spray cooling on micro structured surfaces

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International Journal of Heat and Mass Transfer 50 (2007) 4089–4097

Spray cooling on micro structured surfaces

Christof Sodtke, Peter Stephan *

Chair of Technical Thermodynamics, Darmstadt University of Technology, Petersenstrasse 30, 64287 Darmstadt, Germany

Received 5 July 2006Available online 26 April 2007

Abstract

Spray cooling experiments have been performed on a smooth heater surface. The working fluid water was atomized through a fullcone nozzle into a low pressure spray chamber. Different coolant mass fluxes were studied by varying the distance between nozzleand heater. Observations obtained with an infrared camera indicated that the length of the three phase contact line increased as the heatflux in the experiments was raised. Motivated by this finding, the effect of different micro structured surfaces, which lead to an increase inthe three phase contact line, on the spray cooling performance was studied. The micro structures consisted of micro pyramids with dif-ferent heights. A significant enhancement in the heat transfer performance due to the surface structures could be observed, especially atlow coolant fluxes.

Additionally, high spatial resolution temperature measurements on a smooth heater using thermochromic liquid crystals wereobtained. These measurements indicate high local temperature gradients for a regime where the coolant film on the heater is ruptured.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Spray cooling; Micro structures; Contact line; TLCs; Surface temperature distribution

1. Introduction

Spray cooling is a very efficient means for dissipatinghigh heat fluxes with low coolant mass fluxes at low wallsuperheats. It is used in a wide range of applications frommetal quenching over cooling of high power electronics tomedical treatments. Using water as coolant, spray coolingheat fluxes up to 1000 W/cm2 have been reported [1].Depending on the spray parameters and surface properties,the coolant forms a cohesive or ruptured thin liquid film,which evaporates on the hot surface. With decreasing filmthickness the transferred heat flux at a given surface tem-perature increases [1].

Generally, sprays can are generated in different ways,most frequently used are pressure and air blast atomizers.In a pressure atomizer, only one phase is used for the atom-izing and the subsequent cooling. In the case of a air blast

0017-9310/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijheatmasstransfer.2006.12.037

* Corresponding author. Tel.: +49 0 6151 16 3159; fax: +49 0 6151 166561.

E-mail address: [email protected] (P. Stephan).

atomizer, the mass flow rate of the liquid coolant is usuallysmall compared to that of the air. Pressure atomizers areconveniently used in closed systems. The advantage of airatomizers is that they can work with lower liquid coolantflow rates.

Three different regimes can be determined in spray cool-ing heat transfer [2], first a low temperature regime, whereliquid evaporates at the free liquid–vapour interface, sec-ond a high temperature regime, where liquid films are ina film-boiling-like state and vapour bubbles are generatedat the superheated hot wall. The third regime is the transi-tion regime from the low temperature to the high tempera-ture region. In his experiments Toda [2] observed thatsubcooling had only minor effects on single phase andnucleate boiling heat transfer. A dominant effect on CHFwas also not observed.

Several studies were performed on the influence of thespray parameters on the cooling heat flux, it was found thatthe volumetric spray flux has a dominant effect on the heattransfer [3,4] compared to other hydrodynamic parametersof the spray. Pautsch et al. [5] found that if a pressure

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Nomenclature

d10 average droplet diameter (lm)_m mass flux (kg/h)p pressure (bar)_q heat flux (W/cm2)Ra surface roughness (lm)t temperature (�C)Dt temperature difference (K)k thermal conductivity (W/(m K))s time constant (s)

Subscripts

con experimental containercyl heaterres reservoirw wall

4090 C. Sodtke, P. Stephan / International Journal of Heat and Mass Transfer 50 (2007) 4089–4097

atomizer is used, the film thickness decreases with increas-ing flow rate, while Yang et al. [6] found that for an airatomizer the coolant flow rate has only little effect on thefilm thickness.

Sehmbey et al. [7] studied the effect of surface propertieson the cooling heat flux using air atomized nozzles. Theyfound that a higher surface roughness decreases the coolingperformance of the spray, due to an increased film thick-ness. Hsieh and Yao [8] conducted experiments studyingthe influence of surface micro structures on silicon waverson the spray cooling heat flux using a pressure atomizernozzle. Their results show an increased heat flux on struc-tured surfaces due to capillary forces of the surface actingon the film. Smaller structures resulted in a better heattransfer. However, the improvement in heat transfer islower than the increase in surface area. Silk et al. [9] studiedthe effect of cubic fins, pyramids and straight fins on theheat transfer performance up to CHF. They found thatall surfaces tested improved the heat transfer performancecompared to a flat surface, the straight fins performed best,followed by cubic fins and pyramids. The straight finsresulted in a �50% higher CHF value compared to thatof a flat surface. Investigating also the influence of dis-solved gas, Silk et al. [9] found the magnitude of theimprovement was lower for the case of a not degassed fluid.

Recently, Horacek et al. [10] performed a study on thebasic heat transfer mechanisms of spray cooling using atransparent microheater array consisting of 96 square heat-ing elements, each having an edge length of 100 lm. Theyfound that apparently dry spots appear in the otherwisecohesive liquid film covering the cooled surface at wallsuperheats in excess of 10 �C. According to [10], the heatflux is directly related to the contact line length of the threephases gas–liquid–solid and not to the wetted area.

There is some discussion about the temperature varia-tions encountered on a spray cooled surface. While Guet al. [11] found that compared to other cooling techniques,e.g., jet cooling, spray cooling results in a relatively uni-form temperature distribution over the cooled surface,Shedd and Pautsch [12] found quite significant temperaturevariations over their test heater reaching as high as 17 �C.

Despite the advantages of spray cooling over competingcooling techniques, there is a reluctance to incorporate

spray cooling in demanding cooling situations, which isattributed to the very limited understanding of the heattransfer mechanisms and practical concerns such as thelimited repeatability of cooling performance for seeminglyidentical spray nozzles [13].

For the present work experiments were conducted tostudy the effect of surface structures and coolant mass fluxon the heat transfer in the low surface temperature regimeat low system pressures. Additionally, the influence of thecoolant behavior on the heat transfer performance wasinvestigated by observing the heater surface with a high-speed infrared camera and performing high resolution tem-perature measurements on a thin spray cooled foil heater.In the following section, the experimental set-up isdescribed, in Section 3 experimental results are presentedand discussed.

2. Experimental set-up and procedure

2.1. Experimental set-up

A schematic of the experimental set-up used is shown inFig. 1. A Plexiglas spray chamber was constructed, whichallows spray cooling at system pressures as low as0.005 bar. The spray is generated using deionised water, agear pump and a full cone pressure atomizer (SprayingSystems, TG SS 0.3). A heat exchanger inside the spraychamber ensures constant temperature for all experiments(Dtcon = ±1 K), independent of the ambient temperature.A second heat exchanger inside the reservoir is used to con-trol the subcooling of the coolant (Dtres = ±0.4 K). Thecoolant mass flow rate pumped through the nozzle is mea-sured with a coriolis flow meter and can be accuratelyadjusted using a bypass controlled by a needle valve. Ahighspeed infrared imaging system (Phoenix Midas) canbe used to observe the coolant distribution and behavioron the heater. Alternatively, the infrared camera can bereplaced by a standard CCD-camera.

The heater surfaces are the upper end faces of differentlytreated copper cylinders which are placed on the bottom ofthe spray chamber one at a time. A fixation with a conicaltop ensures that excess coolant can run off towards theintercepting tank and does not accumulate on the cylinder

20mm

35m

m

1mm

4mm

7mm

thermocouples

conicalholder

cartridge heaters

coppercylinder

insulation

g

Fig. 2. Copper heater embedded in the fixation system for the spraychamber.

Table 1Dimensions of surface structures

Structure Height (in lm) Width (in lm)

S1 75 150S2 150 300S3 225 450

P

nozzle

Plexiglas chamber

CCD / IR

P F

vacuum pumppump

flowmeter

bypass

intercepting tank

heater

reservoir

heat exchanger 1

heatexchanger 2

isolation

Fig. 1. Schematics of the experimental set-up.

C. Sodtke, P. Stephan / International Journal of Heat and Mass Transfer 50 (2007) 4089–4097 4091

surface. That way, only the upper end face of the coppercylinders get in contact with the coolant and the coolantdoes not accumulate on the heater surface. The cylindersare electrically heated by cartridge heaters and are wellinsulated at the circumference. The upper end face in con-tact with the spray has a diameter of 20 mm. The dissipatedheat flux and the surface temperature are calculated usingthree thermocouples spaced 3 mm apart from each otheralong the axis of the copper cylinder (see Fig. 2). The upperthermocouple is positioned 1 mm below the heater surface.The thermal conductivity of the copper cylinders was mea-sured via their electrical conductivity using the relationshipbetween the electrical and the thermal conductivities to bekcyl = 394 W/(m K). A 3D heat conduction calculationwith Fluent has shown that the temperature profile is veryclose to a one dimensional temperature profile in the upperpart of the copper cylinder. Hence, the assumption of a onedimensional temperature profile can be used to calculatethe dissipated heat flux based on the three temperaturemeasurements and their distance. The surface temperatureis extrapolated using the measured temperature at the ther-mocouple closest to the surface and the calculated heatflux. Additionally, the temperature and the pressure insidethe spray chamber are monitored, as well as the tempera-tures, of the working fluid in the reservoir and just in frontof the nozzle.

The spacing between heater surface and nozzle can bevaried between 20 mm and 100 mm. For spacings largerthan �25 mm, only a fraction of the spray hits the heater,while for smaller distances the total spray volume flux isdeposited on the heater.

2.2. Micro structured surfaces

The heat transfer performance of three different surfaceswith micro pyramids as surface structures has been com-pared to that of a smooth polished surface. The surfacestructures differ in height and width of the pyramids. Thedimensions of the structures can be inferred from Table 1.All surface structures were machined into the end face ofcopper cylinders. One of the surfaces is shown exemplarilyin Fig. 3. All structures investigated caused an increase insurface area compared to the smooth surface by a factorof

ffiffiffi

2p

. The surface roughness of the smooth polished sur-face was found to be Ra < 0.3 lm using a perthometer.The structured surfaces were fixed in their holders such thatthe bottom of the structures was on the same level as theedge of the conical holder.

One set of calibrated thermocouples is used for eachcopper cylinder. The thermocouples were checked for

Fig. 3. Top view of micro structured surface (pyramids).

electrode electrodePlexiglas

foil heater

glue

black background

nozzle

ring light

objectivecoonection topower supply


range of temperatures between 25 �C and 60 �C to deviateless than Dt = 0.05 K from each other in order to minimizethe error in the heat flux calculation. The temperaturesmeasured during the experiments were in a range from30 �C to 55 �C.

TLC layer

mylar foil

Fig. 4. Schematic of TLC heater.

2.3. Infrared images

The aforementioned high speed infrared imaging systemhas been used to obtain images of the coolant behavior onthe smooth unstructured copper heater. The emissivity ofwater differs strongly from that of copper so that informa-tion what portion of the heater surface is covered with awater film and where that film is ruptured can be easilyextracted from the infrared images. As shown in Fig. 1,the images were taken from the side under an observationangle of �60�. Optical access to the heater was permittedby using an infrared transmissive CaF2-window. Theimages were taken with a frame rate of 300 Hz. The spatialresolution of the camera system was 100 lm � 100 lm/pixel. Using the Matlab-image processing toolbox, theinfrared images were converted to binary matrices consist-ing of ones where the heater surface is covered with waterand zeros elsewhere. The distortion of the images caused bythe viewing angle was removed as well by an algorithmwhich deskews the elliptical image of the circular heaterface so that the final image shows a circular shape. After-wards, an edge detection algorithm was used to calculatethe surface area of film covered portions of the heaterand their perimeter, which corresponds to the three phasecontact line length.

2.4. High resolution temperature measurements

To obtain high spatial resolution temperature measure-ments at a heated surface, the copper cylinder is replaced insome experiments by a thin stainless steel foil heater withthermochromic liquid crystals (TLCs) applied to the lowersurface. A schematic of the foil heater and the appliedTLCs is shown in Fig. 4. The colourplay of the TLCs isobserved from below through the Plexiglas bottom plate

of the spray chamber with a CCD-camera. The foil heaterhas a thickness of 10 lm, a 20 lm thick layer of a glue witha high thermal conductivity is used to have a good contactbetween the backside of the heater and the TLC sheet. TheTLC sheet itself consists of 3 layers, a layer of black paint(�5 lm), a layer of encapsulated TLC (�240 lm) and amylar foil as protection (�125 lm). TLCs reflect a distinctcolour depending on their temperature when illuminatedby white light. Below and above their active temperaturerange they are transparent so that the black backgroundcan be seen, within their working range the reflected lightchanges from red to green to blue with increasing temper-ature. The TLCs used for the current experiment are sup-plied in the form of a foil such that they are protectedfrom environmental influences. Images of the TLCs arecaptured using a three chip colour CCD-Camera and thecolour information is converted from the RGB-signal ofthe camera to the HSV-colourspace (Hue, Saturation,Value). In the HSV-colourspace, the hue-value is measuredin degrees. It contains all the colour information and cantherefore be used as a single value for the temperature mea-surement. An ‘in situ’ calibration method for the TLCs hasbeen developed, where the TLCs can be calibrated withinthe experimental set-up and the temperature of the TLCscan be controlled with a thermostat. A correlation ofhue-value and temperature is obtained by measuring thetemperature of the TLCs with thermocouples and simulta-neously recording their colourplay. A seventh orderregression proved to be a good approximation for the

–2 0 2 4 6 80

5

10

15

20

25

30

35

40

45 spacing 60 mmspacing 20 mmspacing 40 mm

Fig. 5. Spray cooling performance for different nozzle spacings on asmooth surface.


hue-temperature-correlation. The stainless steel foil is elec-trically heated with constant voltage and current, resultingin a constant heat flow density in the foil. Due to the smallthickness of the foil the temperature distribution on theback of the foil does not deviate significantly from thaton the front of the foil. The time constant for the measure-ment system was determined to be s � 0.007 s. The TLCsare illuminated through the Plexiglas base plate of the hea-ter with a ring light, which is connected to a cold lightsource. The TLC colourplay is acquired with a frame rateof 20 Hz. Thus, the temperature information can only beregarded as snapshots, since the time constant of the foilheater is much smaller than the frame rate. The spatial res-olution of the TLC images is 25 lm � 25 lm/pixel. Due tothe limited working bandwidth of TLCs (5–20 K), the pres-sure inside the Plexiglas container has to be controlled suchthat the saturation temperature of water is well between thelimits of the TLC working bandwidth.

2.5. Experimental procedure

Prior to each set of experiments the heater surface is firstcleaned with diluted hydrochloric acid, rinsed with deion-ised water, cleaned with acetone and again rinsed withdeionised water. Also, the working fluid water is welldegassed before each set of experiments. Then the spraychamber is partly filled with water such that the heatexchanger 2 inside the experimental container (see Fig. 1)is in contact with water. The spray chamber is evacuatedto pcon = 0.055 bar, while the heat exchanger is set to atemperature above the saturation temperature inside thespray chamber so that the water inside the spray chamberevaporates and creates a vapour atmosphere. Also, thetemperature of the working fluid in the fluid reservoir isset to tres = 22 �C.

The coolant mass flow rate through the nozzle is keptconstant at _m = 16 kg/h for all experiments. For this massflow rate, the droplet diameter was found by PDA mea-surements to vary between d10 = 40 lm and d10 = 60 lmover the spray cone of a TG SS 0.3 nozzle. The mass fluxof the spray used for cooling can be varied by varyingthe nozzle to heater spacing. This way, the spray character-istics remain roughly constant for all volume fluxes.Finally, the cartridge heaters are switched on. When asteady state is reached, data is acquired for 180 s. After-wards, the power is increased to the next step.

The same nozzle has been used for all experiments andthe pressure drop across the nozzle was monitored to bewithin Dpnozzle = ±0.1 bar throughout all experiments.

3. Results and discussion

In this section the experimental results obtained fromthe heat performance measurements on the different sur-face structures are presented and compared, followed bythe presentation results of the infrared and the TLC imageanalysis.

3.1. Spray cooling performance on smooth surfaces

First some general results found for spray cooling on asmooth heater will be presented.

Generally, it can be stated that for a given wall super-heat the dissipated heat flux could be increased by decreas-ing the nozzle spacings. However, it was observed that forsome wall superheats, a higher heat flux could be dissipatedusing a higher nozzle spacing and thus a lower coolant flux.Comparing the data for a smooth surface shown in Fig. 5,it can be seen that for a wall superheat between Dtw = 4 Kand Dtw = 6 K, a higher heat flux can be dissipated with anozzle spacing of 60 mm than with a spacing of 40 mm.For a nozzle spacing of 60 mm the coolant film on the hea-ter ruptures at a wall superheat Dtw � 3 K leading to onlysmall increases in Dtw when the heat flux _q is increased. Ata wall superheat of Dtw � 6 K, the effect of the higher cool-ant mass flux becomes dominant again, so that a higherheat flux can be removed with a lower nozzle spacing. Also,for the nozzle spacing of 60 mm, the removed heat fluxtends towards the maximum heat flux that can be removedwith this coolant mass flux, such that small increases inheat flux lead to large increases in wall superheat.

Thus, in a small region of wall superheats, the dissipatedheat flux _q is higher for the larger nozzle spacing than forlower spacings and the corresponding higher coolantfluxes. A similar behavior was observed for a nozzle spac-ing of 80 mm.

3.2. Infrared observations

Observations on a smooth heater surface using an infra-red camera system allow a distinct determination of thewetted and not wetted heater surface area. Additionally,the three phase contact line (water, vapour, copper) sur-rounding the wetted area could be easily obtained by


analysing the infrared pictures. A plot of wetted surfacearea and contact line length versus heat flux is shown inFigs. 6 and 7, where Fig. 7 also shows the correspondingIR-images for different heat fluxes. As can be seen in Figs.6 and 7, the area of the wetted surface decreases withincreasing heat flux, while the contact line length increasesalmost proportional to the heat flux. This observation com-pares well to the findings of Kim et al. [9], who performedsimilar measurements on a transparent heater. Based onthis observation, it can be inferred that increasing the threephase contact line length leads to an enhanced cooling per-formance. Thus, using a structured surface like the pyra-mid structures S1–S3 at coolant mass fluxes low enoughsuch that the tips of the surface structures protrude outof the coolant film should lead to an improved cooling per-formance in terms of wall superheat at a given heat flux.

Fig. 7. Contact line length versus heat flux with corresponding IR-images.

3.3. Spray cooling performance on micro structured surfaces

The spray cooling performance of heaters with differentsurfaces geometries has been investigated for different noz-zle spacings. The results have been compared to the spraycooling performance of a smooth polished surface usingthe same spray nozzle.

For the spray cooling on the surface with the smalleststructures (S1), no significant difference in the spray cool-ing performance compared to the smooth surface couldbe observed until a certain wall superheat was reached.At this wall superheat, the coolant film ruptured and thecapillary forces of the structure are believed to have drawnthe coolant into the structure such that the upper parts ofthe surface structure protruded out of the coolant film.Hence, the contact line length was increased and a strongreduction in wall superheat was observed, despite anincreased heat flux. This behavior could be observed forlarger to intermediate nozzle spacings. For very low nozzle

0.5 1 1.5 2 2.5 3

x 105

1.5

2

2.5

3

3.5

4x 10

4

Fig. 6. Wetted area versus heat flux.

spacings, no effect of the surface structure S1 could beobserved within the wall superheat range investigated. Aplot of heat flux versus wall super heat for two differentnozzle spacings is shown in Fig. 8. As can be seen, for awall superheat of approximately Dtw = 1 K a higher heatflux can be dissipated when the nozzle spacing is largerand the coolant mass flux is lower. Also, the aforemen-tioned characteristic reduction in wall superheat can beobserved for both nozzle spacings.

As shown in Fig. 9, the jump towards lower wall super-heat Dtw with increasing heat flux can only be observed forthe largest nozzle spacing in case of the surface with thelargest structures investigated (S3). Infrared images takenduring the spray cooling experiments with a nozzle spacingof 60 mm show that the tips of the micro pyramids pro-trude out of the coolant film for every wall superheat inves-tigated, thus enhancing the heat transfer also for lower heatfluxes. For the surface structure with the intermediatestructure size (S2), a characteristic reduction in the temper-

–4 –2 0 2 4

0

5

10

15

20

25

30

35 spacing 80 mmspacing 60 mmspacing 40 mmspacing 20 mm

Fig. 9. Spray cooling performance on surface S3.

-2 0 2 4 60

5

10

15

20

25

30S2S1S3smooth

Fig. 10. Comparison of spray cooling on different surfaces (nozzle spacing60 mm).

Fig. 11. Temperature distribution under spray cooled surface.

–2 0 2 4 60

10

20

30

40

50

60

70spacing 40 mmspacing 60 mm

Fig. 8. Spray cooling performance on surface S1.


ature could be observed. However, this temperature jumpoccurred at lower wall superheats and lower heat fluxesthan for the surface structure (S1) as can be seen in Fig. 10.

A comparison of the spray cooling performance on thethree surface structures investigated and on the smoothsurface is shown in Fig. 10. The nozzle spacing for all mea-surements was 60 mm. As can be seen from the figure, thereis a significant enhancement in heat transfer due to the sur-face structures. For the surface structure S3 an increase inheat flux with a factor of 2–5 can be obtained for a wallsuperheat in the range of Dtw = 2–3 K. Also, the gradient

d _qdDtw

is significantly larger for structured surfaces. The steep-est gradient was observed when the surface structure S1was used. A steep gradient is advantageous from an appli-cation point of view, since the wall temperature can be keptfairly constant over a broader range of heat fluxes.

3.4. High resolution temperature measurements

For a first evaluation of the temperature distributionunderneath a flat spray cooled surface, two different condi-tions have been studied. In both conditions, the spacingbetween nozzle and heater was sufficiently large so thatthe heater was well within the spray cone. The first condi-tion corresponds to the low heat flux, low surface superheatregime, where the heater is fully covered with a water film.In this case, comparatively small temperature gradientsunderneath the surface could be observed. A typical tem-perature profile for this regime is shown in Fig. 11.

The second condition investigated is that of a rupturedfilm on the heater, which usually occurs for higher heatfluxes and wall superheats. The ruptured film results inhigher temperature gradients. The hotter areas correspondto the areas covered with the fairly thick liquid, while thefilm is ruptured in the colder areas and the small spray

Fig. 12. Temperature distribution beneath ruptured spray film.


droplets can directly evaporate on the heater or agglomer-ate with other droplets to form larger wetted areas. Thelower temperatures beneath the ruptured film clearly indi-cates that the direct evaporation of spray droplets leadsto a better heat transfer. The drawback of this regime arehigher temperature gradients. A typical temperature distri-bution for this regime is shown in Fig. 12. While the tem-perature beneath the heater completely covered with acoolant film varies by approximately 1 K, the temperaturebeneath the heater only partly covered with a coolant filmvaries by more than 2 K. By comparing Figs. 11 and 12 itbecomes obvious that the temperature gradients below theruptured coolant film are significantly larger than belowthe cohesive coolant film. In case of the ruptured film,higher temperatures are observed beneath agglomeratedwater. While the droplets from the spray nozzle evaporatecomparatively fast if they get in direct contact with the hea-ter and hence lead to a good heat transfer, agglomerateddroplets lead to a thicker water layer with a higher thermalresistance.

While such small temperature variations have beenobserved for large nozzle spacings, for smaller distances,when the heater was only partly covered by the spray cone,high temperature gradients occurred at the edges of thespray cone, such that the temperature difference between

Fig. 13. Temperature distribution for low nozzle spacing.

the middle of the spray cone and its edge was found toexceed 18 K. A plot of the temperature distribution belowthe heater surface from the middle of the spray conetowards its edge is shown in Fig. 13. Thus, the resultsobtained for small nozzles spacings have some similarityto the temperature variations found by Shedd and Pautsch[12], while for larger nozzle spacings small temperaturevariations have been found as observed by Gu et al. [11].No significant influence of the nozzle spacing on the tem-perature variations were found once the heater was com-pletely inscribed in the spray cone.

4. Conclusion

The experiments have shown that spray cooling onmicro structured can lead to significantly improved coolingperformances compared to smooth surfaces at the samewall superheat. The authors believe this effect is due toan increased length of the three phase contact line thatforms on the structures which leads to a very efficient thinfilm evaporation. Using an infrared camera, it could beshown that for a smooth surface the dissipated heat fluxincreases with increasing contact line length, which occurson a smooth surface when the coolant film covering thesurface at low surface superheats ruptures. Additionally,it could be shown that the temperature distribution showsstronger temperature gradients when the coolant film rup-tures. Also, small nozzle spacings lead to large temperaturegradients on the heater surface.

Acknowledgements

The authors wish to acknowledge the support of theGerman Research Foundation (DFG) via the Emmy-Noe-ther-Program.

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spray cooling on micro structured surfaces

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