Local Heat Transfer Coefficient Measurements, Using a Transient Imaging Method With an Inverse Scheme

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1 Local Heat Transer Coeicient Measurements, Using a Transient Imaging Method With an Inverse Scheme A. EL ABBADI, D. BOUGEARD, B.BAUDOIN Ecole des Mines de Douai, Département Energétique Industrielle, 941, rue Charles Bourseul, B.P 838, DOUAI, Cede France, el-abbadi@ensm-douai.r Abstract Local heat transer coeicient (LHTC) on heat exchangers in suraces is usually measured by means o transient or steady methods. Usually, in transient method, it s determined using the assumption o pure convective lux ( no lateral conduction in in). However this assumption is not totally validates since a lateral conduction lux still exists inside the ins. We present in this paper several improvements we brought to this transient method and particularly the use o inverse 2-D scheme to correct LHTC obtained without taking into account the lateral heat conduction. The inverse scheme is implemented and then validated using a numerical test case with a speciic LHTC variation. Then the method is used in a real experiment to determine LHTC on a single inned tube. 1. Introduction The estimation o convective heat transer distribution is a main task in designing compact heat exchangers. For instance the knowledge o local heat transer coeicient is o a particular importance to design new heat transer surace or highperormance heat exchanger. Usually two main methods have been used to determine local heat transer on suraces: - The steady state - Transient method The irst methods was used by Eibeck and Eaton [1], Pauley and Eaton [2] and consist o a constant heat lux suraces with thermocouple array in a steady state condition. This steady method was also used by Herchang Ay et al [3] to measure local heat transer coeicient o plate inned-tube heat exchanger by inrared thermography. Steady state heat transer with a constant lux density is conceptually simple and easy to analyse but the provision o a constant lux surace poses experimental diiculties. The use o electrically heated oils is possible, but uniorm lux density can be diicult to achieve in practice. On the other hand, transient methods using Inrared Thermography or Thermochromic Liquid Crystals are reported by Ireland and Jones [4], Dong et al [5] and Tourreuil and Bougeard [6]. They oers advantages o lexibility because it being comparatively easy to alter the geometry o the surace being studied. In the study o Tourreuil et al [6], Fiebig et al[7], the transient technique was used in the case o a thin wall with a very low thermal conductivity in order to neglect the conduction lux along the wall. They investigate numerically this assumption o negligible heat conduction along the wall. Their computation show that signiicant heat conduction or a thin wall o low thermal conductivity occurs only at the positions where the distribution o heat transer coeicients has local extrema with large second derivatives. There the local experimental error due to heat conduction can reach 10%. However, to study and develop enhanced suraces o heat exchangers, a best knowledge o local heat transer coeicient is required to determine the optimal values o these enhanced suraces parameters. We present in this paper a transient method and visualization technique using inrared thermography. And an inverse 2-D scheme to take into account the lateral conduction along the in surace in order to obtain local heat transer coeicient on compact heat exchangers suraces. D.15.1

2 2. Transient Inrared Thermography Method 2. 1 Temperature measurement o the in surace Our investigation technique (more detailed in our precedent paper El Abbadi et al[8]) requires an accurate knowledge o the spatial distribution o the in surace temperature. This measurement is made with an inrared camera (AGEMA 900 Long Wave) equipped with an HgCdTe sensor cooled by a Stirling motor. The inrared camera is placed at its minimal distance in order to give maximal spatial resolution (see igure 1).The electromagnetic energy radiated in the inrared spectral band by an element o the in is converted into an electronic signal rom the camera sensor. Then this signal is ampliied and digitally recorded with a 12-bit dynamic range. In order to convert this signal (expressed by numeric level (NL)) into temperature, an in-situ calibration is made using a thermal sensor. The calibration procedure use a special high thermal conductivity plate coated with the same black painting as the in, and placed at the same location. In order to enhance the thermal resolution, the calibration curve uses the whole dynamic range (12 bit) o temperature variation measurement o the model during the experiment. More over the spatial resolution is enhanced using a speciic image restoration technique [8]. Thanks to these various treatments, our experimental technique allows accurate measurements o the in temperature with an overall uncertainty o about ± 0. 3 C. IR camera ZnSe window IR emitter tube in honeycomb air Nozzle an S4 S1 h ( Tube S5 in S3 S1 St h ( Tube S6 y dy dx S3 rad conv x S2 cond e cond Fig.1. experimental test bench and test model D.15.2

3 2. 2 Local heat transer calculation with the assumption o negligible heat conduction The heat transer measurement is perormed using a transient technique based on the work o Ireland and Jones [4]. The knowledge o the time temperature variation on the in surace allows to calculate the heat lux in each small element o the in and hence the heat transer coeicient. The heat luxes balance in an element gives: m H (1) = + + conv cond rad t in order to simpliy the problem several assumption could be made : - constant temperature across the plate thickness (i.e., negligible temperature gradient in the z direction) this assumption is validated because the thickness and material o the in are chosen in order to gives a Biot number value under negligible radiative luxes. - constant heat transer coeicient during the experiment. The precedent equation becomes: 2 2 T T T ρ Cp e dxdy = 2h( dxdy( Tin T ) + λ ρ dxdy( + ) (2) 2 2 t x y Usually researchers neglect the term o conduction and integrate equation 3 between 0 and t to get simpliied expression o LHTC: ρ Cp e T T ( y, 0 ) in h ( = ln (3) ln 2 t Tin T ( y, t ) Since the plate is cooled rom both sides, Eq. (3) gives the heat transer coeicient locally averaged or the upper and lower sides o the plate Correction o local heat transer measurement In real problem, h ( is not known and must be determined rom transient temperature measurements on the in surace. This kind o problem is similar to an inverse conduction problem. More precisely in our study the unknown LHTC is determined using an iterative process (written in Matlab.6 code) as described bellow : - Firstly we determine the LHTC using the assumption o negligible heat conduction (eq 3). - Secondly the direct 2-D heat conduction scheme is used to determine the time variation temperature ield. The general governing equations is o this 2-D problem is (eq 2), where h is the coeicient calculated by mean o the expression (eq 3). The numerical calculation was perormed using the second-order central dierencing scheme or spatial axis and implicit method or temporal step. - Thirdly, or the time, t, corresponding to the experimental acquisition o the temperature iled at the end o the experiment, the calculated temperature, Tc, is compared to the experimental one. The comparison criterion is C( = T exp ( T c ( I the value o this criterion is as great as 0.1, the new local heat transer is then calculated by the relation: ' h ( = h( + α sign( C( ) h( 1 Whereα is a correction coeicient lower than 10 and sign is a Matlab6 unction which gives de sign o the array C. The correction loop continues until the calculated transient temperature inormation o each pixel on the in surace matches the experimental data within the convergence criterion. D.15.3

2. 4 Validation o the inverse scheme First o all, this inverse scheme was validated using a numerical test case beore its use to calculate the heat transer coeicient on in surace rom experimental

The low boundary and initial conditions are chosen as ollow: - Given heat transer coeicient on the aces S5 and S6 (see Fig 2,3) h ( y ) = 10+ abs( 60cos( x )) π π π 3 π π 0.

4 2. 4 Validation o the inverse scheme First o all, this inverse scheme was validated using a numerical test case beore its use to calculate the heat transer coeicient on in surace rom experimental data. The numerical test model chosen is ormed rom a lat plate without tube. Its thermal conductivity was varied rom 0.1 (PVC) to 100 W/m.K (steel). The low boundary and initial conditions are chosen as ollow: - Given heat transer coeicient on the aces S5 and S6 (see Fig 2,3) h ( y ) = 10+ abs( 60cos( x )) π π π 3 π π 0. 9 π i ( x, y ) 0 :, 0 : 2 2 :, : h ( x, y )= cste = 80 π 3 π π 0. 9 π i ( x, y ) :, : Adiabatic suraces S1, S2, S3 and S4. - Uniorm initial temperature on in suraces S5 and S6. The direct scheme is used to calculate the cooling o the in due to the LHTC given above. Figures (2,3 and 4) show the real LHTC, the estimated one (h ln) calculated using equation 3 and the calculated one using the inverse scheme. We can clearly see that h ln is very dierent rom the real imposed coeicient h. As shown in igure 5 real heat transer coeicient was successully recovered, by mean o this inverse scheme method. y(pixel) h(w/m².k) Fig.2. real h ( Fig.3. h ln ( with the assumption o negligible conduction lux Fig.4. h ( corrected with the inverse method h (W/m².K) real h 30 corrected h Fig.5. real and corrected LHTC along the in center line D.15.4

5 2. 5 Experimental validation Once this method was numerically validated, it was applied on a real case. Figure 6 represent a map o heat transer coeicient obtained experimentally on a model o a inned tube. The in used, which is made o a PVC material, has an thermal conductivity o 0.1W/m.K. More detail about this study is published in [8]. On the Figure 7, we plot the real and corrected local heat transer coeicient along the tube center line. As we can note, globally there isn t a big dierence between the two coeicients because o the low thermal conductivity o the in. But in the area where LHTC has extrema, the deviation is more visible. Tube h(w/m².k) h ln hlog_ligne hcorrigé_ligne corrected h Fig.6. map o h on a inned tube x(px) Fig.7. h along the tube center line tube This technique, gives a good results in the cases o low thermal conductivities in (0-10W/m.K). But in the case o ins o high thermal conductivities, a iltration technique o the temperature must be used because o the noise o experimental temperature. Our inverse technique could be improved using a iltering technique like the one used by S.Rainieri and G.Pagliarini [9] to estimate local heat transer coeicient in the presence o noise. 3. Conclusion A transient Inrared Thermography method was developed to measure the local heat transer coeicient on inned tube heat exchangers. The local heat transer coeicient calculated without taking into account the conduction along the in surace was corrected by mean o an inverse 2-D conduction scheme. This inverse scheme was numerically validated beore its test on a inned tube o low thermal conductivity. On these low thermal conductivity ins, results show that the error on global heat transer is not important i we neglect the conduction but it s not the case or local heat transer coeicient. This method can also be used or a in with a relatively high thermal conductivity 0-10 w/m².k but or a very high thermal conductivity material, a iltration technique is needed. Nomenclature Bi Biot number ( = he 2λ ) / β Coeicient o thermal expansion per unit volume, [K -1 ] Cp Fin speciic heat, J/kg K t Cooling Time, s e Fin thickness, m g Gravity, m/s 2 h Heat transer coeicient, W/m² K D.15.5

6 h ln H m Heat transer coeicient with the assumption o negligible heat conduction Fin enthalpy, J/kg Fin weight, Kg T Fin temperature, C T T exp c Final experimental temperature, C Final calculated temperature, C T Air inlet temperature, C in t End cooling time, s In c Fin or inal Inlet Calculated sign ( c ) ( = 1 i C>0 ) or (= -1 i C<0 ) or (= 0 i C=0 ) λ Fin thermal conductivity, W/m K ρ Fin density, kg/m 3 REFERENCES [1] P.A. Eibeck, J.K. Eaton, - Heat transer eects o longitudinal vortex embedded in a turbulent boundary layer, ASME J. O Heat transer 109, 16:23, 1987 [2] W.R Pauley, J.K. Eaton, - The eect o longitudinal embedded vortex arrays on turbulent boundary layer heat transer, ASME J. O Heat transer 116, 871:879, 1996 [3] Herchang Ay, J.Y.Jang, J.N.Yeh, - Local heat transer measurements o plate inned-tube heat exchangers by inrared thermography, IJMHT 45, 4069:4078, 2002 [4] P.T. Ireland, T.V. Jones Detailed measurements o heat transer on and around a pedestal in ully developed channel low, 8 th International heat transer conerence, Vol. 3, San Francisco, , 1986 [5] Y. Dong, S. Tiggelbeck, M. Fiebig, N. K. Mitra, - Inluence o delta-winglet vortex generators on heat transer and drag o a in-tube, Eurotherm Seminar n 9, Bochum, Heat Transer in Single phase lows, July 10-11, 1989 [6] J. Tourreuil, D. Bougeard, B. Baudoin, - Inluence o conjugate heat transer in compact heat exchangers with vortex generators, 3 rd International Conerence on Compact Heat Exchangers and Enhancement Technology or the Process Industries, p , Davos, 2001, Begell House Inc., ISBN [7] M. Fiebig, A. Valencia, N. K. Mitra, - Local heat transer and low losses in in-and-tube heat exchangers with vortex generators : a comparison o round and lat tubes, Experimental thermal and Fluide sciences, 8:35-45, 1994 [8] A. El abbadi, D.Bougeard, B.Baudoin - Experimental Study o Heat Transer Distribution on a Single Finned Tube, 4 th European Thermal Sciences Conerence, Birmingham, UK, 2004 [9] Sara Rainieri. Fabio Bozzoli, Giorgio paliarini - Wiener iltering technique applied to themographic data reduction intended or the estimation o plate ins perormance, Experimental thermal and Fluide sciences 28, 179:183, 2004 D.15.6

Analysis of Non-Thermal Equilibrium in Porous Media

Analysis of Non-Thermal Equilibrium in Porous Media Analysis o Non-Thermal Equilibrium in Porous Media A. Nouri-Borujerdi, M. Nazari 1 School o Mechanical Engineering, Shari University o Technology P.O Box 11365-9567, Tehran, Iran E-mail: anouri@shari.edu