusivity was determined based on

non-stationary moisture absorption measurements

[432,433].

Packed bed combustion of coke particles was investi-

gated experimentally and data are reported for tempera-

ture, gas concentration, particle size and sphericity, and

void fractions [434]. A coupled internal-external gas-

phase model of the combustion of a porous carbon par-

ticle in oxygen was developed to predict the formation of

CO and CO

[435]. An experimental parameter study of

solid waste incineration on a full-scale moving bed pro-

duced rich data set that includes internal NO

proﬁles

[436]. Forced-ﬂow smoldering in ﬂat polyurethane foams

was simulated in wind tunnel tests to determine the cou-

pling between the external boundary layer and front

propagation [437]. Data on ﬂame temperature, location

of the vapor–liquid interface, vapor region propagation,

and fuel residue distribution in non-spread diﬀusion

ﬂames of liquid soaked porous beds were reported and

compared to predictions of a Stefan-type model [438].

Experiments on combustion in media show that there

are critical conditions for the initiation and extinction

of super-adiabatic combustion in steady ﬂow [439].A

numerical model of planar premixed methane ﬂames in

ceramic media suggest that heat transfer between phases

remains decoupled from the initial ﬂame chemistry [440].

The role of adsorption and phase change in the char-

acterization of low moisture materials was modeled with

the phase change rate related to local non-equilibrium

through a delay coeﬃcient [441]. An improved variable

switching scheme for multi-phase transport in soils with

a non-aqueous liquid phase developed [442]. Related

studies considered similar processes for large scale geo-

logic systems, including fracture ﬂow and imbibition ef-

fects [443–446]. Mineralization and ore body formation

in hydrothermal/sedimentary basins was successfully

modeled in terms of the pore-ﬂuid velocity and the equi-

librium concentration [447,448].

Optimal sublimation rates in a porous half-space

were determined in terms of the vapor mass concentra-

tion at the sublimation front [449]. Direct contact

R.J. Goldstein et al. / International Journal of Heat and Mass Transfer 48 (2005) 819–927 835

melting of ice particles was found to exhibit distinct re-

gimes for very small and large particle diameter [450].

Convective melting of a granular bed under micrograv-

ity was experimentally investigated and successfully

decoupled buoyancy eﬀects due to density diﬀerences

[451]. Preferential ﬂow paths formed during the dissolu-

tion of a porous medium were found to depend on the

properties of the medium at the pore scale [452]. Heat

transfer with phase change in an inclined packed enclo-

sure was numerically determined, and a Nusselt-versus-

Rayleigh–Darcy number was developed [453].

Moisture transport in paperboard was modeled in

terms of a linear driving force transport at the interface

of a system of continuous hygroscopic ﬁbers and voids

and found dependent on relative values of diﬀusion

and adsorption parameters [454]. Convective heat and

moisture transport coeﬃcients in cotton material were

measured and modeled in terms of the speed of air pene-

trating the material [455,456], and a companion study

considered periodic air ﬂow, such as occurs in walking

[457]. Fabric thickness and porosity were shown to sig-

niﬁcantly aﬀect moisture transfer via a model that incor-

porates liquid diﬀusion in the mass and energy

conservation equations [458]. Related studies incorpo-

rate evaporation and mobile condensates in ﬁbrous insu-

lation and building systems [459–461]. Moisture content

and eﬀects of non-uniformity in percolation were inves-

tigated with respect to drying of potatoes [462].

7. Experimental methods

7.1. Introduction

The need for measurements in heat transfer and re-

lated ﬂow studies remains strong. This is particularly true

in situations which cannot be completely deﬁned in fairly

straightforward numerical modeling. This includes,

among other things, two phase ﬂow, and many turbulent

ﬂow situations. Modeling of the turbulent heat transport

process is still not reﬁned to the point of making accurate

predictions in particular in ﬂows that have not been well

studied and well measured. Thus, if nothing else, the

measurements must be used to reﬁne turbulence models

and to some extent numerical methods. In addition ﬂow

and thermal measurement are required in many indus-

trial and, for that matter, consumer-used systems. Accu-

rate and reliable data are required, which gives rise to the

need for good methods of measuring temperature, heat

transfer and velocity, and also other ﬂow parameters,

as well as property measurements of real materials.

7.2. Heat transfer

Visualization techniques have been used in a number

of heat transfer measurements. This can mean an appli-

cation of a thermochromic liquid crystal (TLC) and a

transient experiment in which the change in local tem-

perature on a surface with time, deduced from the local

color changes of the TLC, are used to calculate the local

heat ﬂux. Such a system has been applied in a super-

sonic blowdown tunnel for Mach-three ﬂow over a sur-

face [463]. An uncertainty analysis [464] shows the

potential error, when obtaining local heat transfer coef-

ﬁcients, from discrete random uncertainties in TLC

measured temperatures. Luminescent coatings are used

[465] to measure surface heat transfer rates in a short-

duration hypersonic ﬂow at Mach numbers between

9.5 and 11.1. A new simpliﬁed model [466] can be used

for data reduction of transient heat transfer measure-

ments in internal channel heating and cooling investiga-

tions. A two dimensional transient heat conduction

analysis [467] improves the reliability of heat transfer

measurements for erodable ribbon-element heat ﬂux

gauges used in internal combustion engines. A design

analysis [468] of a heat ﬂux sensor based on the trans-

verse Seebeck eﬀect demonstrates how measurements

of instantaneous values of heat ﬂux can be obtained

in a free convection boundary layer. The operating prin-

ciples and calibration procedure for a new-design diﬀer-

ential calorimeter used for heat transfer measurement

have been described [469].

7.3. Temperature measurement

A telocentric objective lens used with a digital camera

eliminates the angular dependence in the color determi-

nation which is critical in use of thermochromic liquid

crystals for precision measurements [470]. An interfacial

temperature sensor of 1 lm thickness, developed using

microfabrication techniques, has measured temperatures

in a simulated rapid solidiﬁcation process [471]. Fluores-

cence properties of a special thermographic phosphor

permit high spatial- and temporal-resolution tempera-

ture measurement [472]. Black-body optical-ﬁber ther-

mometers with a metallic coated sensing tip are used

for measurements in high temperature environments

[473]. Numerical experiments [474] evaluate the use of

a passive acoustic thermal tomograph for providing

spatial resolution of temperature on a surface. An

infrared-charge-coupled device (ccd) camera provides

the temperature distribution at the cutting edge of a

machine tool [475].

7.4. Velocity measurement

A closely-spaced array of hot-ﬁlm sensors is used

[476] to determine the skin friction distribution on a cir-

cular cylinder. A thermal tuft of cool air near a specially

coated TLC surface can indicate very low velocities in

weakly separated ﬂows [477]. A reﬁned analysis [478] im-

proves a speckled tomography technique to reconstruct

836 R.J. Goldstein et al. / International Journal of Heat and Mass Transfer 48 (2005) 819–927

both large-scale structure and microstructure in turbu-

lent ﬂows. Flow patterns can be deduced using process

tomography [479]. A cross correlation technique [480]

improves the time resolution of ultrasonic velocity mea-

surements in turbulent ﬂows. A numerical analysis for

the two dimensional heat transfer from a circular cylin-

der in Couette ﬂow [481] indicates the correction needed

for hot wire measurements near a wall.

7.5. Miscellaneous

Pattern recognition analysis applied to a rake of

resistive probes [482] indicates the presence of bubble

clusters in turbulent bubbly ﬂow. An X-ray tube and

scintillation counters can measure the void fraction in

ﬂows of an air–water mixture [483]. Two phase gas

liquid ﬂows have been studied [484] with an extraction

device in which the air and liquid ﬂows are measured

separately. A wire mesh sensor used with a newly devel-

oped algorithm for special ﬁeld reconstruction [485]

provides local instantaneous true gas velocities in a bub-

ble ﬂow. Surface reﬂectance measurements in the far

infrared are used to determine condensate ﬁlm thickness

on a surface [486]. A special pressure-sensitive paint is

used [487] in a cryogenic steady ﬂow wind tunnel for

pressure measurements. Silicon-based thermal conduc-

tivity detectors have been used in a number of geome-

tries [488]. A three dimensional ﬁnite model [489]

predicts the thermal response of calorimeters used to

measure pulsed laser energies. Calibration methods have

been applied [490] to temperature-modulated diﬀerential

scanning calorimeters.

8. Natural convection-internal ﬂows

8.1. Highlights

Natural convection in a square or rectangular cavity

continues to receive considerable interest. Most investi-

gations are numerical in nature and address issues such

as localized heating or cooling, partial obstructions, var-

iable ﬂuid properties and internal heat generation. A

two-phase ﬂuid containing shape memory alloy/rubber

membrane particles has been proposed that will increase

in bulk density as the temperature increases creating a

negatively buoyant ﬂuid.

8.2. Fundamental studies

Analysis of symmetries and self-similar forms of the

Navier–Stokes and Fourier–Kirchhoﬀ equations was

used to reduce the order of equations and obtain ana-

lytical solutions to a number of natural convection

problems [491]. A review of similitude criteria applied

to natural convection was given [492]. Measurements

were made in large aspect ratio horizontal layers for

Ra from 10

to 10

that support the logarithmic varia-

tion for velocity and temperature proﬁles in the layer

[493]. The validity of the incompressible ﬂow model

coupled with the Boussinesq approximation that is

widely used in natural convection studies was discussed

[494]. Stability and chaotic characteristics of a vertical

wall plume were studied that showed the ﬂow can be

classiﬁed into four regions [495] (Ishida). An interesting

inverse buoyant ﬂuid was described in which particles

composed of shape memory alloy and rubber bellows

make the bulk ﬂuid negatively buoyant when heated

[496].

8.3. Internal heat generation

Stability and bifurcation were studied numerically for

steady internal heating of a horizontal layer cooled from

above and below [497] and for a vertical channel [498].

Three-dimensional numerical solutions were obtained

for liquid metal contained in a cubic enclosure heated

in a uniform magnetic ﬁeld [499]. Oscillating sidewall

temperature on a cavity containing an internally heated

ﬂuid was able to set up resonance at speciﬁc oscillation

frequencies [500]. Studies of internal heating were also

applied to geoplanetary ﬂows [501–505].

8.4. Thermocapillary ﬂows

A similarity solution was obtained for developing

Marangoni ﬂow over a ﬂat surface [506]. Approximate

similarity of temperature and velocity proﬁles was found

for large Prandtl number in a ﬂoating zone technique

used for crystal production [507]. Thermocapillary ﬂows

were studied in various containers including rectangular

cavities [508,509] and a liquid bridge [510]. Eﬀects of

Marangoni type ﬂows were studied for bubbles, drops

or particles in suspension [511] and for single glycerine

drops [512]. Heat transfer was found to be enhanced

by thermocapillary ﬂows in an ammonia–water absorp-

tion process by adding n-octanol [513].

8.5. Enclosures

Scaling of heat transfer in large Prandtl number ﬂu-

ids [514] and experimental data obtained using high

pressure gases [515] were given for large Rayleigh num-

ber ﬂows in horizontal layers. Eﬀects of time dependent

gravity on the thermal stability of a ﬂuid layer was given

[516]. Rayleigh-Benard type problems were investigated

for square [517] and cubical [518] cavities, truncated cyl-

inders [519], a deep cavity [520] and a layer with an

inclined upper surface [521]. The horizontal layer geom-

etry was also used to study combined heat and mass

transfer [522] and a layer containing two immiscible ﬂu-

ids [523].

R.J. Goldstein et al. / International Journal of Heat and Mass Transfer 48 (2005) 819–927 837

Numerical solutions were obtained for natural con-

vection in square cavities to illustrate numerical meth-

ods [524,525] and to study the eﬀects of magnetic

ﬁelds, temperature dependent ﬂuids and pseudoplastic

ﬂuids [526–528]. The ﬂow of a magnetic ﬂuid in a

square Hele–Shaw cell was observed using a shadow-

graph method [529]. Numerical solutions were obtained

for natural convection in rectangular cavities to investi-

gate combined heat and mass transfer [530,531],

magnetic damping of the ﬂow of a low-conducting

aqueous solution [532] and temperature variation of

the uninsulated upper wall [533]. Variations of rectan-

gular enclosure geometry include an inclined enclosure

heated from below [534], an inclined enclosure with a

wavy lower wall [535] and a vertical enclosure with

two opposing wavy walls [536]. Solutions for cubical

cavities were presented that incorporate various eﬀects

of a magnetic ﬁeld [534,537,538]. A comparison of ten

numerical solutions to benchmark experimental data

on natural convection in a tilted cubical enclosure con-

taining air was presented [539]. Localized thermal

sources and sinks in rectangular cavities have been

investigated numerically [524,540–542]. Several studies

of partial internal partitions in rectangular enclosures

have been made [543–548]. Vertical [549] and inclined

[550] open cavities have been studied numerically. Res-

onance inside a rectangular cavity heated from the side

with an oscillating moving bottom wall was studied

experimentally using air [551]. Additional geometries

considered include a semi-cylindrical cavity [552], an in-

clined arc-shaped enclosure [553], a dome [554] and a

spent fuel cask [555].

8.6. Vertical cylinders, ducts and annuli

Heat transfer in a vertical cylinder was studied for the

case of conducting walls [556], the eﬀects of a strong

magnetic ﬁeld on air [557,558] and in an annulus heated

from below [559]. Natural convection was studied for a

vertical duct with triangular, circular, square, and rect-

angular cross sections [560]. Measurements of velocity

were made in turbulent ﬂow contained within symmetri-

cally and unsymmetrically heated vertical channels [561].

The eﬀect of partial obstructions in a vertical channel

was modeled for perfectly conducting or adiabatic

obstructions located near the entrance, exit or in the cen-

ter of the channel [562].

8.7. Spherical and horizontal cylindrical annuli

The stability of ﬂow in a spherical annulus was inves-

tigated using a Galerkin–Chebychev spectral method for

axisymmetric disturbances for a wide range in Prandtl

number and aspect ratio [563]. Real-time holographic

interferometry was used to study convection in a spher-

ical annulus when both thermal and electric ﬁeld driving

forces are present [564]. Numerical methods were used

to solve the natural convection ﬂow in horizontal eccen-

tric cylindrical annuli [565–567]. Three-dimensional ﬂow

was studied in a horizontal concentric annulus with

open ends [568]. Numerical methods were used to study

the eﬀects of aspect ratio and eccentricity on the heat

transfer from an isothermal horizontal cylinder to its

square enclosure [569].

8.8. Mixed convection

Experimental [570] and numerical [571] approaches

have been used to investigate the ﬂow patterns in hori-

zontal ducts heated from below. Flow reversal of cold

ﬂuid ﬂowing downward in a vertical rectangular duct

has been studied when the walls are given a constant

heat ﬂux boundary condition [572]. Experiments were

performed using air and water to study the inﬂuence

of variable properties on natural convection in a vertical

annulus [573,574]. Transient spin up of the contents of a

vertical cylindrical container with the bottom heated

showed diﬀerential spin up rates depending on the tem-

perature of the ﬂuid [575]. Various air return locations

were investigated to determine their performance on

the displacement ventilation airﬂow pattern in a room

[576]. Other studies of mixed convection include falling

ﬁlms [577], open enclosures [578], a square cavity with

an internal protrusion [579] and an inclined ice melting

layer [580].

8.9. Fires

Numerical solutions were presented for several rele-

vant problems including ventilation and ﬁre spread in

highway tunnels [581]. A three-dimensional forest ﬁre

model was described that included drying, pyrolysis and

combustion of the emitted gases [582]. Additional model-

ing has been conducted for the incineration of solid waste

on a moving bed [583] and a one-dimensional model for

pyrolysis of charring materials [584]. Experiments were

performed to study the eﬀect of a red phosphorous ﬂame

retardant [585].

8.10. Miscellaneous

Double diﬀusive convection [586,587] and thermal

convection in near-critical ﬂuids [588] were studied

under microgravity conditions. Double diﬀusive ﬂow

structures were visualized by injecting glycerine into

the bottom of a water layer [589]. Numerical methods

for simulating aerosol growth and transport in natural

convection ﬁelds were summarized [590]. Air ﬂows in

heated attic spaces were simulated numerically including

the installation of ceiling fans to mix the stratiﬁed ﬂow

[591]. A mathematical model was developed for the

reduction of magnesium in a vertical retort [592].

838 R.J. Goldstein et al. / International Journal of Heat and Mass Transfer 48 (2005) 819–927

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