IOP PUBLISHING MEASUREMENT SCIENCE AND TECHNOLOGY

Meas. Sci. Technol. 21 (2010) 025903 (10pp) doi:10.1088/0957-0233/21/2/025903

A new method for simultaneousmeasurement of convective and radiativeheat flux in car underhood applicationsM Khaled1,2, B Garnier1, F Harambat2 and H Peerhossaini1,3

1 Thermofluids, Complex Flows and Energy Research Group—Laboratoire de Thermocinetique,CNRS-UMR 6607, Ecole polytechnique—Universite de Nantes, rue C Pauc, BP 50609,44306 Nantes cedex 3, France2 PSA Peugeot Citroen—Velizy A Center, 2 route de Gisy, 78 943 Velizy Villacoublay, France

E-mail: Hassan.peerhossaini@univ-nantes.fr

Received 4 September 2009, in final form 30 November 2009Published 6 January 2010Online at stacks.iop.org/MST/21/025903

AbstractA new experimental technique is presented that allows simultaneous measurement ofconvective and radiative heat flux in the underhood. The goal is to devise an easilyimplemented and accurate experimental method for application in the vehicle underhoodcompartment. The new method is based on a technique for heat-flux measurement developedby the authors (Heat flow (flux) sensors for measurement of convection, conduction andradiation heat flow 27036-2, © Rhopoint Components Ltd, Hurst Green, Oxted, RH8 9AX,UK) that uses several thermocouples in the thickness of a thermal resistive layer (foil heat-fluxsensor). The method proposed here uses a pair of these thermocouples with different radiativeproperties. Measurements validating this novel technique are carried out on a flat plate with aprescribed constant temperature in both natural- and forced-convection flow regimes. The testflat plate is instrumented by this new technique, and also with a different technique that isintrusive but very accurate, used as reference here (Bardon J P and Jarny Y 1994 Procede etdispositif de mesure transitoire de temperature et flux surfacique Brevet n◦94.011996,22 February). Discrepancies between the measurements by the two techniques are less than10% for both convective and radiative heat flux. Error identification and sensitivity analysis ofthe new method are also presented.

Keywords: heat-flux measurement, heat-flux separation, convective and radiative heat flux,fluxmeter, foil heat-flux sensor, car underhood compartment, aerothermal management,experimental methods

(Some figures in this article are in colour only in the electronic version)

Nomenclature

A constante thickness (m)f view factorh heat-transfer coefficient (W m−2 K−1)K coefficientn number of thermocouplesR thermal resistance (K m2 W−1)

3 Author to whom any correspondence should be addressed.

T temperature (◦C)U voltage (V)

Subscripts and superscripts

1 fluxmeter 12 fluxmeter 2a airad adhesivec convectivecor correction

0957-0233/10/025903+10$30.00 1 © 2010 IOP Publishing Ltd Printed in the UK

Meas. Sci. Technol. 21 (2010) 025903 M Khaled et al

eq equivalentf fluxmeterg globalmax maximalr radiatives surface′ in the presence of fluxmeter

Greek symbols

ϕ heat flux, W m−2

ε emissivityλ thermal conductivity (s m−1 K−1)σ Stefan–Boltzmann constant (567 × 10−9 W m−2 K4)� difference

1. Introduction

In recent years the car underhood compartment has beensubject to compactness and sealing specifications. Studiesby car manufacturers have focused on engine performanceand controlled climate systems, at the same time takinginto account geometry restrictions arising from styleconstraints. Thus, a confined space must be imposed inthe car underhood that restrains its airflow. In addition,a large number of components must be housed in theunderhood compartment. The result is that complex heat-transfer phenomena (convection and radiation) arise in theconfined underhood geometry. Experimental analyses of thesephenomena are rare and studies have essentially focused ontemperature analyses by numerical simulations [3–8].

Convective and radiative heat transfer normally occursimultaneously in the underhood region, but analysis ofthe physical phenomena occurring in the compartmentrequires characterizing each heat-transfer mode (convection orradiation) separately. Novel experimental techniques must bedevised to meet this fast-growing challenge, techniques that areaccurate, fast and easily implemented in the difficult-to-accesscar underhood compartment. Work on the heat-flux separationtechnique is rare in the literature, and the related previous work[9] has been focused on radiative heat-flux calculation frommeasured overall heat flux.

Most heat-flux sensors are based on one of the threefollowing methods: (1) temperature-gradient measurement,(2) temperature–time change measurement and (3) surfaceheating [10–13]. Heat-flux measurement based on (2) requiresintrusive techniques and sophisticated experimental design,and the surface-heating method (3) necessitates complexcalculations of inversion between temperature and heatflux. Thus, temperature-gradient sensors applied directlyappear most suitable for underhood applications. Heat fluxesmeasured by these types of fluxmeters are obtained from thetemperature gradient between the upper and lower surfaces of athin solid sheet of known thermal properties (normal gradient)or through its surface (tangential gradient). The present studyconsiders normal-gradient fluxmeters.

The fluxmeters used here are based on temperature-gradient calculations across a material of known

Figure 1. Heat-transfer modeling in the vehicle underhood.

thermophysical properties (kapton in our case). Thesegradients result from heat conduction across a sensor of1.8 mm thickness and 17 × 8 mm2 section mounted on thesurface whose heat flux is to be measured. The fluxmetersinclude n thermocouples fixed in the sensor’s thickness(n � 2). These thermocouples, connected in series, measure avoltage proportional to the temperature gradient generated inthe fluxmeter thickness.

This paper presents the results of an experimental studyto validate a fast and accurate technique for simultaneousmeasurement of convective and radiative heat fluxes in thecar underhood compartment. The paper is organized asfollows. Section 3 describes the basic operating principle ofthe proposed method for heat-flux separation and section 4discusses the errors due to the type of sensor and sensitivityanalysis. In section 5 this novel technique is experimentallyvalidated in both the natural- and forced-convection flowregimes.

2. Theoretical grounds

The thermal situation of a component in the underhoodcompartment is modeled by a component (E) of emissivityε and surface temperature TS (figure 1) that exchanges heatby convection with the surrounding air and by radiationwith n other underhood components of temperatures Ti

(i = 1 → n).For the component under consideration (E) of the surface

S, one can write

�x ∈ S ⇒ ϕg = ϕc + ϕr (1)

ϕc = hc(Ts − Ta) (2)

ϕr = εσ

n∑i=1

fi

(T 4

s − T 4i

)(3)

where �x is the position vector of a point on the element surface;ϕgis the global heat flux; ϕc is the convective heat flux; ϕr is theradiative heat flux; hcis the convective heat-transfer coefficient;Ta is the air temperature; σ is the Stefan–Boltzmann constant;fi (i = 1 → n) are the radiative view factors between thecomponent E and the other components.

The mean radiative temperature Tr of the component E isdefined as the temperature of a fictive component (figure 2)with which the component E exchanges heat by radiation witha view factor equal to 1, the same heat flux as with the nother components. Introducing the notion of mean radiativetemperature simplifies the overall heat flux to

ϕg = ϕc + ϕr = hc(Ts − Ta) + εσ(T 4

s − T 4r

)(4)

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Meas. Sci. Technol. 21 (2010) 025903 M Khaled et al

Figure 2. Mean radiative temperature.

Figure 3. Separation of convective and radiative heat fluxes (above);a photograph of fluxmeters applied on a flat plate (below).

where the mean radiative temperature Tr is

Tr = 4

√√√√ n∑i=1

fiT4i . (5)

The heat-flux separation method proposed here involves usingon a surface (whose heat flux is to be measured) of emissivityεs two fluxmeters of different emissivities ε1 and ε2, as shownin figure 3. Therefore, the two fluxmeters measure differentoverall heat fluxes:

fluxmeter 1: ϕ1 = hc1(Ts1 − Ta) + ε1σ(T 4

s1 − T 4r

)(6)

fluxmeter 2: ϕ2 = hc2(Ts2 − Ta) + ε2σ(T 4

s2 − T 4r

). (7)

The surface temperatures measured by the two fluxmeters arealmost the same:

Ts1 ≈ Ts2 = Ts. (8)

Also

hc1 ≈ hc2 = hc (9)

since the two fluxmeters are in the same aerothermalconditions.

It should be mentioned that, in the present study,lateral heat fluxes are considered negligible compared to thattransferred in the normal direction. In fact, the lateral heat

Figure 4. Overall heat flux as a function of emissivity.

fluxes in free convection are less than 1% of the normal heatflux; they are less than 2% in forced convection.

From the two points (ε1;ϕ1) and (ε2;ϕ2) in the (ε;ϕ)

plane, the linear evolution of the overall heat flux as a functionof the emissivity ε can be deduced by ϕ = f (ε), as shown infigure 4.

Then, from the function f (ε) obtained experimentally,one can calculate several variables as follows:

ϕc = f (0) (10)

ϕg = f (εs) (11)

ϕr = f (εs) − f (0) (12)

Tr = 4

√T 4

s − f (εs) − f (0)

εsσ. (13)

3. Errors and sensitivity analyses

As shown in section 2, the separation of the convectiveand radiative contributions to the overall heat flux is basedon the measurement by two fluxmeters of the overall heatfluxes (for the same element E) and the known values of theelement’s surface and fluxmeter emissivities. Thus, errors inthe convective and radiative heat flux can be caused by errorsin the overall heat-flux measurements. On the other hand, thistechnique is sensitive to the preliminary determination of thedifferent emissivities. Section 3.1 discusses which errors canbe neglected or avoided and how inevitable errors can bereduced; section 3.2 analyzes the sensitivity of the methodthrough determination of the different emissivities.

3.1. Error identification

Errors related to the fluxmeter operating mode are of twotypes: errors due to the integration of the fluxmeter on theelement surface and errors due to data acquisition. Integrationerrors are those due to the attachment of the fluxmeter on thesurface (pasted, stuck, . . . ) and errors due to the difference inemissivity between the fluxmeter and the surface to which it isattached. Errors in data acquisition are directly related to theprecision of the data acquisition systems and to the conversionbetween measured and desired values; these latter errors arenormally very small compared to integration errors and can be

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Meas. Sci. Technol. 21 (2010) 025903 M Khaled et al

readily controlled by using accurate devices (the precision ofT- and K-type thermocouples is around 0.375%). Therefore,sensor errors are essentially those caused by sensor–surfaceattachment:

�ϕ = �ϕ(attachment) + �ϕ(emissivity). (14)

The attachment of a fluxmeter of thermal resistance Rf

(figure 5) directly to the surface of a component E withan adhesive of thermal resistance Rad introduces errors inthe surface temperature and in the heat-flux measurement.By neglecting the effect of heat-flux line distortion (sincecalculations based on formulations in [14] show a distortioneffect of 0.5% in the heat-flux measurement), the relative errorsdue to attachment can be expressed as

|�ϕ|attachment

ϕ= 1 − Req

R′eq

(15)

where

Req = R + Ra (16)

R′eq = R + Rad + Rf + Ra = e

λ+

ead

λad+

ef

λf

+1

h′ (17)

where the prime designates parameters measured in thepresence of the fluxmeter; Req is the equivalent thermalresistance of the overall system; R is the element E thermalresistance; Ra is the air thermal resistance; Rad is the adhesivethermal resistance; Rf is the fluxmeter thermal resistance; h isthe overall heat-transfer coefficient.

One can see from equation (15) that errors in heat-fluxmeasurement due to fluxmeter attachment |�ϕ|fixation can bereduced by letting R′

eq tend as much as possible to Req.This can be done only by reducing the thermal resistanceof the adhesive, since that of the fluxmeter is invariable oncethe fluxmeter material is chosen. Thus, the fluxmeter shouldbe attached with a very thin layer of conductive adhesive.On the other hand, in some cases where the heat flux tobe measured is high, errors due to fluxmeter attachmentbecome uncontrollable and a correction must be applied tothe measured flux. In fact, the heat flux in the presence of thefluxmeter can be written as

ϕ′ = ϕRa

Ra + Rintegration(18)

where Rintegration = Rad + Rf and R is negligible. Then

ϕ′

ϕ= Ra

Ra + Rintegration= 1

1 + Rintegration

Ra

. (19)

Thus, to obtain a measured heat flux as close as possibleto the true heat flux, one must minimize the ratio Rintegration

Ra;

that is, one must minimize Rintegration. The lowest possiblevalue of the integration thermal resistance is Rintegration = Rf

(6.8 × 10−3 m2 K W−1 for constantan, used in the fluxmetershere), representing the ideal case in which the fluxmeterbinding has negligible thermal resistance. On the other hand,for better precision the air thermal resistance should be high;that is, measurements are more accurate for a low overall heat-transfer coefficient. Finally, with direct fluxmeter binding, thehigher the heat fluxes measured in forced convection, the

greater the absolute measurement errors (since one can neverreduce Rintegration to zero and the greater the air convectiveheat-transfer coefficient, the farther ϕ′ is from ϕ).

We present below some order of magnitudeapproximations to suggest why our method is moreaccurate for natural convection (low heat flux) than forcedconvection (high heat flux). For natural convection and forsurface temperatures in the present domain, some typicalvalues are

h ≈ 10 W m−2 K−1 ⇒ Rair ≈ 10−1 m2 K−1 W−1 (20)

Rintegration = Rad + Rf = 9 × 10−3 m2 K−1 W−1 (21)

Rintegration

Ra

= 9 × 10−3

10−1= 0.09. (22)

In forced convection, typical heat-transfer coefficients arehigher:

h ≈ 40 W m−2 K−1 ⇒ Ra = 2.5 × 10−2 m2 K−1 W−1 (23)

Rintegration = Rad + Rf ≈ 9 × 10−3 m2 K W−1 (24)

Rintegration

Ra

= 9 × 10−3

2.5 × 10−2= 0.36. (25)

Equations (23)–(25) show that the convective heat-transfercoefficient is the limiting factor for application of the presentmethod.

However, since the convective heat-transfer coefficientvaries weakly with the surface temperature, the discrepancybetween the measured and real heat flux is induced largelyby the lack of precision in the surface temperatures at theinterfaces between the different materials constituting thefluxmeter arrangement (fluxmeter and binding), which resultsfrom the difference between the materials’ thermal resistances.Therefore, the precision of measured heat fluxes can beincreased by knowing either the precise surface temperaturesor the precise thermal resistance values.

In the temperature range[T ′

s ; Ts

](figure 5(b)), the

convective heat-transfer coefficient can be considered to varyweakly with temperature, so that one can write

h = ϕcor

Ts − Ta

= ϕ′

T ′s − Ta

. (26)

Then

ϕcor = ϕ′ ·[

Ts − Ta

T ′s − Ta

]= Kcor · ϕ′ (27)

where ϕcor is the corrected heat flux; Kcor is a correction factor.Generally, corrections can be made by knowing a priori

the thermal properties (particularly the thermal resistances) ofthe different materials in the fluxmeter arrangement. In theexperimental validation developed here (see section 5),the correction is done via the surface temperatures, not thethermal resistances, since one rarely knows precisely thethermal resistances of the different elements in the system(in particular, there is some variability in the thermal contactresistance Rc since the attachment of the heat-flux sensor tothe component’s surface is difficult to reproduce). The twocorrections (by thermal resistance or surface temperature)

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Meas. Sci. Technol. 21 (2010) 025903 M Khaled et al

(a)

(b)

Figure 5. Schematic diagrams and temperature evolutions of (a) without and (b) with fluxmeter.

should lead effectively to the same result, since it is thedifference in thermal resistances that causes the differencein interface temperature. However, correction by interfacetemperatures necessitates measuring the real interface andsurface temperatures with high precision, and this can inducenew integration procedures and thus new integration errorsin the system (the relevant component and the differentsensors). In validating the flux-separation method (by accuratemeasurement of the overall heat-flux density and surfacetemperature by the reference method) in forced convection, theabove correction procedure is applied to the values measuredby the fluxmeters.

Generally, a fluxmeter’s surface emissivity differs fromthat of the surface on which it is affixed, and hence errors canbe induced in the measurement of the overall heat flux. Byassuming that

• the thermal resistance of the fluxmeter is negligible(Rf

∼= 0),• the fluxmeter is perfectly attached to the surface of the

component whose heat flux is to be measured (Rad = 0),

we find that the relative error in the overall heat-fluxmeasurement due to an ideally fixed fluxmeter of emissivity ε′

fixed on a surface of emissivity ε is given by

|�ϕ|emissivity

ϕ= A

∣∣ε′ − ε∣∣

ε(28)

where A is a constant.To reduce the error in the heat-flux measurement related to

the emissivity difference |�ϕ|emissivity, one must use fluxmetersof surface emissivity as close as possible to that of the surfaceson which they are fixed. One solution is to paint the fluxmeterthe same color as the surface, so that the fluxmeter emissivity isthe same as that of the component (though complete matching

is difficult). To obtain approximately the same emissivity ofthe component and the fluxmeter, one can paint them boththe same color (the usual recommendation is black). Howeverin this case, it is not the real heat flux that the componentexchanges (when not painted) that is measured. Therefore, thefirst solution is more promising than the second if the fluxmeteremissivity ε′ can be very close to the component’s emissivity ε.

Finally, the error in the overall heat-flux measurement is

�ϕ = �ϕ(attachment) + �ϕ(emissivity) (29)

which must be reduced as much as possible.

3.2. Sensitivity analysis

Here the sensitivity of the separation method to the emissivitydetermination is analyzed. From the separation methodprinciple described in section 3, the convective and radiativeheat fluxes are given by

ϕc = f (0) =[ϕ1 − (ϕ2 − ϕ1)

ε1

ε2 − ε1

](30)

ϕr = ϕ(εS) − ϕc = (ϕ2 − ϕ1)εs

ε2 − ε1. (31)

By considering dε, the error caused during the determinationof the fluxmeter and surface emissivities, one can write

ε1 − dε < ε1 < ε1 + dε (32)

ε2 − dε < ε2 < ε2 + dε (33)

εs − dε < εs < εs + dε. (34)

Therefore, two cases of emissivity error can arise: in the firstcase, the errors in the different fluxmeter emissivities are in thesame direction (for example, ε1 − dε and ε2 − dε respectivelyinstead of ε1 and ε2 are measured) and in the second case, the

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Meas. Sci. Technol. 21 (2010) 025903 M Khaled et al

Figure 6. Parametric evolution of relative error in radiative heat-fluxcalculation as a function of surface emissivity.

errors in the emissivity are in opposite directions (for example,ε1 − dε instead of ε1 and ε2 + dε instead of ε2 (or vice versa)are measured).

Case 1: emissivity errors are in the same direction. In thiscase, convective and radiative heat fluxes calculated from theoverall heat fluxes measured by the two fluxmeters are differentfrom what should have been obtained because

ϕc,calculated = ϕ1 − (ϕ2 − ϕ1) .ε1 + dε

ε2 − ε1(35)

ϕr,calculated = (ϕ2 − ϕ1)εs + dε

ε2 − ε1. (36)

Therefore,

ϕc,calculated = ϕc,real − (ϕ2 − ϕ1)dε

ε2 − ε1(37)

ϕr,calculated = ϕr,real + (ϕ2 − ϕ1)dε

ε2 − ε1. (38)

Thus, relative errors in the convective and radiative heat-fluxcalculations due to errors in the emissivity determination are

|dϕr |dε

ϕr

= dε

εs

(39)

|dϕc|dε

ϕc

= dε

Fεs

with ϕc = Fϕr. (40)

Figure 6 shows the evolution of the relative error inthe radiative heat-flux measurement as a function of thecomponent surface emissivity for different errors in theemissivities. It is observed that the greater the emissivity ofthe surface to which the fluxmeters are attached, the smallerthe relative error due to the radiative heat-flux measurement.In the underhood compartment of real vehicles, most surfacesare black with average emissivities of around 0.9. Figure 6shows that the maximal relative error for a surface emissivityof 0.9 among the different dε is 11%, precision sufficient forunderhood applications.

On the other hand, it is noted from figure 6 that the methodis much more sensitive to the determination of emissivities atlow component surface emissivities than at high emissivities.

Figure 7. Parametric evolution of relative error in convective heatflux calculation as a function of error in surface emissivity (forsurface with emissivity ε = 0.9).

Compare, for example, the two situations corresponding tosurface emissivities of 0.2 and 0.9. For an emissivity of 0.2,varying the error in the emissivity measurements from 0.01 to0.1 yields a variation in relative error in the radiative heat-fluxmeasurement of between 5% and 50%. For an emissivity of0.9, the relative error varies from 1% to 11%.

Figure 7 shows the evolution of the relative error inthe convective heat-flux calculation as a function of theerror in the emissivity determination dε for different ratiosF between the convective and radiative heat flux and for asurface emissivity of 0.9. It is observed that the greater theratio between the two heat fluxes, the smaller the relativeerror in the convective heat flux. Moreover, at low ratios,the method is far more sensitive to error in the emissivitymeasurement than at high ratios. Compare, for example, thetwo ratios 0.2 and 2: for a heat-flux ratio of 0.2, varying theerror in the emissivity measurement between 0.01 and 0.1yields a variation in relative error between 5% and 55%, versus0.5% to 5.5% for a ratio of 2. It is also noted that for heat-flux ratios greater than 1, the relative error in the convectiveheat-flux measurement does not exceed 7% regardless of theerror in the emissivity determination. Indeed, beyond a ratioof 1, the separation method becomes insensitive to error in theemissivity measurement.

Case 2: emissivity errors are in opposite directions.Repeating the calculation procedure above for this case yields∣∣∣∣dϕr

ϕr

∣∣∣∣dε

=∣∣∣∣ (εs + dε)(ε2 − ε1)

εs [(ε2 − ε1) + 2dε]− 1

∣∣∣∣ (41)∣∣∣∣dϕc

ϕc

∣∣∣∣dε

= 1

F

∣∣∣∣ (εs + dε)(ε2 − ε1)

εs [(ε2 − ε1) + 2dε]− 1

∣∣∣∣ . (42)

Figure 8 shows the evolution of the relative error in theradiative heat-flux calculation as a function of the differencein emissivity between the two fluxmeter surfaces for differenterrors in emissivity. It is observed that the greater thedifference in fluxmeter emissivity, the smaller the relativeerror in the radiative heat-flux measurement. For smallemissivity differences, the relative error in the radiative heat-flux measurement is more sensitive to the error in emissivity

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Meas. Sci. Technol. 21 (2010) 025903 M Khaled et al

Figure 8. Parametric evolution of relative error in radiative heat-fluxcalculation as a function of difference in emissivity.

Figure 9. Parametric evolution of relative error in convectiveheat-flux calculation as a function of error in surface emissivitydetermination (for an emissivity difference of 0.6).

determination. Compare, for example, the two emissivitydifferences 0.3 and 0.8. For 0.3, varying the error in theemissivity determination from 0.01 to 0.1 yields a variationin the relative error from 5% to 33%. This relative error rangesfrom 1% to 11% for an emissivity difference of 0.8.

Figure 9 shows the evolution of the relative error in theconvective heat-flux calculation as a function of the error inthe emissivity for different heat-flux ratios F and an emissivitydifference of 0.6. It is observed that the greater the heat-fluxratio, the smaller the relative error in the convective heat-fluxcalculation. Moreover, for low ratios, the method is much moresensitive to error in the emissivity determination than for highratios. Compare, for example, the two ratios F = 0.5 and F = 5:for F = 0.5, varying the error in the emissivity measurementsbetween 0.01 and 0.1 yields a variation in the relative error inthe radiative heat-flux measurement from 4% to 34% versus0.4% to 3.4% for a flux ratio of 5. On the other hand, forF > 2, the relative error does not exceed 8.3% regardless ofthe error in emissivity determination. In addition, beyond thisratio, the separation method becomes insensitive to the errorin emissivity determination.

Finally, to ensure that the separation method worksas accurately as possible and is insensitive to emissivitydetermination, it is recommended that

(a)

(b)

Figure 10. (a) Top view of experimental setup used for validations,(b) side view of instrumentation of the test-section flat plate for thereference method.

• one of the fluxmeters have emissivity as close as possibleto 1. In practice, we recommend painting the fluxmeterblack (emissivity close to 0.9);

• the other fluxmeter have emissivity as close as possible to0–0.1. In practice, we recommend painting this fluxmeterin a low-emissivity color (for example, aluminum color,with emissivity between 0.45 and 0.5).

From an application point of view

• this technique is more accurate for high-emissivitysurfaces (which is the case for a large number ofunderhood components),

• the precision of the separation method depends, by andlarge, on the ratio F of the convective to radiative heatfluxes. The more the convective heat flux dominates,the more accurate the method and insensitive to error inemissivity determination.

4. Experimental validation

4.1. Experimental apparatus and methods

To test the validity of the method, two fluxmeters were fixedon a metallic flat plate of 80 × 80 mm2 and thickness20 mm (figure 10(a)), a configuration selected for convenientimplementation of an already proven flux measurementtechnique as the reference method. The test section was inturn mounted on a controlled heating plate that could imposea constant temperature on the test-section surface.

The reference method for heat-flux measurement consistsin fixing, in the thickness of the flat-plate test section,five thermocouples of bead diameter 80 μm at accuratepositions in order to create a fluxmeter (figure 10(b)).

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Meas. Sci. Technol. 21 (2010) 025903 M Khaled et al

Figure 11. Surface temperature versus prescribed heatingtemperature measured in natural convection.

These K-type thermocouples permit deduction of the surfacetemperature and overall heat flux by linear extrapolationof temperature measurements in the steady-state regime(for unsteady applications, see [15]). Two normal-gradientfluxmeters painted two different colors (black and aluminum)are attached on the upper face of the flat plate of the test sectionby a conductive epoxy adhesive. The separation method wasvalidated in both the free- and forced-convection regimes.

To test the method in free convection, the test section plateis positioned on the temperature-controlled heating device inair at 20 ◦C. Experiments are carried out for different heatingtemperatures from 40 ◦C to 130 ◦C in 10 ◦C steps. In forcedconvection, the experimental setup (the test-section flat plateon the temperature-controlled heating device) is mounted ina small wind tunnel with an airflow velocity of 3 m s−1 attemperature 20 ◦C.

Experiments are carried out for different temperatureranges from 110 ◦C to 160 ◦C in 10 ◦C steps. In each run (foreach prescribed temperature), the overall heat flux is measuredby the reference method, and the convective and radiativeheat fluxes are obtained from the overall fluxes measured bythe two fluxmeters and by the separation method proposedhere. For the comparison, the radiative and convective heatfluxes of the flat-plate test section are calculated respectivelyfrom the surface temperature and the overall heat flux, bothmeasured by the reference method: the radiative heat-fluxdensity is calculated from the test-section surface temperature(obtained by the reference method), the air temperature, andthe emissivity of the test-section surface. The convective heatflux was calculated by subtracting the calculated radiative heatflux from the overall heat flux measured by the referencemethod.

4.2. Validation in natural convection

Figure 11 shows the surface temperatures measured by thereference method and also by the thermocouples integratedin the black and the aluminum fluxmeters. Measured surfacetemperatures are identical for the two fluxmeters and veryclose to that measured by the reference method. Thisconfirms the previous assumptions that in natural convection,the two fluxmeters measure the same convective heat flux(section 3) since the convective heat-transfer coefficient

Figure 12. Overall heat fluxes versus prescribed heatingtemperature measured in natural convection.

Figure 13. Radiative heat fluxes versus prescribed heatingtemperature measured in natural convection.

depends essentially on the surface temperature. On the otherhand, the relative error in the surface temperature measurementby the fluxmeters with respect to the surface temperaturemeasured by the reference method,

E(%) = Ts,fluxmeter − Ts,reference

Ts,reference, (43)

is less than 4% and has mean value around 2.6%, showing asatisfactory precision for car underhood applications.

Figure 12 shows the overall heat fluxes measured by thereference method, the black and the aluminum fluxmeters, asa function of the prescribed heating temperature. The overallheat flux measured by the black fluxmeter is closer to thatmeasured by the reference method. This difference is due tothe difference in the radiative heat flux measured by the twofluxmeters; in fact, the black fluxmeter measures a radiativeheat flux closer to that obtained by the reference method. Thisconfirms that overall heat flux can be measured with precisionif care is taken in the attachment and emissivity effectsdescribed in section 4.1. On the other hand, a clear differenceis discerned between the heat-flux evolutions measured bythe fluxmeters, and this difference permits separation of theconvective heat flux (which is the same for the two fluxmeters)and radiative heat flux.

Figures 13 and 14 compare respectively the radiativeand convective heat fluxes obtained by the flux-separationmethod to those obtained by the reference method. Heat fluxes(convective and radiative) obtained by the separation methodare close to those obtained by the reference method.

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Meas. Sci. Technol. 21 (2010) 025903 M Khaled et al

Figure 14. Convective heat fluxes versus prescribed heatingtemperature measured in natural convection.

Figure 15. Surface temperatures versus prescribed heatingtemperature measured in forced convection.

The mean relative errors in the fluxes compared to thereference method are

• 10.51% in overall flux,• 10.49% in convective flux,• 10.42% in radiative flux.

Therefore, this heat-flux separation can distinguish convectiveheat flux from radiative heat flux in natural convection withsufficient accuracy for car underhood applications.

4.3. Validation in forced convection

In forced convection, it is observed that the surface temperatureevolutions measured by the thermocouples integrated in thetwo fluxmeters are very close, which also confirms that for agiven airflow velocity the two fluxmeters measure the sameconvective heat flux (see figure 15).

On the other hand, figure 16 shows again that the blackfluxmeter measures an overall heat flux closer to the referencemethod. Radiative and convective heat fluxes obtained by theseparation method are also plotted on the same figure forcomparison.

Figure 17 compares the convective and the radiative heatfluxes obtained by the separation method and the referencemethod. The relative mean error is 8.28% in the overall heatflux, 9% in the convective heat flux and 5% in the radiativeheat flux. It should be noted that overall heat fluxes measuredby each fluxmeter are corrected by the method proposed insection 4.1 before the application of the separation method.

Figure 16. Heat fluxes versus prescribed heating temperaturemeasured in forced convection.

Figure 17. Convective and radiative heat fluxes versus prescribedheating temperature measured in forced convection.

Overall, it can be claimed that this method can estimateeach heat flux with good accuracy in forced convection forapplications in the car underhood.

5. Conclusions

For a better understanding of the physical phenomenaoccurring in the underhood region, for each componentone must measure separately and with sufficient accuracyconvective and radiative heat fluxes at specified surfacetemperatures. A peculiarity of the car underhood compartmentis that the airflow is extremely complex and the air passages arehard to access. The geometry of the underhood compartmentis also complex. Therefore, the sensors employed in the carunderhood must satisfy all these conditions and should beaccurate and easy to implement.

In this work, we introduced the concept of separated fluxmeasurement. We used two normal-gradient fluxmeters ofdifferent surface emissivities attached on the surface on whichtemperature and heat flux are to be measured. Theoreticalgrounds were developed that, by separate measurementsof each fluxmeter, yield access to the surface temperature,convective heat flux and radiative heat flux across thesurface.

An error analysis showed that the main sources of error influx measurement are errors in the attachment of the fluxmeterto the surface and in fluxmeter emissivity measurement. Also,

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Meas. Sci. Technol. 21 (2010) 025903 M Khaled et al

sensitivity analysis of the flux separation method showed thatfor accurate results one of the two fluxmeters should haveemissivity close to 1 (painted black) and the other an emissivitybetween 0 and 0.1 (painted, for example, aluminum color withε = 0.4−0.5). The accuracy of the separation method dependsalso on the ratio F of convective to radiative fluxes: the higherthis ratio, the more accurate the results.

The flux separation method was validated against anaccurate but intrusive technique on a flat-plate test sectionin both free and forced convection. The separation methodwas shown to be able to measure simultaneous convectiveand radiative heat fluxes with errors less than 10%. Thismethod thus satisfies the major criteria for applications in carunderhood aerothermal measurements; indeed, this techniqueis very general and can also be used in other applications.

Acknowledgments

This work was supported by PSA Peugeot-Citroen carmanufacturing. Dr Vincent Herbert is acknowledged formonitoring this grant. The authors are indebted to ProfessorJ P Bardon of the University of Nantes for his suggestions.

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