dataesr/scientific-paragraphs-categorization huggingface dataset:
However, although two-phase flows have been widely studied in the last decades for a comprehensive range of operating conditions in terms of pipe geometry and fluids, most of the works available are related only to vertical or horizontal tube arrangements, whereas flow boiling, condensation and gas-liquid heat transfer data for inclined surfaces are relatively scarce. As a consequence, while there are numerous correlations which may be employed to predict the two-phase heat transfer coefficient in horizontal and vertical tube orientations, very limited prediction tools take into account the effect of the inclination angle and the available heat transfer coefficients prediction methods were mostly conceived by considering few databases with limited amount of points. Moreover, to the authors' knowledge, there are currently no practical tools able to determine whether the effect of gravity on two-phase heat transfer is significant or negligible for specific applications.
The first objective of the present paper is to provide a critical literature review of the influence of the tube inclination angle on the two-phase heat transfer coefficient, by collecting data from boiling, condensation and heated gas-liquid flows. In the second part of the paper, we provide a useful tool able to state whether the heat transfer coefficient is affected by the tube orientation or, instead, whether the typical prediction methods for horizontal flows may be used. The nondimensional parameter Inclination effect Ih is therefore defined, representing the maximum relative variation of the local heat transfer coefficient with the channel inclination. This parameter is finally correlated to physically-driven nondimensional numbers through a statistic tool, providing useful information for the correct design of condensing and evaporating units conceived to work at a specific inclination angle.
Presentation of the database The present study relies on the analysis of experimental results available in the literature that deal with twophase flows in inclined channels. A thorough literature review has been carried out to collect most of the available data for the heat transfer coefficient at multiple tube inclinations, for the three types of two-phase flows of interests (flow boiling, flow condensation and heated air-water flows). Only the experimental works that deal with multiple pipe inclination angles (including studies of both horizontal and vertical configurations only) are considered in this review, to perform a fair comparison of the heat transfer coefficients at different tube orientations by employing the same test facility and exactly the same operating conditions. A total amount of 5408 data points was collected.
Flow boiling database The research has highlighted 15 studies of flow boiling at multiple channel orientations and different operating conditions in terms of the tube geometry, fluid, saturation temperature, heat and mass flux, vapor quality and inclination angles investigated, from which 2371 heat transfer coefficient data have been collected. In some cases, especially for multi-minichannel geometries, the authors did not directly provide the heat transfer coefficient values, which have been included in this database by calculation from the boiling curves and the available information. Table  1  summarizes the mentioned studies in chronological order, along with the values and ranges of the main operating conditions. Specifically, the inclination angle & has been defined with respect to the horizontal disposition, ranging from -90° (vertical downward) to +90° (vertical upward).
However, only a few studies focused on the entire possible range of &, and even in these cases, the number of inclination angles employed is very limited. A significant part of the database is instead related to only two or three configurations (exploring vertical upward, vertical downward and horizontal dispositions, at most). Regarding the tube geometry, only six works employ regular surfaces (smooth and circular single channels), whereas in other papers, enhanced heat transfer tubes (corrugated, grooved or even internally finned) are used. The remaining works are related to enhanced cooling systems with particular attention to the CHF phenomenon in rectangular multi-minichannel heat sinks (with hydraulic diameters below 1. 0 mm) working in different orientations. Additionally, according to the transition criteria of Kandlikar and Grande  [14] , the tube diameters cover both the miniscale (1.
Convective condensation database For condensing flow, a total amount of 1878 heat transfer coefficient data points coming from 11 independent studies has been collected. Table  2  summarizes the authors and the related operating conditions. Unlike the flow boiling database, there are no multi-minichannel heat sink geometries, and most of the studies are related to smooth circular channels. Among the exceptions, the work of Akhavan et al. [15]  is performed with an internally finned tube of 8. 92 mm internal diameter, whereas Koheini et al  [16]  used a corrugated channel with a similar diameter of 8. 32 mm. Finally, Del Col et al. [17]  presented a comprehensive study of the condensation of R134a and R32 in a square cross-section minichannel having an equivalent internal diameter of 1. 18 mm, thus representing the narrowest tube of the condensation database for multiple orientations.
Except for Wang et al. [18] , in which the working fluid is water condensing at 105 °C in smooth circular tubes having 4 different diameters, all the experiments have been performed using refrigerants (especially R134a) condensing from 29 to 55. 4 °C. Similar to the flow boiling database, the investigated inclination angles range from the vertical downward (-90°) to the vertical upward (+90°) disposition. In some papers (Akhavan et al. [15] , Khoeini et al. [16] , Mohseni et al. [19]  and Del Col et al. [17] ), the two-phase heat transfer coefficient is obtained using at least 3 upward and downward inclination angles. More detailed analyses were performed by Lips et al. [20] , Meyer et al. [21] , Olivier et al. [22]  and Ewim et al. [23] , which shared the same test facility with a circular smooth tube of 8.
38 mm ID and included up to 20 values of & for each operating condition. Wang et al. [18]  and Mozafari et al. [24]  limited their analysis to the upward orientation. The first used 4 inclination angles from 0 to 45°, whereas the latter studied the condensation of isobutane (R600a) in a helicoidally shaped condenser at 0, 30, 60 and 90°, with a saturation temperature of 43 °C. Finally, Xing et al. [25]  evaluated the heat transfer performance of vertical upward, vertical downward and horizontal flows for the refrigerant R245fa at 55. 4 °C in a macrochannel of 14. 81 mm ID, which is also the largest diameter in the present condensation database. The investigated mass fluxes have similar values to those collected for the flow boiling database, ranging from 11. 4 to 705. 4 kg/m 2 s. The heat flux ranges instead from 6.
Gas-liquid flow database The results of the literature review on heat transfer for nonboiling heated gas-liquid flow in multiple pipe orientations are quite scarce compared to those for condensation and flow boiling. In the present study, 1159 heat transfer coefficient data points have been collected from 6 different sources, as summarized in Table  3. All the works are related to heated air-water flows at atmospheric or nearly-atmospheric pressure at inlet temperatures close to ambient  (20-25 °C). Similar to the abovementioned condensation works, for all the airwater data the applied heat flux is not given in the original reference and its value cannot be extrapolated from the information at disposal. Due to the differences in the fields of applications, all the tubes are smooth, single and circular, having diameters considerably higher than those shown in the previous boiling and condensation reviews, so that no heat transfer coefficient data fall into the micro or mini-scale.
The works of Bhagwat and Ghajar  [26]  [27] and Hossainy et al. [28]  share the same test facility, with an internal diameter of 12. 5 mm, which is the smallest tube in the heated air-water database. In the experiments by Ghajar and Tang  [29] , the pipe diameter is 27. 9 mm, and finally it goes up to 49. 2 mm for the papers by Hetsroni et al  [30] [31]. The range of orientations investigated is very limited compared to those in the previous databases. Only the work of Hetsroni et al. [31]  provides all the possible orientations from the vertical downward (-90°) to the vertical upward (+90°) using small steps of 15°. A comprehensive analysis of the effect of inclination for upward and downward flows is also performed by Bhagwat and Ghajar  [26]  [27], but it is split into two different studies that do not share exactly the same operating conditions.
Range of experimental conditions in terms of nondimensional parameters The three databases involve very different types of fluids and channel diameters. To compare the various experimental conditions, nondimensional numbers can be used. For any kind of two-phase flow, the value of the heat transfer coefficient is indeed a direct consequence of the flow pattern occurring in the tube, which can in turn be influenced by the gravity effects and, therefore, by the orientation of the channel  [20] [32]. Note that in the case of a boiling flow, the effects of the nucleation phenomenon and capillary forces might also play important roles and should therefore be taken into account  [33]. As reported by different researchers  [34] [35] [36]  [37]  [38] , the effect of gravity is progressively reduced when the inertia and/or the surface tension become significant.
Later, the same authors  [38]  found that the two-phase friction factor in annular flow was not dependent on gravity approximately when FrV>100. Finally, Layssac et al. [34]  and Lillo et al. [37]  showed inertia-driven fluid characteristics and heat transfer for lower vapor Froude numbers (around FrV>4). As a first analysis, Figure  1  provides the overall variations of the Bd and FrV dimensionless numbers for the collected heat transfer coefficient data points for the three types of heat transfer processes. The differences between the Froude and Bond number ranges for the three different configurations can be explained by the various applications of these three types of flow. For instance, the greater diameters used in experiments for condensation heat transfer lead to higher Bond numbers and a smaller range of Froude numbers than do those used for boiling heat transfer.
Effect of inclination on flow boiling To highlight the inclination effect during flow boiling, examples of experimental results are extracted from the corresponding database and presented in Figure  2. The evolution of the nondimensional heat transfer coefficient (which is the ratio of the heat transfer coefficient to the minimum value found by the authors for those operating conditions) is presented as a function of the inclination angle for vapor Froude and Bond numbers. The example extracted from the work of Layssac et al. [33]  (Figure  2a ) corresponds to a small Bond number that is, however, high enough to not consider the channel as being microscale. There is neither a clear effect of the FrV nor a particular recurrent optimum angle of inclination that maximizes the heat transfer performance.
Similar trends with a clear decreasing inclination effect relative to the vapor Froude number have also been found by other authors  [41]  [43], even if the threshold FrV value for inclination dependency is different according to each paper and no general outcomes can be extrapolated. A global analysis of the database is performed by determining the inclination angles that lead to the minimum and maximum heat transfer. In the present study, & ' ( and & ') are thus defined as the tube orientations at which the heat transfer coefficient respectively reaches the maximum and minimum values among the inclination angles investigated by each author. Figure  3  presents the & ' ( and & ') combinations for the flow boiling experiments. The size of each disk is related to the frequency of the corresponding combination, whereas the color bar reflects the effect of the inclination in terms of maximum-over-minimum heat transfer coefficient ratio over the range of investigated orientations.
Effect of inclination on convective condensation The inclination effect on convective condensation is different from that on convective boiling. Figure  5  shows examples of the variation of the heat transfer coefficient (referring to the minimum value obtained) with the inclination angle for two different Bond numbers and for various Froude numbers. Although the experiments had a narrow channel (Bd=2. 7), the data from Del Col et al. [17]  (Figure  5a ) presents a nonnegligible effect of gravity, with a heat transfer coefficient variation of up to 80% upon changing the tube orientation. The increase of the Froude number lowers this effect up to a threshold of approximately FrV = 2, in which the heat transfer coefficient differences are included within a 20% range. In most experiments, the inclination angle that maximizes the heat transfer coefficient is 60° (even if the trends forecast a possible further increase for the vertical upward configuration, which has not been investigated), whereas the minimum heat transfer coefficient is found for &=-45°.
Different trends are found by Mohseni et al. [19]  (see Figure  5b ), in which the tube diameter is larger (Bd=115) and the effect of gravity is significant up to a vapor Froude threshold value of approximately 0. 5. The inclination angle of 30° gives the maximum heat transfer performance, which is penalized for both vertical upward and downward configurations. Other authors in the present database  [18]  [24] [23]  [22] , though they found a strong variation of the heat transfer coefficient with the channel inclination, do not show a vapor Froude-dependent behavior. (between -20° and 30°), whereas the values of & ' ( are distributed throughout the whole range of orientations, with higher frequencies of the vertical downward disposition. The most significant & ' ( /& ') combination is -90°/0°, while other recurring combinations at which + ') /+ ' ( is higher than 2.
0 also include -30°/30° and -90°/-20°. One can note that the range of the inclination effect is higher for convective condensation (+ ') /+ ' ( up to 3. 2) than for convective boiling (+ ') /+ ' ( up to 2. 0), which means that this type of flow is more sensitive to the inclination angle. The trends that are observed can be explained by the fact that contrarily to flow boiling, heat transfer during flow condensation is governed by convective phenomena, as the main thermal resistance is mainly induced by heat transfer conduction in the liquid film. In this regard, Figure  7  shows the maximum-over-minimum heat transfer coefficient ratio (obtained under the same operating conditions by changing only the tube inclination) as a function of the liquid film-over-thermal boundary layer for the condensation database.
Inclination effect on heated air-water flows The comparison of the behavior of these three types of flows should enable the identification of the main phenomena affected by the inclination angle. The relative evolution of the heat transfer coefficient with the inclination angle, taking into account the vapor and liquid Froude numbers, is shown in Figure  8  for two different Bond numbers for data belonging to the heated gas-liquid database. Unlike flow boiling and condensation, for the air-water experiments, the liquid and gas superficial velocities can be independently imposed. The diagrams therefore consider this further degree of freedom by using the liquid Froude number, which is defined as: SL L u Fr gd = (4) The works found for heated air-water are very limited, and the range of inclinations investigated is not very wide, further complicating the overall analysis.
The most significant & ' ( /& ') combination in terms of heat transfer coefficient variation and frequency are found for 0°/7° and 0°/90°. In the first case, the ratio between maximum and minimum heat transfer coefficient can reach 10, which is considerably higher than the values observed for boiling and condensation two-phase flows. Keeping in mind the weakness of the air-water flow database, the comparison between Figure  6  and Figure  9  is interesting, as the differences between condensing and air-water flows mainly rely on the additional convective thermal resistance that occurs in air-water flows between the liquid and gas phases and on the behavior of the small bubbles which tend to collapse quickly in condensing flows, contrarily to the case in air-water flows. If vertical flows are rarely the best configuration for condensing flows, this is not the case b) a) for air-water flows: vertical air-water flows induce more small bubbles, which may break the thermal boundary layers and thus enhance the heat transfer.
In conclusion, a global summary of the present qualitative analysis is shown in Table  4. The effect of the inclination angle on the heat transfer coefficient in terms of the maximum ratio h/hmin is not the same for the three heat transfer mechanisms. First, in the case of boiling and condensation, the relative variation is somehow restrained (<320%) compared to the greater ratios observed in the heated air-water studies. Then, the most recurring orientations that minimize (& ' ( ) and maximize (& ') ) the heat transfer coefficients are also different according to the three databases. Finally, even if a non-negligible effect of the Froude and Bond numbers on the gravity influence is observed, their threshold values are not unique for the three heat transfer mechanisms and are seen to change from one author to another, implying that single investigations of these two numbers are not sufficient to disclose the overall physics.
Assessment of existing correlations for inclined tubes Few researchers have tried to quantify the effect of the tube orientation on the two-phase heat transfer coefficient by including the inclination angle in their prediction methods. For flow boiling heat transfer, Akhavan-Behabadi and Esmailpour  [43]  provided a simple expression of the two-phase Nusselt number, which was developed for their own database with a corrugated tube of 8. 3 mm ID: 0. 92 1. 02 0. 11 0. 00379 L L tt Pr Nu Re F X β   = ⋅ ⋅ ⋅     (5) The parameter 8 9 takes into account the inclination angle and is obtained according to the experimental vapor quality: F x x F x x β β β β = + ⋅ + ⋅ ≤ = - ⋅ -°> (6) The calculated heat transfer coefficients from Akhavan-Behabadi and Esmailpour  [43]  are compared with the boiling database in Figure  10a.
This prediction method largely underestimates the collected points, especially when the heat transfer coefficient is high and in the vertical upward disposition, and it works reasonably well only with the original authors' database or under similar operating conditions. By defining the mean absolute error (MAE) as: exp exp 1 100 pred h h MAE N h - = ⋅ ∑ (7) the overall calculated MAE for this correlation is 69. 9%. For flow condensation heat transfer, Adelaja et al. [55]  modified the original Cavallini et al. [56]  correlation developed for horizontal smooth tubes. The authors categorized the flow in the gravity and wall temperature difference-independent region (for annular, annular-wavy, intermittent and mist flows, in which the nondimensional gas velocity : ; is higher than a threshold value : ;, ) and in the gravity and wall temperature difference-dependent regime (for smooth stratified and stratified wavy flows, in which : ; 0 : ;, ).
5 V V L V xG J gd ρ ρ ρ =   -   (11) and its transition value was defined as follows, as a function of only the Martinelli parameter: ( ) 1/3 3 3 , 1. 111 7. 5 2. 4 4. 3 1 V T tt J X - - -         = +     +       (12) The comparison of the Adelaja et al. [55]  prediction method against the present condensation database is shown in Figure  10b. Most of the data are underestimated, regardless of the value of the inclination angle, providing an overall MAE of 60. 1%. A similar approach has been followed by Shah  [58] , who proposed a suite of correlations for condensation heat transfer in conventional and micro-scale geometries in all orientations, by using a linear interpolation between the heat transfer coefficients evaluated at 0° and at -90°. Due to the length and complexity of the mathematical expression, the details of the equations are available in the reference mentioned.
The comparison of the correlation by Shah  [58]  against the condensation database is shown in Figure  10c. The prediction method works reasonably well for high heat transfer coefficients at positive inclination angles, whereas it fails at lower heat transfer efficiencies for all orientations; however it provides an overall MAE of 26. 4%. Finally, Ghajar and Kim  [59]  proposed a heat transfer model for heated gas-liquid flow, taking into account the effects of the tube orientation with the inclination parameter Z and the flow pattern factor 8 = : ( ) ( ) 2 sin 1 L V L SL gd Z u ρ ρ β ρ - = + (13) 2 , L eff p S F d π   =     (14) The first parameter represents the relative force acting on the liquid phase in the flow direction due to the momentum and gravity forces, while the flow pattern factor tries to capture the realistic shape of the gasliquid interface and the effective wetted perimeter.
Further details on the mathematical expression are available in the original reference  [59]. This correlation is then tested against our heated air-water database in Figure  10d , in which it is clear that most of the points are strongly overestimated, especially for horizontal and downward flow orientations. A better agreement is instead found for positive channel inclinations, for which all the data are included in a ±30% error band. However, the overall calculated MAE is very high (661%).
Inclination effect Ih: definition and development of a practical tool The assessment of the existing correlations has shown a very poor agreement with the experimental data, and this is mostly due to the shortage of experimental points available in open literature. The limited database, in fact, does not allow the development of a solid prediction method for the evaluation of the two-phase heat transfer coefficient as a function of the experimental conditions including the inclination angle. In this regard, the aim of the present work is to provide a simple tool to establish whether the heat transfer coefficient might be affected by the channel orientation or whether a typical correlation for horizontal tubes can be used. The analysis is limited to boiling and condensation heat transfer, since the amount of data in the case of heated air-water is scarce and the investigated values of the inclination angles are quite limited to nearly horizontal or nearly vertical configurations.
The heat flux (q) for boiling heat transfer is considered in the Boiling number Bo. For condensation heat transfer, the heat flux is not considered as a parameter, since not all the original sources shared this information. Moreover, most of the data for condensation heat transfer fall within the ΔT (wall subcooling)-independent regime according to the classification given by Cavallini et al. [56] , and therefore, the effect of heat flux should not be significant. The effects of the vapor quality x and the thermophysical properties are taken into account in the group and in the Martinelli parameter A BB. The ratio of the liquid film thickness to the thermal boundary layer ,. / /δ D calculated in the model by Hulburt and Newell  [54]  accounts for the inertia (G), vapor quality (x) and liquid thermal conductivity (E.