International Journal of Refrigeration 27 (2004) 492–502 www.elsevier.com/locate/ijrefrig
Influence of thermophysical properties on pool boiling heat transfer of refrigerantsq Dieter Gorenflo*,1, Untung Chandra, Stephan Kotthoff, Andrea Luke2 Thermodynamik und Energietechnik, ThEt, Universitaet Paderborn, Waerme- und Kaeltetechnik, Warburger Str. 100, D-33098 Paderborn, Germany Received 24 September 2003; received in revised form 6 March 2004; accepted 6 March 2004
Abstract The correct prediction of the heat transfer performance of the boiling liquid within the evaporator of a refrigeration unit is one of the essential features for the successful operation of the whole unit. A theoretically consistent calculation method for the heat transfer coefficient a in nucleate boiling, which should be based on the physical phenomena connected with vapour bubbles growing, departing and sliding on the wall and with the interactions of bubbles and of neighbouring nucleation sites within the microstructure of the heating surface, does not yet exist, despite the increasing number of papers on the subject in the recent past. Instead, the predictive methods for a available at present are empirical or semiempirical, especially for heat transfer conditions relevant in practice. Many of these correlations have been established in the form of power laws in which the relative influences of the main groups of variables on a are treated by separate factors. One of these may stand for the influence of the thermophysical properties of the boiling liquid or these properties will be included in several of the factors. New experimental results are presented for pool boiling heat transfer from a single horizontal copper tube (8 mm OD) to HFC-refrigerants (R32, 125, 134a, 143a, 152a, 227ea) and hydrocarbons (propane, i-butane). The results are compared to experimental data from the literature, and methods are discussed, how to incorporate the data in semiempirical correlations to describe the influence of the thermophysical properties of the fluids on the heat transfer performance. q 2004 Elsevier Ltd and IIR. All rights reserved. Keywords: Refrigerating system; Evaporator; Pool boiling; Thermodynamic property; Physical property; Heat transfer; R32; R125; R134a; R143a; R152a; R227ea
Influence des proprie´te´s thermophysique sur le transfert de chaleur lors de l’ebullition libre de frigorige`nes Mots-cle´s: Syste`me frigorifique; Evaporateur; Ebullition libre; Proprie´te´ thermodynamique; Proprie´te´ physique; Transfert de chaleur; R32; R125; R134a; R143a; R152a; R227ea
1. Introduction q
Extended version of a paper presented at Eigth UK National Heat Transfer Conference, Oxford; September 2003 * Corresponding author. Tel.: þ49-5251-60-2393; fax: þ 495251-60-3522. E-mail address:
[email protected] (D. Gorenflo). 1 President of IIR commission B1. 2 Secretary of IIR Commission B1. 0140-7007/$35.00 q 2004 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2004.03.004
One of the important features for the successful operation of refrigeration units is the performance of the boiling liquid within the evaporator. The optimum design of the evaporator depends on the correct prediction of the nucleate boiling and the convective contributions to heat
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Nomenclature a0 c0p d0 dp g Gr Dhv lm M Nu OD pc ps pp pp0 pL 9 Pa;p;pm = Pq;t;Z ; Ra Ra0 Rp;old P5p Pr q_ q_ 0 rA rc RB Ts TW Tp DT DTA x; z
thermal diffusivity of the saturated liquid (m2/s) isobaric heat capacity of the saturated liquid (kJ/(kg K)) bubble departure diameter (m) particle size of corundum grain (mm) gravitational acceleration (m/s2) Grashof number heat of vaporization (kJ/kg) gauge length (mm) molar mass (g/mol) Nusselt number outer tube diameter (mm) critical pressure (bar) saturation pressure (bar) normalized pressure (ps =pc Þ normalizing pressure at pp ¼ 0:1 sandblasting operation pressure (bar) standardized roughness parameters according to DIN EN ISO 4287 (mm) normalizing roughness of 0.40 mm (mm) Gla¨ttungstiefe acc. to DIN 4262 (1960) (mm) roughness parameter describing a single cavity (mm) Prandtl number heat flux density (W/m2) normalizing heat flux density of 20000 W/m2 (W/m2) radius of bubble in active surface cavity at transition to free convection (mm) minimum radius of a stable bubble nucleus (mm) radius of the ball that produces envelope curves or areas (mm) saturation temperature (K, 8C) surface temperature of the heated wall (K, 8C) normalized temperature ðTs =Tc Þ superheat of the tube surface (K) superheat of the tube surface at transition to free convection (K) coordinates of the topographies (mm)
Greek a a0 ; a0:1 b0 g h0 l0 lc n0 r0 ; r00 s
heat transfer coefficient (W/(m2 K)) normalizing heat transfer coefficient at pp0 ; q0 ; Ra0 (W/(m2 K)) volume expansivity of the saturated liquid (1/K) contact angle (8) dynamic viscosity of the saturated liquid (Pa s) thermal conductivity of the saturated liquid (W/(m K)) cut-off (mm) kinematic viscosity of the saturated liquid (m2/s) density of the saturated liquid or vapour (kg/m3) surface tension (N/m)
transfer. A theoretically consistent calculation method for the heat transfer coefficient a in nucleate boiling, which should be based on the physical phenomena connected with vapour bubbles growing, departing and sliding on the wall and with the interactions of bubbles and of neighbouring nucleation sites within the microstructure of the heating
surface, does not yet exist, despite the increasing number of papers on the subject in the recent past (cf. e.g., the literature review in [1]). Instead, the predictive methods for a available at present are empirical or semiempirical, especially for heat transfer conditions relevant in practice. Many of these correlations have been established in the form
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Table 1 Standardized roughness parameters (according to DIN EN ISO 428) and information about surface treatment and measurement for the new test tube with twice sandblasted surface
Mean Max. Min. s
Pa (mm)
Pq (mm)
Pp (mm)
Pp;m (mm)
Pt (mm)
PZ (mm)
0.563 0.879 0.383 0.098
0.701 1.123 0.488 0.120
2.138 4.612 1.148 0.517
1.506 2.782 1.024 0.263
3.749 6.539 2.364 0.713
2.706 4.304 1.931 0.462
Heating element: copper tube, OD ¼ 8 mm. Surface treatment: sandblasted with fine Corundum grain (F320, dp ¼ 20 – 30 mm) at pL ¼ 3 bar; then sandblasted with medium Corundum grain (C220, dp ¼ 50 – 80 mm) at pL ¼ 1:5 bar: Surface measurement: stylus: ultrasound stylus nanoswing, stylus velocity: vT ¼ 0:01 mm=s; gauge length: lm ¼ 0:5 mm; cutt-off: lc ¼ 1:
of power laws in which the relative influences of the main groups of variables on a are treated by separate factors. One of these may stand for the influence of the thermophysical properties of the boiling liquid or these properties will be included in several of the factors. The paper presents new experimental results of heat transfer from a single horizontal copper tube (8 mm OD) to HFC-refrigerants (R32(CH 2F2 ), R125(CHF 2·CF3), R134a(CH2F·CF3), R143a(CH3·CF3), R152a(CH3·CHF2), R227ea(CF3·CHF·CF3)) and hydrocarbons (propane, ibutane). The results are compared to experimental data from the literature, and methods are discussed, in which way the data could be incorporated in semiempirical correlations to describe the influence of the thermophysical properties of the fluids on the heat transfer performance. 2. New experimental results The measurements have been performed in a version of the so called Standard Apparatus for pool boiling heat transfer measurements developed earlier (cf. e.g., [2,3]).
Fig. 1. Top: example for the roughness profile of the new twice sandblasted surface. Bottom: distributions of the cavity sizes within the roughness profiles of three copper tubes with different surface treatment. Example: size parameter P5p [6] calculated from new threedimensional analysis of surface topographies [4].
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Fig. 2. Double logarithmic plot of the heat transfer coefficient a as function of the heat flux q for propane boiling at constant pressure on single horizontal copper tubes with 8 mm OD with different surface treatment DTA : superheat of the tube surface at transition from nucleate boiling to single phase free convection (circle symbols).
The surface of the copper tube (8 mm OD) was twice sandblasted: by fine corundum grain, type F320 in a first step, and by the coarser ((medium) type C220 in a second, resulting in the surface structure characterized by the standardized roughness parameters in Table 1 (Pa ; Pq ; etc. of the new standard correspond to Ra ; Rq ; etc. in the former), and by the example for the profile in Fig. 1, top. This procedure has been chosen in order to produce a broader distribution of the cavity sizes within the roughness profile than on a surface, which has been sandblasted only with the fine grain F320, see the comparison of the two pertaining distributions in Fig. 1 bottom, using the roughness parameter P5p as an example (which has been calculated applying a new three-dimensional analysis of roughness topographies [4] giving a more realistic representation of the microstructure within the roughness profile than the former two-dimensional, particularly in the case of the emeried surface). Thus the distributions existing on surfaces used in practice (as e.g., turned or drawn) will be simulated in a more appropriate manner. On the other hand, the heat transfer surfaces within evaporators assembled in practice will contain less reentrant cavities than emeried surfaces with many neighbouring scrapes, see the very broad distribution in Fig. 1, bottom. Furthermore, it should be easier to combine the roughness parameters of sandblasted surfaces with bubble formation and heat transfer than for emeried ones, because their microstructures are more homogenous in all directions. In the following discussion, the heat transfer coefficient a is defined by the ratio of the heat flux q and the difference DT between the surface temperature TW of the heated wall
and the saturation temperature Ts ðps Þ of the boiling liquid,
a ¼ q=DT
ð1Þ
The overall experimental limits of error for a extend from ^3% at low pressures and high heat fluxes up to ^ 20% at high pressures and low heat fluxes (cf. e.g., [5]). The purity of all test fluids investigated has been controlled and was better than 99.5%, and in the case of the refrigerants it was better than defined in the ISO standards. In Fig. 2, results of three surfaces prepared by the same procedures as those of Fig. 1, bottom, are given as examples in the commonly used double logarithmic plots of the heat transfer coefficient a as function of the heat flux q for propane boiling at ps ¼ 4:247 bar: This pressure corresponds to 10% of the critical pressure pc of propane and lies within a range where the heat transfer coefficient a at nucleate boiling on horizontal tubes is known to be particularly sensitive to—even slight—differences in bubble formation [7]. In correspondence with the data in the literature, a increases markedly with q at nucleate boiling for all of the three surfaces, but there are slight differences in the absolute values of a at constant heat flux and in the slopes n of the straight interpolation lines (according to a , qn ), which can be related to the differences in the microstructures of the (dummy) surfaces shown in Fig. 1. At transition from nucleate boiling to single phase free convection which corresponds to the intersections of the three lines with the dash-dotted line for laminar flow according to [8], Nu ¼ 0:6ðGrPrÞ0:25 ;
ð2Þ
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Fig. 3. Experimental a; q-dependencies for two of the eight substances tested with the new tube as examples, Parameter: saturation pressure ps related to the critical pressures pc of the fluids. Dotted: parameter lines for constant values of superheat DT:
both of the effects (slightly different values of a or n; respectively) result in a marked decrease of the superheat DTA ðDTA ¼ 3:65=2:35=1:47 KÞ of the tube surface with increasing size of the biggest cavities existing (in a sufficient number) on the three surfaces (P5pmax ¼ 3:0=4:3=5:7 mm; cf. Fig. 1). On the other hand, the differences in the smallest cavities are significantly less ðP5pmin ¼ 0:25=1:0=1:4 mmÞ as is the case for the mean values P5pm : This is reflected in the
smaller differences between the heat transfer coefficients at high heat fluxes, cf. e.g., the a-values at q ¼ 100 kW=m2 in Fig. 2. (In the comparison of Figs. 1 and 2, it has to be taken into account that the data of the emeried and the fine þ medium sandblasted surfaces in Fig. 1 were not taken from the test tubes, but from two dummies, because the emeried tube of the earlier measurements does not exist any longer, and the new surface had to be analyzed on a dummy,
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Fig. 5. Comparison of the new experimental data with results of three emeried copper tubes taken from papers published in 1973 [9]; 1991 [5]; 2002 [10].
in terms of the slopes n of interpolation lines as in Fig. 3 for constant normalized pressure pp ; which correspond to the proportionality a , qn ; and the second as the heat transfer coefficients a at the intermediate heat flux q0 ¼ 20 kW=m2 ; normalized by their values a0 at constant normalized saturation pressure pp0 ¼ 0:1: In both cases, the experimental results are compared with the correlations given in the VDI Heat Atlas [8], see calculation method #3 in Table 2, nðpp Þ ¼ 0:9 2 0:3pp0:3 and
a=a0:1 ¼ Fðpp Þ ¼ 1:2pp0:27 þ 2:5 þ
Fig. 4. Pressure dependence of the heat transfer coefficient a at q0 ¼ 20 kW=m2 (bottom: absolute; middle: relative) for the eight fluids boiling on the tube with fine þ medium sandblasted surface. Top: pressure dependence of the exponent n in Eq. (3).
because the heat transfer measurements with the new tube were running simultaneously.) In Fig. 3, the experimental a; q-dependencies for two of the eight substances tested with the new tube so far are given as examples; parameter is the saturation pressure ps related to the critical pressures pc of the fluids. The strong relative increases of a with q or pp ¼ ps =pc ; visible in Fig. 3, are explicitly demonstrated in Fig. 4 (top and middle), the first
ð3Þ 1 pp 1 2 pp
ð4Þ
The new a; q- and a; pp -dependencies are stronger than those following from the correlations which had been developed from all reliable experimental data available 20 years ago. Similar deviations occur with other (in general more recent) experimental data, see e.g., the small extract of the whole database in Fig. 5. The absolute values of the heat transfer coefficients a0 at the normalizing conditions (q0 ; pp0 ) span from 4.32 kW/(m2 K) for i-butane to 6.55 kW/(m2 K) for R32, see the diagram at the bottom of Fig. 4. The pertaining relative difference, however, remains almost constant throughout the pp -range of approximately one decade,
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Table 2 Selection of more recent calculation methods of a; particularly apt to discuss the influence of the variation of thermophysical properties with pp in the upper pp -range # Reference
Author year
Equation
1 [10]
Jung et al. 2002
p 0 20:25 q_ d C1 ðp Þ p0:1 n ad Nu ¼ 10 0 0 p ð1 2 T p Þ21:4 0 ¼ 00 l Ts a l with C1 ðpp Þ ¼ 0:855ðr00 =r0 Þ0:309 pp20:437
2 [14]
Leiner 1993
d0 : see Stephan, Abdelsalam 1978 p p a a T00 L00 2=15 q_ 00 nðp Þ2n0 q_ nðp Þ Ra 2=15 p ¼ n0 0 12n Fðp Þ a00 q_ 00 q_ 0 L00 q_ 0 q_ 00 0 Ra0 a0 T00 L00 2=15 with n0 12n0 ¼ A ¼ 0:4368C 0:2113 K 20:0521 Zc20:9166 Ra0 q_ 0 q_ 00 C ¼ cp;L;pp ¼0:1 =R ¼ cp;L;pp ¼0:1 Mmol =Rmol K ¼ 5:37ð1 þ vÞ with v ¼ 2log10 ðpT pp ¼0:7 Þ 2 1 Zc ¼ pc =ðrc RTc Þ ¼ pc Vc;mol =ðRmol Tc Þ with T00 ¼ Tc ; q00 ¼ pc ðRTc Þ1=2 ; L00 ¼ ðkTc =pc Þ1=3 ; a00 ¼ pc ðR=Tc Þ1=2 ; n0 ¼ 0:75
3 [8]
4 [15]
VDI Heat Atlas Gorenflo 1984
Cooper 1984
a0 ; q0 ; Fðpp Þ; nðpp Þ : see Gorenflo, 1984 nðpp Þ a q_ Ra 2=15 ¼ Fðpp Þ a0 q_ 0 Ra0 with a0 ¼ a for pp0 ¼ 0:1; q0 ¼ 20 kW=m2 ; Ra0 ¼ 0:4 mm; and material: copper 1 pp nðpp Þ ¼ 0:9 2 0:3pp0:3 ; Fðpp Þ ¼ 1:2pp0:27 þ 2:5 þ 1 2 pp 0:67 pð0:1220:2lgRp;old Þ p 20:55 20:5 a ¼ Cq p ð2lgp Þ M with C ¼ 95 (copper) or C ¼ 55 (stainless steel) Rp;old ¼ Ra =0:4 in mm, q in W/m2
5 [16]
Nishikawa, Fujita et al. 1982
a ¼ a~GðRp;old ; pp ÞFðpp Þq4=5 ; q; a; Rp;old ¼ Ra =0:4 in W/m2, W/(m2 K), mm, respectively 31:4p0:2 p c ; GðRp;old ; pp Þ ¼ ð8Rp;old Þð12p Þ=5 ; Fðpp Þ ¼ pp0:23 =ð1 2 0:99pp Þ0:9 M 1=10 Tc9=10 q_ d 0:674 r00 0:297 Dhv d02 0:371 r0 2 r00 21:73 a0 2r0 0:35 Nu ¼ 0:23 0 0 0 0 0 l Ts r a2 r sd0 0:5 2s with d0 ¼ 0:0146g ; contact angle g ¼ 358 gðr0 2 r00 Þ 0 0 0 0 2 12n 00 4n21 gb cp ðr l Þ r Dhv 3 n 3 a ¼ CrAð4n21Þ=3 q ; with C ¼ 0:1512n ; n ¼ 0:7; 0 h 2sTs with a~ ¼
6 [13]
Stephan, Abdelsalam 1978
7 [9]
Bier, Gorenflo, Wickenha¨user 1973
rA = radius of bubble in active surface cavity at transition to free convection. (For dimensions see [9] or nomenclature at the beginning)
investigated with all of the eight substances ðpp ¼ 0:065 – 0:70Þ:
3. Comparison with other experimental data In Fig. 5, results for three other copper tubes (with emeried surfaces) from 1973 [9], 1991 [5] and 2002 [10] have been added extending the number of hydrocarbons and halocarbon refrigerants included in the comparison. Furthermore, the data of 1973 enlarge the pressure range up to 98% of the critical (not all shown in the figure), where some thermophysical properties, e.g., surface tension s; vary drastically.
On the other hand, the refrigerants measured only at one saturation temperature Ts ¼ 7 8C by Jung et al. 2002 [10] could be included in the comparison, because the pertaining normalized pressures vary between 4.5 (R142b) and 17.5 (R32) percent of the critical; their n-values, however, have not been included in the comparison, because they fit in the common, well established trend of Fig. 5, top, only in part. (The roughness parameter Pa ¼ 0:35 mm of the Korean tube has been determined from a dummy tube in Paderborn). As can be seen from Fig. 5, the relative variation of a with q and pp is similar to the new data of Fig. 4 for the twice sandblasted tube (small symbols in Fig. 5), with a slight tendency of a weaker increase of a with q and pp ; particularly in the range of higher normalized pressures pp
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on the heat transfer coefficient a can be separated in two parts, † one part resulting from the variation of the properties with saturation pressure along the vapour pressure curve (VPC), in fact being caused by the dependence of the properties on the saturation temperature Ts ; and † another part resulting from the variation of the properties for different fluids at constant normalized pressure pp ; e.g., at pp0 ¼ 0:10: The latter part is significantly smaller than the first, at least for the two hydrocarbons and the six fluorocarbons shown in this diagram. The fact that the first part results in a rather uniform variation of a with pressure for a much greater variety of fluids (than included in Fig. 5) by normalizing ps to the critical pressure pc at the vapour/liquid critical state of the fluid, cf. e.g., [8], has induced many authors to apply the principle of corresponding states to pool boiling heat transfer, starting with the group of Borishanskij and coworkers (see e.g., [11]). In parallel, others tried to reduce the influence of thermophysical properties and other parameters on a to power laws of a few dimensionless numbers (see e.g., Stephan [12], or Stephan, Abdelsalam [13]). In Table 2, a few calculation methods for a have been put together in order to demonstrate various approaches to quantify the dependence of a on the properties: One group—see #2 – 5—separate in two parts as already discussed above, with † a pressure dependent part 1 which is a function of the normalized pressure pp ¼ ps =pc (and contains no other properties depending on pressure), and † a part 2 which is independent of pressure and models the dependence of a on the properties of different fluids at constant normalized pressure.
Fig. 6. Relative pressure dependence of a : comparison of the experimental data of Fig. 5 with correlations of Table 2: top: #2–5; bottom: #1 and 7. Scatter in #7 and in A#7 (solid lines in the lower diagram) by variation of the properties of eight fluids comprised in the evaluation (#1 is shown only for propane).
(0.5– 0.8), where also the thermophysical properties important for bubble formation vary significantly.
4. Influence of thermophysical properties The results for the eight fluids in Fig. 4, bottom, demonstrate that the influence of thermophysical properties
A second group—represented by #6 and 7—do not use any separate functions of pressure, and in correlation #1, both approaches have been mixed together with the important part of the pressure term being expressed by the normalized temperature T p ¼ Ts =Tc : In the following, the discussion will be concentrated mainly on the pressure dependent term and will only be given for part of the methods #1 – 7. The comparison of the experimental results of Fig. 5 (symbols) with three (four) of the calculation methods in the upper diagram of Fig. 6 shows that the relative increase of a due to the variation of the properties along the vapour pressure curve is predicted too weak by all methods included in the diagram, with the Heat Atlas method being closest to the experiments. On the other hand, the pressure dependence of a predicted by method #1 is too strong (see the dashed curve #1 in the lower diagram of Fig. 6), and it is dominated by the term B#1 as function of T p ; while the contribution of the other
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Fig. 7. Relative dependence of a on the fluid properties according to calculation method #7: influence of the exponent n of Eq. (3).
(pressure dependent) properties, summarized in the factor A#1 is negligible over wide ranges of pp : Method #7 represents the experimental a; pp -dependence comparatively well (see curve #7), despite various simplifying assumptions that have been applied in its development
[9]. It uses the well-known Thomson equation to calculate the excess pressure Dp necessary for a stable bubble with radius r to exist within a cavity of the roughness profile of a heating surface. Assuming thermodynamic equilibrium between vapour bubble and superheated liquid at temperature Ts þ DT; Dp can be replaced by DT calculated from the vapour pressure curve (VPC) with the additional assumption that the last nucleation centers remaining activated at transition from nucleate boiling to free convection will always be the same and therefore, their radius rA belonging to DTA —cf. e.g., the circles in Fig. 2—will be independent of pressure, and the DTA —values can be calculated for all pressures, using only one experimental value. Starting from the boiling conditions with DTA ; the heat transfer coefficients a can be calculated for various pressures at q ¼ const using the slopes n of the a; q-dependencies at constant pressure (see e.g., the three straight lines in Fig. 2). Using some further assumptions (see the detailed explanation in [9]), correlation #7 in Table 2 is received which contains two terms with thermophysical properties of the fluid: the first resulting from single phase free convection (with turbulent flow) and therefore being almost independent of pressure, see A#7 in Fig. 6, bottom, and the second resulting mainly from the equations of Thomson and Clausius – Clapeyron for the nucleate boiling part (see B#7 ) which contains the steep increase of a with pp : The very narrow scatter of the curves for correlation #7 evaluated for the eight fluids investigated with the new tube so far, indicates a uniform dependency on the normalized pressure pp : The same holds for each of the properties, too
Fig. 8. Representation of influence of the fluid properties on the heat transfer coefficient a0 at constant normalized pressure Pp0¼ 0:10 for the eight fluids of Fig. 4. Property-parameter with (bottom) or without simplifications (top).
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(see Bier, Gorenflo [17], and it is also reflected in the uniform relative increase of a with pp in the experiments of Fig. 4 (and 5). The evolution of the calculation method #7 demonstrates that the characteristics of the microstructure on the heating surface, e.g., distributions of sizes and local distances of cavities from each other, also influence the dependence of a on the properties of the fluid via the exponent n: In Fig. 7, the extent of this influence is shown using a somewhat higher (constant) exponent n ¼ 0:8 which is closer to the experimental values of the new measurements (see Fig. 7, top) than the value used in the original version of correlation #7 ðn ¼ 0:7Þ: As can be seen, the representation of the experimental data is not as good as before, although n ¼ 0:8 is more realistic. Obviously, the good agreement of the original correlation #7 with the measurements, results—at least in part—from various simplifications mutually compensating their effects on the relative pressure dependence of a: Finally, the second—minor—influence of thermophysical properties on the heat transfer coefficient a for different fluids at constant normalized pressure pp0 ¼ 0:10 is analyzed in Fig. 8 for correlation #7 as example. Here, the radius rA of bubbles in active surface cavities on the tube at transition to free convection is treated in the same way as discussed above, resulting in the parameter 2sTs =ðr00 Dhv Þ after applying all simplifying assumptions as before (cf. [18]), see the lower diagram. For comparison, the main part s=ð›p=›TÞVPC within this parameter is also used for the representation (as in [5]) without any simplifications (upper diagram). Both diagrams result in similar, comparatively uniform representations of the experimental heat transfer coefficients a0 at pp0 ¼ 0:1; q0 ¼ 20 kW=m2 for the eight fluids by common interpolation curves. A more thorough examination reveals that some deviations of the measured a0 – values from the curve have increased in the lower diagram containing the simplifications. At the present stage, it seems to be too early to deepen this analysis, because the fluids investigated with the new tube so far do not differ too much, except in the molar mass M: As can easily be seen, however, from the neighbouring a0 – values of propane and R134a or i-butane and R227, respectively, with their different molar masses, a simple inclusion of M in the correlations as in the method #4 would increase the scatter (cf. also [18]).
5. Conclusions (1)
(2)
The influence of thermophysical properties of the fluids on pool boiling heat transfer can be investigated very effectively by increasing the saturation pressure up to high normalized pressures pp ¼ ps =pc ; where the properties vary markedly along the vapour pressure curve. The relative influence of the properties on the heat transfer coefficient a is similar for different fluids
(3)
(4)
501
resulting in a comparatively uniform relative pressure dependence of a; if the principle of corresponding states is applied in a simple way, as is also the case for the various properties themselves [17]. The dependence of a on the thermophysical properties is also influenced by the microstructure of the heating surface, to be expressed e.g., via the exponent n of the proportionality a , qn : The present investigation will be continued with other fluids and the same heating surface, and the correlating methods will be improved in order to reduce the extent of simplifying assumptions.
Acknowledgements The authors thank Deutsche Forschungsgemeinschaft (DFG), Bonn, for financial support and Solvay Fluor and Derivate GmbH, Hannover, for supplying the refrigerants.
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