Effect of jet diameter on the rewetting of hot horizontal surfaces during quenching

Experimental Thermal and Fluid Science 42 (2012) 25–37

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Effect of jet diameter on the rewetting of hot horizontal surfaces during quenching C. Agrawal a, R. Kumar a,⇑, A. Gupta a, B. Chatterjee b a b

Department of Mechanical and Industrial Engineering, Indian Institute of Roorkee, Roorkee, Uttranchal 247 667, India Reactor Safety Division, Bhabha Atomic Research Centre, Mumbai 400 085, India

a r t i c l e

i n f o

Article history: Received 9 September 2011 Received in revised form 21 March 2012 Accepted 22 March 2012 Available online 9 May 2012 Keywords: Jet impingement Transient cooling Stagnation Nusselt number Rewetting Wetting delay

a b s t r a c t A horizontal stainless steel surface of 0.25 mm thickness and at 800 ± 10 °C initial temperature was cooled by a round water jet. The water jet at 22 ± 1 °C temperature impinged onto the hot surface through tube type nozzles of 250 mm length. The experiments were performed for the jet diameters in the range of 2.5–4.8 mm and the jet Reynolds number remained within 5000–24,000. The transient cooling performance of the test surface was determined on the basis of rewetting temperature, wetting delay and the rewetting velocity. A rise in the rewetting temperature and the rewetting velocity has been observed with the increase in jet diameter and jet Reynolds number, leading to decline in the wetting delay. The results of the steady state cooling are in agreement with the findings of other investigators. The correlations have also been developed to evaluate the stagnation and the local Nusselt number for the steady state cooling condition. These correlations predict 80% experimental data within an error band of ±10%. Ó 2012 Published by Elsevier Inc.

1. Introduction The rewetting phenomenon takes place during the transient cooling of a hot surface. When a hot surface at very high temperature is quenched with a stream of cold fluid, initially a vapor film is formed between the hot surface and the fluid layer over the surface [1–3]. This vapor film averts the quenching fluid to wet the hot surface, resulting in lower heat dissipation from the hot surface. The formation of thin vapor film is due to the high surface temperature. It has been reported that the effective surface cooling takes place only after the surface is below the rewetting temperature and the phenomenon of sharp temperature drop is called as rewetting [4,5]. At the rewetting condition, fluid stream is able to depart vapor layer from the hot surface and re-establish the contact with the hot dry surface [5]. It has been reported that during rewetting the coolant fluid temperature is sufficiently low to condense vapor bubbles, which leads to wetting of hot surface [6]. Once the rewetting condition is attained, the surface temperature drops drastically. The heat transfer regime changes from film boiling to the transition or nucleate boiling [7,8] and finally reaches to the forced convective heat transfer under the steady state condition. The consensus over the definition of surface rewetting is still not established, however, a large number of researchers have ⇑ Corresponding author. Tel.: +91 1332 285740 (O); fax: +91 1332 285665/ 273560. E-mail address: [email protected] (R. Kumar). 0894-1777/$ - see front matter Ó 2012 Published by Elsevier Inc. http://dx.doi.org/10.1016/j.expthermflusci.2012.03.018

described rewetting as the onset of transition or minimum film boiling point [7,9]. During the quenching of hot surface, the minimum film boiling point is the point of the onset of sharp surface temperature drop or the point corresponding to the minimum heat flux (Fig. 1). Though, some of the investigator assumed surface rewetting at the location of maximum change in the slope of time temperature curves or the location of maximum heat flux [10,11]. Kim [12] proposed the apparent rewetting temperature to explain the rewetting phenomena, which is further quantified by Barnea and Elias [13]. They reported that the apparent rewetting temperature is approximately 20 °C higher than the rewetting temperature [13]. Carbajo [5] in his review on the rewetting of hot surfaces discussed the relevance of these definitions and reported that the rewetting temperature for different surface-coolant combinations in the range of 167–700 °C. The rewetting condition at the minimum film boiling point is observed for the larger coolant flow rate, whereas, for spray and droplet cooling, it is considered to be at Leidenfrost point [5,14]. The maximum heat flux condition or the CHF condition is taken as rewetting state when single rod geometry is cooled by a liquid film [5]. The jet impingement cooling technique is one of the quenching methods to cool the high temperature surfaces. This cooling technique is quite common in many industrial applications viz. metal, electronic, nuclear and many more due to the ability of high heat removal rate [15,16]. During the jet impingement cooling a hot surface, initially, a wet patch is formed below the jet and subsequently the wetting front starts progressing over the hot surface [3,17]. The wet patch

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C. Agrawal et al. / Experimental Thermal and Fluid Science 42 (2012) 25–37

Nomenclature surface area of sheet (m2) Biot number (hw/ks) power factor for AC supply nozzle exit or tube exit diameter (m) heat transfer coefficient (W/m2 K) electric current (A) thermal conductivity (W/m K) heat flux (W/m2) Nusselt number (hd/kj) Reynolds number (U d/t) radial distance (m) time (s) wetting delay period (s) temperature (°C) apparent rewetting temperature (°C) maximum heat flux temperature, (°C)

TRW U u V z z/d

rewetting temperature (°C) nozzle exit velocity (m/s) local rewetting velocity (m/s) voltage drop (V) distance between nozzle exit to target surface (m) dimensionless nozzle exit to surface spacing

Suffix e j i o p s x

experimental value jet initial value stagnation value predicted value surface local

15.0

850 800 750

12.5

o

surface temperature, Ts, C

700

TAR

650

TRW

600

10.0

550 500 450

Tm

-2 o

surface temperature temperature gradient

film boiling regime

transient boiling regime

Nucleate boiling regime

single phase convective heat transfer regime 7.5

400 350 300

5.0

250

td

200 150

temperature gradient, dT/dt x10 , C/s

A Bi Cos / d h I k q Nu Re r t twet T TAR TCHF

2.5

100 50 0.0

0

0.0

0.5

1.0

1.5

2.0

2.5

time, t, sec Fig. 1. Surface temperature and temperature gradient curve under transient cooling condition.

expands in the downstream direction once the surface ahead obtains the rewetting temperature. The delay in wet patch spreading or the progress of quench front after the application of jet is termed as the wetting delay [17] or the resident time [10,18]. The spreading of wetting front over the hot surface is evaluated by the rewetting velocity. The rewetting velocity is the measure of time elapsed before the rewetting takes place between two marked locations [4,7]. In fact, the rewetting velocity is the ratio of distance between marked locations and the difference of wetting delay between these marked locations. A number of experimental investigations have been carried out for the round jet impingement surface cooling under transient and steady state condition and some of them are shown in the Tables 1 and 2. It has been found that the parameters like jet velocity, surface properties, surface and coolant temperature affects the quenching phenomena and has bearing on the rewetting temperature, wetting delay and the rewetting velocity. However, any study is not available for the effect of jet diameter on rewetting phenomena of a Stainless Steel surface at 800 °C temperature. Therefore, an experimental investigation has been carried out to study the rewetting behavior of such surfaces with jet of different diameters. The

experiments were performed with jet Reynolds number in the range of 5000–24,000 and jet diameter of 2.5, 3.5 and 4.8 mm. Though, the study for the effect of jet diameter on the heat transfer under steady state condition is available in the literature. However, any correlation is not available that predicts the stagnation and local Nusselt number under the steady state cooling conditions. Therefore, a generalized correlation to predict the Nusselt number for the single phase convective heat transfer during steady state cooling condition has also been proposed for the jets having the diameter in the range of 2.5–4.8 mm.

2. Experimental setup and procedure The experiments were performed for the cooling of a hot horizontal stainless steel surface using the water jet of 22 ± 1 °C temperature. The water was injected onto the hot SS test-surface through a straight tube type nozzle. The schematic of the experimental set-up is shown in Fig. 2. Initially water was collected in a reservoir (9) and supplied to the nozzle assembly (1) with the help of a water pump (8). A turbine flow meter (6) and a flow

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C. Agrawal et al. / Experimental Thermal and Fluid Science 42 (2012) 25–37 Table 1 Round water jet impingement cooling under steady state condition. Author year

Jet diameter

Jet type and direction

Surface material and dimensions

Fluid type and Temp.

Re/jet velocity

Observations

Ruch et al. [19]

0.21–0.433 mm 2, 2.5 mm

Cu cylinder, diameter 0.508 in. Cu, 11, 21 mm diameter

R-113 16 °C

Monde and Katto [20] Ma and Bergles [21] Stevens and Webb [22]

1030–4120, 1.23–6.87 m/s 2.04–17.3 m/s

Tube 1.81 mm

Free surface upward at diff. angles Free surface upward and downward Submerged horizontal

Tubes 2.2–8.9 mm

Free surface down ward

Pan et al. [23]

Contoured Tube, Sharp edge, 10.9 mm

Free surface upward

SS foil 0.0254 mm

Water from lab supply

16,500–43,500

Womac et al. [24] Garimella et al.a,b [25,26]

Converge 0.978– 6.55 mm 0.79–6.35 mm

Free surface and submerged downward Submerged and Confined downward

Cu, 12.7  12.7 mm2, 3 mm thickness SS foil, 10  25 mm2, 0.075 mm thickness

Water and 3 M FC77 FC-77 20 °C

600–34,000

Liu and Wang [27]

Tube type, Dia. 10 mm

Free surface downward

SS, 12  12 mm2, 2 mm thickness

Water 20–95 °C

1–3 m/s

Heat transfer and heat flux for nucleate and film boiling Correlation for burnout heat flux Heat flux at nucleate boiling state with hysteresis effect Correlation for stagnation, local and Avg. Nusselt number Velocity profile and turbulence level, correlation for stagnation Nusselt number in term of velocity gradient Correlations for Avg. Nusselt number a Correlation for stagnation and average Nusselt number. bEffect of nozzle aspect ratio and diameter on local, stagnation and average Nusselt number Theoretical correlation for stagnation Nusselt number, heat flux for transition and film boiling

Constantan, 5  5 mm2,10 lm thick SS, 15  80 mm2, 0.0508 mm thick

Water, Freon-113, Tsub 3–30 °C R 113, Tsub 0– 20.5 °K Water from lab supply

1.08–10.05 m/s 4000–52,000

4000–23,000

Table 2 Round water jet impingement cooling under transient condition. Author year

Jet direction, type and diameter

Surface material and dimensions

Fluid type and Temp.

Re/jet velocity

Initial surface temperature

Observations

Piggott et al. [17] Hatta et al. [28]

Free surface, horizontal, 1.5–3.0 mm diameter Downward, free surface, tube 10 mm diameter

Inconel, gold and silica tube, 6.3–25.4 mm diameter SS, 200  200 mm2, 10 mm thickness

Water 20–80 °C

1.5–15 g/s

500–800 °C

Wetting delay

Water 20 °C

Flow 0.1–7.0 l/m

900 °C

Chen et al. [29]

Free surface upward converging dia, 4.76 mm

SS, 355  254 mm2, 6.35 mm thickness

Water 25–27 °C

2.3 m/s

88, 240 °C

Mitsutake and Monde [30]

Upward, Free surface, 2 mm diameter

Cu, brass, steel diameter 94 mm 60 mm thick

Water 20–80 °C

10,000–30,000

250 °C

Hammad et al. [31] Woodfield et al. [32]

Upward, free surface, 2 mm diameter Upward, free surface, 2 mm diameter

Cu, brass, Steel diameter 94 mm 59 mm thick Cu, brass, Steel diameter 94 mm 59 mm thick

Water 20–95 °C

3–15 m/s

250, 300 °C

Water 20–95 °C

3 m/s

300–400 °C

Mozumder et al.a,b,c [18,8,33]

Upward, free surface, 2 mm diameter

Cu, brass, steel diameter 94 mm 59 mm thick

Water 20–95 °C

3–15 m/s

250–400 °C

Xu et al. [34]

Downward, free surface, tube 19 mm diameter

Water 30–80 °C

0.88–2.64 m/s

700–900 °C

Islam et al. [3]

Upward, free surface, 2 mm diameter Downward, free surface, tube 3, 4 mm diameter

Carbon steel, SS 280  280 mm2, 10 mm thick Brass, steel diameter 94 mm 59 mm thick SS cylinder, 26.67 mm outer diameter

Heat transfer coefficient for stagnation region and movement of black cooling zone radius Local heat flux and heat transfer coefficient for stationary and moving surface Wetting front movement and transient surface heat flux Maximum surface heat flux during transient cooling Flow behavior and boiling sound during transient surface cooling a Correlations for wetting delay, bCorrelations for maximum heat flux, c Maximum heat flux propagation Transient surface heat flux at the stagnation region

Water 20–95 °C

3–15 m/s

500–600 °C

Water 20–80 °C

5, 7.75 m/s

250–800 °C

Downward, free surface, tube 3 mm diameter Downward, free surface, tube 9 mm diameter

SS-314 cylinder, 50 mm diameter, 20 mm height Ni, 175 mm diameter, 5 mm thickness

De-ionized water

7980, 18,900 2.5, 6.25 m/s 1.39 m/s

900 °C

Akmal et al. [35] Karwa et al. [6] Gardeck et al. [36]

Oil in water emulsion, Water, 20 °C

450–500 °C

Transient surface cooling phenomenon Speed of wetting front propagation and change in microstructure Maximum heat flux and wetting front movement Maximum heat flux and wetting velocity

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C. Agrawal et al. / Experimental Thermal and Fluid Science 42 (2012) 25–37

Water inlet

1. Nozzle assembly 5. Test-surface 9. Water reservoir

2. Work table 6. Turbine flow-meter 10. By pass line

3. Data-acquisition system 7. Flow control valve

4. vertical slide 8. Pump

Fig. 2. Schematic of experimental setup.

control valve (7) were installed between the pump and a by pass line (10). The nozzle was mounted on a vertical slide (4) on the work table (2) and the test-surface (5) was placed underneath to the nozzle assembly. A total of seven ungrounded K-type thermocouples were attached on the back side of the test-surface and were connected to the Data Acquisition System (3). The test-surface was heated up-to desired temperature with high ampere current through an auto-transformer. The voltage drop across the testsurface was measured with a digital voltmeter and corresponding current supply was measured by a digital ammeter using a current transformer (CT) arrangement. Fig. 3a shows the details of nozzle assembly and the target surface that comprises of a water nozzle (6), vertical slide (2), rack (3) and pinion (4). The rack and pinion arrangement facilitated the movement of vertical slide to adjust the nozzle exit and target surface spacing. The nozzle was a straight tube of 250 mm length to deliver the fully developed flow at the nozzle exit. Three different size of tube with 2.5, 3.5, 4.8 mm diameter were used for the experiments. The complete nozzle assembly was mounted on the vertical support (12) attached at the sides of the main frame (11) of the work table. A number of holes on these vertical supports were also provided to vary the nozzle exit to test-surface spacing. The vertical movement of nozzle was directly measured with a pointer (15) on a scale (5). The test-surface with the Teflon base (9) was clamped on a movable work table (10). The position of the test-surface underneath the impinging jet was adjusted with a lateral (13) and transverse (14) lead screws. Fig. 3b shows the complete test-surface assembly. The test-surface was a Stainless steel rectangular surface of 130 mm length, 38 mm width and 0.25 mm thickness. A total of seven minerally insulated K-type ungrounded thermocouples of 0.25 mm sheath diameter were attached at the back side of the test-surface. The first thermocouple was fixed at the geometrical centre of test-surface. The other thermocouples were attached at 4 mm radial pitch with the nearest thermocouple except the thermocouple marked as (2), which was placed at 2 mm distance from the centre. The marking for thermocouples locations was done from the centre of the target-surface using an optical micrometer. The thermocouples were firmly attached on these marked locations with small pieces of SS foil, which was spot welded on the test-surface. Thus,

a total of three thermocouples, parallel to the longer side were fixed on both sides of the centre of the test-surface. With the help of this arrangement the test-surface temperature was recorded with an increment of 2 mm radial distance up to 12 mm distance. The reverses side of the target surface was insulated with ceramic insulation and the Teflon base. Initially all the regulating valves were closed except the bypass line valve (10). The pump (8) that supplied water to the nozzle assembly (1) remained operative for the entire duration of experiments. The supplied water flow rate was regulated through a control valve to vary the jet Reynolds number and was measured with a turbine flow meter. The target-surface was connected to a 15 kVA auto transformer and heated till the steady temperature of 800 ± 10 °C was attained. At this surface temperature, the supplied voltage and the current were recorded before the jet impingement on the target-surface. Then the bypass line valve was closed and the main valve (1) of nozzle assembly was opened, resulting in the jet impingement on the hot target surface. The change in surface temperature with time under transient and steady state cooling conditions was recorded at the rate of 100 samples per second. During the steady state condition the voltage drop and the supplied current were once again recorded as the test section was heated throughout the experiments. The experiments were repeated for various Reynolds number, Re, and jet diameter, d. Initially for transient cooling condition the nozzle exit to target surface spacing was maintained as z/d = 4, however under steady state condition it was varied between z/d = 4–16. For each set of experiments a new test surface was prepared to avoid any effect of change in surface properties, oxidation and sagging from the previous experiment. The operating ranges of experimental parameters are shown in the Table 3. The measurement uncertainties for the experiments are shown in the Table 4. Since, the diameter of thermocouple wire was 0.25 mm, the uncertainty in the thermocouple location was taken as 0.25 mm instead of 0.1 mm. Therefore, the highest uncertainty in thermocouple location was 12.5% at 2 mm distance which reduced to 2.1% for the extreme location, i.e. at 12 mm. Similarly, maximum uncertainty in wetting delay at the stagnation region was 25% which reduced to 0.67% at 12 mm location. The rewetting velocity has the highest uncertainty of 27% at the stagnation region

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C. Agrawal et al. / Experimental Thermal and Fluid Science 42 (2012) 25–37

(a) 1. Valve 2. Vertical scale 3. Pinion for vertical movement 4. Rack 5. Scale 6. Nozzle 7. Test-surface 8. Clamps 9. Teflon base 10. Movable Table 11. Main frame 12. Ve rtical support 13. Lateral movement handle 14. Transverse moveme nt handle 15. Scale pointer

(b) All dimensions are in mm 1. Thermocouples location 2. Copper terminal 3. Test-surface 4. Ceramic insulation 5. Teflon base Fig. 3. Schematic of (a) nozzle assembly and (b) test-surface.

Table 3 Range of operating parameters.

Table 4 Uncertainty in the measurements.

Experimental parameter

Operating range

Parameter

Accuracy

Reynolds number (Re) Jet velocity (U) Water flow rate Jet exit to surface spacing (z/d) Nozzle diameter (d) Thickness of test-surface (w) Water temperature Initial surface temperature

5000–24,000 0.92–8.40 m/s 0.5–4.7 lpm 4 2.5, 3.5, 4.8 mm 0.25 mm 22 ± 1 °C 800 ± 10 °C

Water flow rate Nozzle diameter Test-surface length and width Test surface thickness Location of the thermocouples Time Temperature

0.10 lpm 0.10 mm 0.02 mm 0.01 mm 0.10 mm 0.01 s 1.5 °C at 500–800 °C 0.5 °C at 200–500 °C 0.1 °C at 100–200 °C

that reduced to 2% at 12 mm location. For the steady state cooling the uncertainty in the Nusselt number was in the range of 5–6%. Since, the test-surface was of 0.25 mm thickness and the jet impingement cooling had high heat transfer coefficient. The Biot number, Bi, of the test-surface during the rewetting condition was less than 0.1, Bi  0.1, therefore, the test-surface was treated

as a lumped surface. The temperature at the back side of the test surface was considered to be the same for top of the surface exposed to the water jet. Under transient cooling condition the rewetting temperature and the wetting delay at a certain spatial location was obtained with the surface temperature and the surface temperature gradient plots (Fig. 1). The rewetting velocity at

C. Agrawal et al. / Experimental Thermal and Fluid Science 42 (2012) 25–37

a particular location was determined by the ratio of linear distance from the stagnation point with the observed wetting delay period for the same spatial location. Though, the supplied heat flux to the test surface has no bearing on the rewetting parameters, as these depend only on the initial surface temperature [11], the test-surface was continuously heated during the experiments. During the transient cooling the heat dissipated from the hot surface was more than the joule heat supplied to the test surface. It was estimated that conductive heat loss through the Teflon base was less than 2% of heat extracted at rewetting condition and 0.2% of the heat extracted at the maximum heat flux condition. It has been estimated that the change in thermo physical properties remains within percent, when the test-surface was cooled from its initial temperature of 800 °C to the rewetting condition. Therefore, the effect of change in thermo physical properties with temperature has been ignored while determining the rewetting parameters. The rewetting parameters under transient cooling were determined with the help of time dependent surface temperature observations. However, to evaluate the heat transfer performance under steady state condition, heat flux supplied to target-surface, surface temperature and the jet temperature were required. The heat flux supplied to the test surface under steady state cooling condition was determined by using the following equation:

q¼

VI cos / A

ð1Þ

The conductive and convective heat loss from the target surface under steady state cooling condition were estimated to be less than 1% without considering the effect of contact resistance and heat loss through the Teflon base. In fact, the total heat flux from the test surface was assumed to be dissipated from the top surface through the water jet. The local single phase forced convective heat transfer coefficient from the hot surface and the Nusselt number under steady state cooling condition were determined by the following equations 2 and 3:

h¼

q Ts  Tj

ð2Þ

hd kj

ð3Þ

Nu ¼

During the experiments only bottom side surface temperature was measured, therefore, under steady state cooling condition, the test surface temperature, Ts, was determined through 2D heat conduction equation. The solution of the following heat conduction equation for cylindrical coordinates was evolved using finite difference method.

!   1 @ @T @2T þ ks 2 þ q_ ¼ 0 ks r r @r @r @Z

at r ¼ 0;

Z ¼ w;

@T ¼0 @r

@T ¼0 @Z

Z ¼ w; T ¼ TðrÞ

ð4Þ

ð5Þ

ð6Þ ð7Þ

The determined stagnation and local Nusselt number for steady state cooling condition were compared with the corresponding predicted Nusselt number from available correlations in the literature to establish the integrity of the test set-up.

3. Results and discussion The results reported below are based on the experimental findings for the transient and the steady state cooling of the testsurface. However, initially the integrity of the experimental setup is established with the results of single phase convective heat transfer performance under the steady state cooling condition. 3.1. Steady state cooling At the steady state cooling condition the stagnation Nusselt number, Nuo, and the local Nusselt number, Nux, are compared with those predicted by the established correlations available in the literature. The stagnation Nusselt number is determined at the jet impingement point and the local Nusselt number is evaluated for different downstream spatial positions on the target-surface. A comparison of the stagnation Nusselt number for all the test runs with those predicted by different correlations, under the steady state condition is shown in Fig. 4. Stevens and Webb [22] correlations are for d = 2.2, 4.1 mm and Re = 4000–52,000, while Wolf et al. [37] correlation is for slot jet of 10.2 mm width and Re = 23,000–46,000. Wang et al. [38] correlation is valid for the fluid having Prandlt number, Pr > 0.5. The experimental stagnation Nusselt numbers are found within ±20% of those predicted by different correlations. In fact, a total of 75% experimental data have been predicted within an error band of ±15%. It is also observed in Fig. 4 that Wolf et al. [37] and Wang et al. [38] correlations underpredict the stagnation Nusselt number particularly for higher jet diameter and jet Reynolds number. This is due to the fact that Wolf et al. [37] correlation has been developed for a slot jet and the Wang et al. [38] correlation is for the jet of laminar flow condition. The stagnation Nusselt numbers, Nuo, in present investigations are found in close agreement with the results reported by Stevens and Webb [22]. It remains within a range of 15% to +20% for the rise in nozzle exit to test surface spacing, z/d = 4–6, and Reynolds number 5000–24,000. The stagnation Nusselt number increases with the rise in jet Reynolds number due to increase in jet velocity and associated turbulence level [22]. However, with the rise in nozzle exit to surface spacing, z/d, even higher than the potential core length, the water jet tends to give up its orderly structure resulting in lower stagnation Nusselt number [15]. Further, the effect of gravity on the jet velocity with the change in nozzle exit to surface spacing becomes predominate at the lower Reynolds number, leading to variation of the stagnation Nusselt number [16,24]. Since, Wolf et al. [37] and Wang et al. [38] correlations did not

predicted stagnation Nusselt number, (Nuo)p

30

300 4.8

3.5

2.5

d (mm)

+ 20 %

Stevens and Webb [22] Womac et. al. [24] Wolf et. a. [37] Wang et. al. [38]

250

+ 15 % - 15 %

- 20 %

200 150 100 50 0 0

50

100

150

200

250

300

experimental stagnation Nusselt number, (Nuo)e Fig. 4. Comparison of experimental stagnation Nusselt number with those predicted by different correlations for steady state cooling condition.

31

24 16 10 5

Re x 10-3 Stevens and Webb [22] Sun et. al. [39]

200

+ 20 %

+ 10 % - 10 %

d = 3.5 mm

- 20 %

150

100

50

0 0

50

100

150

200

250

experimental local Nusselt number, (Nu x)e

predicted local Nusselt number, (Nux)p

(a)

300 24 16 10 5

2.5 3.5 4.8

250

+5% -5%

200

150

100

50 50

100

150

+ 15 %

200 - 20 %

150 - 35 %

100 50 0 100

200

250

300

(a)

Sun et. al. [39]

50

d (mm)

Re x 10-3

d= 4.8 mm

0

300

experimental stagnation Nusselt number, (Nuo)e

Stevens and Webb [22]

250

predicted stagnation Nusselt number, (Nuo)p

250

150

200

250

300

experimental local Nusselt number, (Nu x)e

(b)

predicted local Nusselt number, (Nux)p

predicted local Nusselt number, (Nux)p

C. Agrawal et al. / Experimental Thermal and Fluid Science 42 (2012) 25–37

300

d (mm) 2.5 3.5 4.8

250

+ 10 %

+ 20 %

- 10 % - 20 %

200 150 100 50 0 0

50

100

150

200

250

300

experimental local Nusselt number, (Nux)e

Fig. 5. Comparison of experimental local Nusselt number with those predicted by different correlations for steady state cooling condition.

(b) Fig. 6. Comparisons of experimental data with the proposed correlations (a) stagnation Nusselt number and (b) local Nusselt number.

includes the nozzle exit to surface spacing, therefore, these correlations predict the same value for the stagnation Nusselt number at different z/d. Though, it has been observed that with the rise in the nozzle exit to surface spacing, z/d, stagnation Nusselt number reduces, this is in agreement with the finding of Stevens and Webb [22]. The experimental local Nusselt number, Nux, has been compared with that predicted by Stevens and Webb [22] correlation for 4.1 mm jet diameter and 4000–52,000 Re, and Sun et al. [39] correlation for submerged jet valid for 5000–36,000 Re. The deviation in the local Nusselt number for the jet diameter of 3.5 mm is within ±20% (Fig. 5a), whereas, for the jet diameter of 4.8 mm the predicted values are within an error band of +15% to 35% (Fig. 5b). Sun et al. [39] correlation overpredicts the experimental results, due to higher heat transfer rate under the submerged jet condition as compare to the free surface jet [24]. Whereas, Stevens and Webb [22] correlation underpredicts the local Nusselt number for 4.8 mm jet diameter. This underprediction may be due to the correlation used for the comparison that was developed for 4.1 mm jet diameter, which is 17% lower in size as compare to the experimental nozzle diameter of 4.8 mm. It has already established in the open literature that the local Nusselt number increases with the rise in jet diameter [22,24]. Stevens and Webb [22] have proposed separate correlations of local Nusselt number for each of the jet diameter examined, i.e. 2.2, 4.1, 5.8 and 8.9 mm. Since, no generalized correlation for different jet diameter is observed to determine the local Nusselt number under free surface round water jet impingement steady

state cooling condition. Therefore, two correlations are proposed to predict the stagnation Nusselt number, Nuo, (Eq. (8)) and the local Nusselt number, Nux, (Eq. (9)). These correlations are valid for single phase convective heat transfer regime and for the range of parameters investigated, i.e. 5000 6 Re 6 24,000, 4 6 z/d 6 16 and 2.5 6 d 6 4.8. The dependent variables the same as in the Stevens and Webb [22] correlations proposed for the stagnation Nusselt number.

ðNuÞo ¼ 0:56ðReÞ0:62 ðNuÞx ¼ 0:62ðReÞ0:58

 z 0:08 u0:08 d

ð8Þ

d

 z 0:065  r 0:41 u0:03 d

d

d

ð9Þ

The Eq. (8) predicts the experimental stagnation Nusselt number, Nuo, with an error band of ±5% (Fig. 6a). Whereas, Eq. (9) predicts the local Nusselt number, Nux, within ±20% and 80% of experimental data within ±10% error band (Fig. 6b). 3.2. Transient cooling The transient cooling performance of the hot target-surface is analyzed on the basis of rewetting phenomena. Surface quenching curves obtained for different operating parameters are used to determine the various rewetting parameters. The quenching curves for the experimental range of jet diameters (2.5–4.8 mm),

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C. Agrawal et al. / Experimental Thermal and Fluid Science 42 (2012) 25–37

d = 2.5 mm

800

r, mm

o

600

temperature, Ts, C

0 2 4 6 8 10 12

o

temperature, Ts, C

800

400

200

0.0

0.5

1.0

1.5

2.0

400

200

0.0

2.5

0.5

1.0

1.5

time, t, sec

(a)

(a) 800

r, mm

d = 3.5 mm

o

600

temperature, Ts, C

stg 2 4 6 8 10 12

o

temperature, Ts, C

600

time, t, sec

800

400

200

2.0

2.5

r, mm

Re = 16000 d = 3.5 mm

0 2 4 6 8 10 12

600

400

200

0

0 0.0

0.5

1.0

1.5

2.0

2.5

0.0

0.5

1.0

1.5

2.0

2.5

time, t, sec

time, t, sec

(b)

(b)

Fig. 8. Cooling curves at z/d = 4 for d = 3.5 mm, (a) Re = 10,000 and (b) Re = 16,000.

800

o

0 2 4 6 8 10 12

0

0

temperature, Ts, C

r, mm

Re = 10000 d = 3.5 mm

r, mm

d = 4.8 mm

stg 2 4 6 8 10 12

600

400

200

0 0.0

0.5

1.0

1.5

2.0

2.5

time, t, sec

(c) Fig. 7. Cooling curves at Re = 5000, z/d = 4 for different jet diameters (a) 2.5 mm, (b) 3.5 mm and (c) 4.8 mm.

at 5000 Re are shown in Fig. 7. Whereas, surface quenching curves for other experimental range of jet Reynolds number are shown in Figs. 8 and 9. These surface quenching curves are similar to those reported by other investigators for the jet impingement cooling [31–33], spray cooling [40,41], and for the liquid film cooling system [4,5]. It is evident in these figures that the surface cooling in the stagnation region is initiated within 0.04–0.08 s of the application of jet impingement on the hot target-surface, irrespective of the jet Reynolds number and the jet diameter. However, for the downstream spatial locations, beyond 8 mm, the surface cooling

is somewhat delayed. The immediate cooling at the stagnation point is due to the higher heat transfer rate for the stagnation region [9,29]. Whereas, the quenching front takes certain time to reach the locations away from the stagnation point due to the delay in surface rewetting and the flow retardation after the striking of jet on the test surface [9]. When the wetting front reaches to a particular downstream spatial location on the test-surface a sharp drop in surface temperature is observed [10,33]. Nevertheless, surface cooling rate at different spatial locations vary with the jet diameter and the jet Reynolds number. Fig. 7 shows the variation of surface temperature at different locations for the jet diameters of 2.5 mm, 3.5 mm and 4.8 mm at 5000 Re. A comparison has been made for the cooling rate at each location to cool the surface from initial temperature of 800 °C to 150 °C. For the jet diameter of 2.5 mm at 5000 Re the time taken to reach surface temperature from its initial value of 800–150 °C is nearly 160% higher than that for 12 mm location as compare to the stagnation point (Fig. 7a). The corresponding rise in time is 150% and 140% for the jet diameter of 3.5 mm and 4.8 mm respectively (Fig. 7b and c). With the rise in jet Reynolds number to 24,000 the surface cooling rate is further enhanced, particularly for radial locations away from the stagnation point (Fig. 9). Infact, the enhanced cooling rate can be observed by comparing Figs. 7 and 9. It has also been observed with these figures that surface cooling is rapid for the higher jet Reynolds number and the jet diameters. For 2.5 mm jet diameter, with the rise in Reynolds number from

33

C. Agrawal et al. / Experimental Thermal and Fluid Science 42 (2012) 25–37

600

o

0 2 4 6 8 10 12

400

200

U (m/s)

d (mm )

Re = 5000

r, mm

Re = 24000 d = 2.5 mm

rewetting temperature, TRw, C

o

temperature, Ts, C

800

800

4.8 3.5 2.5

0.92 1.25 1.76

780

760

740

720

0 0.0

0.5

1.0

1.5

2.0

2.5

0

2

4

6

r, mm

Re = 24000 d = 3.5 mm

rewetting temperature, TRw, C

o

temperature, Ts, C

10

12

14

(a)

(a) 0 2 4 6 8 10 12

600

o

800

8

radial distance, r, mm

time, t, sec

400

200

d (mm )

Re = 10000

800

U (m/s) 1.80 2.51 3.53

4.8 3.5 2.5

780

760

740

720

0 0.0

0.5

1.0

1.5

2.0

2.5

0

2

4

6

(b)

10

12

14

(b) r, mm

Re = 24000 d = 4.8 mm

rewetting temperature, TRw, C

o

temperature, Ts, C

0 2 4 6 8 10 12

600

o

800

8

radial distance, r, mm

time, t, sec

400

200

800

780

760

740

d (mm) Re x10-3 U (m/s) 3.5 3.5 2.5 2.5

720

3.98 5.98 5.60 8.40

16 24 16 24

0 0.0

0.5

1.0

1.5

2.0

2.5

time, t, sec

(c)

0

2

4

6

8

10

12

14

radial distance, r, mm

(c)

Fig. 9. Cooling curves at Re = 24,000, z/d = 4 for (a) d = 2.5 mm, (b) d = 3.5 mm and (c) 4.8 mm.

Fig. 10. Rewetting temperature at z/d = 4 for (a) Re = 5000, (b) Re = 10,000, (c) Re = 16,000 and 24,000.

5000 to 24,000 the time for cooling the surface up to 150 °C is reduced by 50% at 12 mm location, which is 55% and 65% for the jet diameter of 3.5 mm and 4.8 mm respectively. Whereas, for the increases in Reynolds number from 5000 to 10,000 with 3.5 mm jet diameter this reduction in cooling time is only 15% at 12 mm location. The enhanced cooling rate for higher jet Reynolds number can be attributed by the rise in water flow rate and jet velocity associated with the higher Reynolds number [42]. The larger liquid flow rate has higher thermal capacity to remove the surface heat and hence result in the rise in surface cooling even for the downstream locations away from the stagnation point.

3.2.1. Rewetting temperature The transient surface cooling and rewetting performance is generally evaluated on the basis of rewetting temperature, wetting delay, local and average rewetting velocity. These rewetting parameters are obtained by obtaining the temperature gradient from the time varying temperature data of the surface quenching. As described by many investigators [43,44], for this study also, the surface temperature, where the sharp rise in temperature gradient is observed is considered as the rewetting temperature (Fig. 1). This point is obtained by evaluating the surface temperature gradient, dTs/dt, between two consecutive surface temperature data. In

C. Agrawal et al. / Experimental Thermal and Fluid Science 42 (2012) 25–37

1.6

Re = 5000

wetting delay, twet, sec

1.4 1.2 1.0 0.8 0.6 0.4 U (m/s)

d (mm )

0.2

4.8 3.5 2.5

0.0

0

2

4

6

8

10

0.92 1.25 1.76

12

14

radial distance, r, mm

(a) 1.6

d (mm )

Re = 10000

4.8 3.5 2.5

1.4

wetting delay, twet, sec

the present investigation the rise in the temperature gradient is observed at the temperature difference of 2.0–2.5 °C between two consecutive observations, i.e. for 0.01 s (frequency of data recording is 100 sps). The surface temperature corresponding to this temperature gradient is considered as the rewetting temperature. The variation of rewetting temperature with the Reynolds number and the jet diameter at different spatial locations on the hot surface is shown in Fig. 10. It is observed that for all the investigated jet diameters and Reynolds numbers, initially rewetting temperature remains unchanged in the stagnation region and then falls for the locations away from the stagnation point. For 5000 Re and 2.5 mm jet diameter, the location for which the rewetting temperature remains constant is 2 mm, which, increases to 4 mm with the jet diameter of 3.5 mm and 4.8 mm (Fig. 10a). This phenomenon is due to the increase in stagnation region with the rise in jet diameter. Thereafter, the rewetting temperature gives up the uniformity and falls rapidly for the downstream locations. The drop in rewetting temperature is sharper for 4.8 mm jet diameter as compared to other two jet diameters (Fig. 10a and b). However, the drop in rewetting temperature for 4.8 mm jet diameter at 10,000 Re is lower than that at 5000 Re. The comparison at 16,000 and 24,000 Re reveals that for 3.5 mm jet diameter the rewetting temperature is almost constant for all the measured spatial locations (Fig. 10c). Whereas, with 2.5 mm jet diameter for the same Reynolds number, the reduction in rewetting temperature from its peak is only 2.5% at 12 mm location. The rewetting temperature is always the highest within the stagnation region due to continuous supply of fresh coolant without any loss in actual injected jet velocity. The drop in rewetting temperature for the downstream spatial locations is due to flow retardation and the rise in enthalpy of spent out fluid [9,43]. The effect of flow retardation and the rise in spent fluid enthalpy for the downstream flow direction is further enhanced with the jet of lower velocity. Perhaps this may lead to the sharper drop in rewetting temperature with 4.8 mm jet diameter at 5000 Re even the coolant flow rate is higher than that for other two jet diameter investigated. For high Reynolds number and jet diameter the larger volume flow rate of coolant overcomes the effect of flow retardation and the enthalpy rise. Therefore, at higher Reynolds number the drop in rewetting temperature for downstream locations is lower with larger jet diameter as compare to the smaller jet diameter. It is also observed in Fig. 10 that for all the measured spatial locations the rewetting temperature increases with the rise in jet Reynolds number, which is inline with the results of Saxena et al. [11] for the liquid film cooling system.

1.2

U (m/s) 1.80 2.51 3.53

1.0 0.8 0.6 0.4 0.2 0.0

0

2

4

6

8

10

12

14

radial distance, r, mm

(b) 1.6

d (mm) Re x10-3 U (m/s)

1.4

wetting delay, twet, sec

34

3.5 3.5 2.5 2.5

1.2

3.98 5.98 5.60 8.40

16 24 16 24

1.0 0.8 0.6 0.4 0.2 0.0

3.2.2. Wetting delay During the experiments it is observed that a wet patch is formed immediately as the water jet strikes the hot test-surface. It is also evident with the results for the stagnation region, where rewetting take place within 0.06–0.08 s after the application of water jet. The quench front moves towards the downstream spatial locations, once the surface rewetting take place in the stagnation region. The quench front movement in the downstream flow direction is delayed due to the flow retardation over the test surface away from stagnation point. Therefore, the wetting delay period increases for the locations away from the stagnation point and become the highest for the extreme spatial position of 12 mm as can be seen in Fig. 11. The wetting delay period is considered as the time taken for surface to rewet after the application of water jet impinging onto the hot surface [17]. It is observed in Fig. 11 that up to 4 mm location, the change in Reynolds number and jet diameter does not affects the wetting delay period, even though coolant flow rate and the jet velocity vary to a great extent. This is in line with the findings of Xu and Gadala [34] that in the stagnation region heat transfer is weakly affected

0

2

4

6

8

10

12

14

radial distance, r, mm

(c) Fig. 11. Wetting delay period at z/d = 4 for (a) Re = 5000, (b) Re = 10,000, (c) Re = 16,000 and 24,000.

by the jet impingement velocity. Further, the wetting delay period rises monotonically for downstream locations away from the 4 mm location. The rise in wetting delay is the highest for 2.5 mm jet diameter. The wetting delay, for 12 mm location compare to the stagnation point is 15 and 21 times higher for jet diameters of 4.8 and 2.5 mm respectively, at 5000 Re (Fig. 11a). The corresponding rise in the wetting delay at 10,000 Re reduces to 8 and 11 times for jet diameters of 4.8 and 2.5 mm (Fig. 11b). This observation reveals that at higher Reynolds number the surface rewetting with larger jet diameter is much faster than the lower jet diameter. The higher volume flow rate of coolant is able to cool the hot surface

35

C. Agrawal et al. / Experimental Thermal and Fluid Science 42 (2012) 25–37

local rewetting velocity, u, mm/s

U (m/s)

d (mm )

Re = 5000

4.8 3.5 2.5

140

0.92 1.25 1.76

120 100 80 60 40 20 0

0

2

4

6

8

10

12

14

radial distance, r, mm

(a) 160

local rewetting velocity, u, mm/s

3.2.3. Rewetting velocity The wetting delay period observed at certain location on testsurface during the transient cooling is used further to evaluate the local rewetting velocity at that spatial position. The local rewetting velocity is the measure of distance travelled by the quenching front per unit wetting delay time at a particular spatial location [4,7]. The variation of local rewetting velocity for different jet diameters at various jets Reynolds number is shown in Fig. 12. The local rewetting velocity is the highest at 4 mm radial location except for 3.5 mm jet diameter at 24,000 Re, for which it is shifted to 6 mm location (Fig. 12c). Since, it has been observed earlier that the wetting delay is nearly constant up to 4 mm spatial location and for the constant wetting delay with the rise in spatial distance the rewetting velocity increases. Therefore the rewetting velocity is continuously increases from the stagnation point to the 4 mm location. After attaining the highest value, the local rewetting velocity decreases for downstream spatial locations for all the investigated jet diameter and Reynolds numbers examined due to rise in wetting delay for downstream spatial locations. The decrease in local rewetting velocity is the highest for 4.8 mm jet diameter, which is further enhanced with the rise in jet Reynolds number. At a constant Reynolds number, the local rewetting velocity is always higher for the larger jet diameter. For 5000 Re at 12 mm location the local rewetting velocity with 4.8 mm jet diameter is 60% higher as compare to 2.5 mm jet diameter (Fig. 12a), which is 80% higher at 10,000 Re (Fig. 12b). In fact, larger coolant flow rate associated with the higher Reynolds number and jet diameter leads to the rise in local rewetting velocity. At 12 mm location the rise in Reynolds number from 5000 to 10,000 increases the local rewetting velocity by 110% for 4.8 mm jet diameter and 80% for 2.5 mm jet diameter. However, this is not true at the higher Reynolds number, the rise in local rewetting velocity is more for the lower jet diameter, possibly due to higher jet velocity associated with the lower jet diameter at higher Reynolds number. The rise in local rewetting velocity is 72% for 2.5 mm jet diameter as compare to 35% for 3.5 mm jet diameter with the increases in jet Reynolds number from 16,000 to 24,000 (Fig. 12c). The surface rewetting performance is also evaluated on the basis of average rewetting velocity as described by the Chan and Banerjee [4]. The average rewetting velocity at certain spatial location on the test surface is determined with the help of average time taken to reach the surface at 700 °C, 450 °C and 225 °C temperature respectively during transient cooling. These temperatures represent the three different regimes of quench front movement on the hot surface [4]. It is observed that same as local rewetting velocity the average rewetting velocity is the highest for the higher jet diameter and jet Reynolds number (Fig. 13). However, the average rewetting

160

U (m/s)

d (mm )

Re = 10000

1.80 2.51 3.53

4.8 3.5 2.5

140 120 100 80 60 40 20 0

0

2

4

6

8

10

12

14

radial distance, r, mm

(b) 160

local rewetting velocity, u, mm/s

with much faster rate, this leads to lower wetting delay at higher Reynolds number and larger jet diameter. It is also observed in Fig. 11 that the wetting delay period reduces with the rise in jet Reynolds number. The reduction in the wetting delay with the rise in Reynolds number is the highest for 2.5 mm jet diameter as compare to the other jet diameter investigated. This may be due to the highest jet velocity associated with 2.5 mm jet diameter as compare to higher jet diameter, at a certain Reynolds number and the higher jet velocity leads to reduction in the wetting delay [17,18]. Fig. 11 also reveal that for all jet diameters the percentage reduction in wetting delay with the rise in Reynolds number increases for higher spatial locations away from the stagnation point. Fig. 11c shows that at 12 mm location wetting delay reduce by 40% for 2.5 mm jet diameter with the rise in jet Reynolds number from 16,000 to 24,000, which is only 20% for 3.5 mm jet diameter.

d (mm) Re x10-3 U (m/s) 3.5 3.5 2.5 2.5

140 120

16 24 16 24

3.98 5.98 5.60 8.40

100 80 60 40 20 0

0

2

4

6

8

10

12

14

radial distance, r, mm

(c) Fig. 12. Local rewetting velocity at z/d = 4 for (a) Re = 5000, (b) Re = 10,000, (c) Re = 16,000 and 24,000.

velocity shows different trends for the measured spatial location with the change in jet Reynolds number. It is observed that at 5000 Re the average rewetting velocity increases up to 8 mm location, then drops monotonically up to 12 mm location (Fig. 13a). However, for 10,000 Re, the average rewetting velocity after attaining the peak at 8 mm location remains constant with ±5% deviations for the extreme spatial location (Fig. 13b). Whereas, for higher Reynolds number, i.e. for 16,000 and 24,000 Re, the average rewetting velocity monotonically rises from the stagnation point to the 12 mm location (Fig. 13c). It is also observed in Fig. 13c that the

C. Agrawal et al. / Experimental Thermal and Fluid Science 42 (2012) 25–37

average rewetting velocity, u, mm/s

36

d (mm )

Re = 5000

4.8 3.5 2.5

30

higher average rewetting velocity. Further, the rise in Reynolds number increases the local turbulence over the hot surface leading to the enhanced forced convective heat transfer. The consequence of both these effects is the enhancement in the surface cooling rate, thus, resulting in the continuous increase of the average rewetting velocity up-to the extreme spatial location, i.e. 12 mm.

U (m/s) 0.92 1.25 1.76

20

4. Conclusions 10

The following conclusions can be drawn from the present investigations of water jet impingement cooling of the hot horizontal test-surfaces.

0 0

2

4

6

8

10

12

14

radial distance, r, mm

average rewetting velocity, u, mm/s

(a)

ðNuÞo ¼ 0:56ðReÞ0:62 d (mm )

Re = 10000

U (m/s)

0:58

ðNuÞx ¼ 0:62ðReÞ

1.80 2.51 3.53

4.8 3.5 2.5

30

20

10

0 0

2

4

6

8

10

12

14

radial distance, r, mm

average rewetting velocity, u, mm/s

(b) 35 30 25 20 15 10

d (mm) Re x10-3 U (m/s) 3.5 3.5 2.5 2.5

5

3.98 5.98 5.60 8.40

16 24 16 24

0 0

2

4

6

1. For a hot flat surface, under steady state single phase convective cooling, following correlations have been developed.

8

10

12

14

 z 0:08 u0:08 d d  z 0:065  r 0:41 u0:03 d

d

d

These correlations predicts the stagnation and the local Nusselt number within an error band of ±5% and ±20% respectively for the range of parameters investigated, i.e. 5000 6 Re 6 24,000, 4 6 (z/d) 6 16, 2.5 6 d 6 4.8. 2. The rewetting temperature at the stagnation point is the highest and then reduces for the downstream spatial location. At a particular position and Reynolds number, the rewetting temperature is higher for larger jet diameter. However, at 5000 Re, beyond 8 mm and at 10,000 Re for 12 mm location, the rewetting temperature is lowest for 4.8 mm jet diameter. For any measured location, with a certain jet diameter, the rewetting temperature increases with the rise in jet Reynolds number. 3. At a particular location, the wetting delay period is the lowest for higher jet diameter and Reynolds number. The wetting delay for any jet diameter and jet Reynolds number is the lowest at the stagnation point and then increases for the downstream spatial locations. The wetting delay is found to be the highest with 2.5 mm jet diameter and 5000 Re at 12 mm location. 4. With the increase in jet diameter and Reynolds number the local as well as average rewetting velocity increases. For all the jet diameters and flow rates, the local rewetting velocity attains the peak at 4–6 mm location and then reduces for the further downstream locations. In fact the increase in the stagnation region with the higher jet diameter leads to the shift in maximum local rewetting velocity towards the higher spatial location. Whereas, the average rewetting velocity is the highest at 8 mm location for 5000 Re and shifts to 12 mm location for 24,000 Re.

radial distance, r, mm

(c) Fig. 13. Average rewetting velocity at z/d = 4 for (a) Re = 5000, (b) Re = 10,000, (c) Re = 16,000 and 24,000.

rise in the average rewetting velocity is more for 3.5 mm jet diameter at 24,000 Re. The change in average rewetting velocity profile at higher Reynolds number as compare to the local rewetting velocity can be attributed by the conduction heat transfer within the hot surface and the convective heat transfer from the hot surface. With the elapsed of cooling time, the conduction heat transfer from the far downstream region to the coldest stagnation region reduces the surface temperature for the extreme spatial location. This results in faster quench front movement over the hot surface and hence,

Acknowledgements First author is grateful to the AICTE, New Delhi, QIP Centre, IIT Roorkee and CTAE, Udaipur for their financial support and permission for the research work. References [1] N. Karwa, T.G. Roisman, P. Stephan, C. Tropea, A hydrodynamic model for subcooled liquid jet impingement at the Leidenfrost condition, International Journal of Thermal Sciences 50 (2011) 993–1000. [2] L. Bogdanic, H. Auracher, F. Ziegler, Two-phase structure above hot surfaces in jet impingement boiling, Heat Mass Transfer 45 (2009) 1019–1028. [3] M.A. Islam, M. Monde, P.L. Woodfield, Y. Mitsutake, Jet impingement quenching phenomena for hot surfaces well above the limiting temperature for solid–liquid contact, International Journal of Heat and Mass Transfer 51 (2008) 1226–1237.

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