1 Introduction

Propane (R290) is an odorless colorless natural refrigerant which was found to have excellent thermophysical properties in the early 1920s. The introduction of chlorofluorocarbon (CFC) and hydrochlorofluorocarbon (HCFC) refrigerants a few years later with their chemical stability and favorable boiling points had caused R290 to be set aside especially in view of the flammability and safety concerns. Since the Montreal Protocol of 1987 addressing the phasing out of CFC refrigerants, however, and later with concerns over global warming, researchers are returning to natural refrigerants. Now, the industry is more open to R290 as a possible substitute for R22, a CFC refrigerant, due to the current transform in the situation and technical advancements towards a more sustainable environment. With a short atmospheric life, R290 will remain in the environment for a short time. Charges in devices utilizing R290, however, should and can be kept well below the lower flammability limit (LFL) to prevent danger due to flammability.

Many reported works have done an extensive review and experimental studies on the R290 as a comparison with conventional and new refrigerants, showing the promising future that motivates researchers with a continuous study on R290 in many areas related to heating and cooling applications. Choudhari and Sapali [1] performed an analysis of natural refrigerant R290 as a potential replacement for R22 in a vapor compression cycle. Although R290 showed almost the same but a slightly lower COP compared to R22, they suggested a higher value could be achieved with a design modification. Yadav et al. [2] reviewed R290 and R1234yf usage, defined both as promising 21st century refrigerants and urged for a more studies to be carried especially on the flammability issues, one of the well-known disadvantages of R290 as an alternative refrigerant a decade ago. Sanchez et al. [3] studied R290 among other refrigerants as a replacement drop-in for R134a in a beverage cooler with the aim to evaluate the energy impact. Their experimental works concluded that R290 showed higher cooling capacity and coefficient of performance than that of R134a.

Several works on R290 reported studies that involved a range of channel diameters and other experimental parameters that showed a different dominant effect of mass flux and heat flux towards two mechanisms of convective heat transfer; forced convective and nucleate boiling. Experiments by Lillo et al. [4] showed a significant effect of heat flux in their 6.0 mm diameter channel which indicated the nucleate boiling dominant. The effect of mass flux on the experimental heat transfer coefficients was insignificant almost all of the experiments conducted. Dry-out incipient was shown to decrease with an increase in the applied heat flux. The heat flux, mass flux, and saturation temperature were set from 2.5 to 40 kW/m2, 150 to 500 kg/m2.s, and 25 to 35 °C, respectively.

de Oliveira et al. [5] studied flow boiling in a 1.0 mm tube for mass flux from 240 to 480 kg/m2s, heat flux from 5 to 60 kW/m2, and saturation temperature of 25 °C. They reported that both the mass flux and the heat flux have a major effect on the heat transfer coefficient. Observations of the two-phase flow pattern revealed the dominance of slug, churn, wave-annular and smooth-annular flow regimes. In most flow patterns for the experiment, convective boiling was found to be prevalent whereas the nucleate boiling is dominant at lower vapor quality.

Allymehr et al. [6] studied heat transfer for R290 in a micro-fin and a smooth channel of 5 mm diameter each. They found that the heat transfer was increasing with an effect of heat flux at a lower vapor quality for both types of tube channel, while at a higher vapor quality, the mass flux was showing a significant effect only for the smooth tube channel. Thus, they did not recommend the use of enhanced geometric tube for R290 at a high mass flux value.

Oh and co-authors [7,8,9,10] had extensively studied heat transfer of R290 as part of the natural refrigerants investigated, with a range of channel diameter from 1.5 to 3.0 mm, mass flux from 50 to 600 kg/m2s, and heat flux from 5 to 20 kW/m2. They stated that both heat flux and mass flux have a significant effect towards their R290 data. Higher heat transfer coefficient was shown with a high value of heat flux at a lower vapor quality. As the vapor quality increased, variation in the mass flux showed an increasing trend of the heat transfer coefficient.

There are many correlations presented today for two-phase convective correlations in conventional channels but existing procedure and correlations for determining the two-phase heat transfer in a large channel cannot accurately forecast the same form of heat transfer in a small channel. Reported data on two-phase flow and heat transfer in small channels have been minimal compared to data for large channels [8]. For small channels, established correlations are still few, most only agreeable with their own data but have large disagreements with newer data. It is essential to emphasize that diameters do not represent fully the effect of channel size on physical mechanisms [11]. A microchannel is not defined just based on criteria for physical channel size categorization. Ullmann and Brauner [12] classified a microchannel based on an Eötvös number, Eo, which is less than (2π)2. Only a few studies have developed correlations for R290 in a small channel as reported by Choi et al. [7], Lillo et al. [4], and Mohd-Yunos et al. [13].

Lesser data is available for vapor qualities above 0.6 because of dry out occurrence. The phenomenon of the dry out is one of the elements influencing the precision of the researcher’s established correlations. Until now, there is still a few studies that highlighted the dry out condition for developing the two-phase convective correlation. The dry-out occurrence usually happens at high vapor quality, where the liquid film at the wall could no longer be maintained, leaving the vapor phase occasionally in contact with the heated surface, resulting in a drastic drop in heat transfer efficiency [4]. In the case of horizontal channels, the dry-out appears first at the top of the wall and ultimately extends to the remaining areas of the channel with increasing vapor quality due to the effect of stratification. Dry out is closely correlated with an annular flow regime that is predominant in small channels saturated flow boiling [14]. Dry out occurs at high heat flux and low mass flux [13].

Having a correlation with a good accuracy for R290 is important to prevent under or over design especially today where for small channels in compact heat exchangers there is still yet an established correlation for the refrigerants that can provide acceptable accuracy. Over design of heat exchanging devices causes excessive consumption of materials, refrigerant, and energy which will increase the manufacturing cost. Accurate prediction of heat transfer coefficient will reduce cost and saves more energy and material. Therefore, it is important to establish an effective and reliable method for estimating the coefficient of heat transfer for the efficient design of compact systems using R290.

2 Methodology

The superposition correlation from Mohd-Yunos et al. [13] has been selected in this study because it was among the latest improved correlation using the method of optimization. This study was undertaken to investigate if further improvement may be achieved with newer data.

As originally suggested by Chen [15], the superposition correlation is the summation of nucleate boiling mechanism and forced convective mechanisms which leads to the heat transfer mechanism in a tube as follows:

$${h}_{tp}={Sh}_{nb}+{Fh}_{fo}$$
(1)

where htp is the two-phase heat transfer coefficient, S is the nucleate boiling suppression factor, and F is a multiplier factor on the convective boiling contribution. The nucleate boiling coefficient, hnb, was taken from Cooper [16] while the single-phase convective heat transfer coefficient, hfo, was taken from Dittus and Boelter [17]:

$${h}_{nb}=55{p}_r^{01.2}{\left(-0.4343\mathit{\ln}.{p}_r\right)}^{-0.55}{M}^{-0.5}{q}^{0.67}$$
(2)
$${h}_{fo}=0.023{\mathit{\operatorname{Re}}}_f^{0.8}{\mathit{\Pr}}_f^{0.4}\frac{k_f}{D}$$
(3)

where pr is the reduced pressure, q is the heat flux (kW/m2), M is the molecular weight (kg/kmol), Ref is the liquid Reynolds number, Prf is Prandtl number, kf is the liquid thermal conductivity (Wm−1K−1), and D is channel diameter (m). The reduced pressure and liquid and vapour Reynolds number are expressed as

$${p}_r=\frac{p_{sat}}{p_{crit}}$$
(4)
$${\operatorname{Re}}_f=\frac{GD\left(1-x\right)}{\mu_f}$$
(5)
$${\operatorname{Re}}_g=\frac{GDx}{\mu_g}$$
(6)

where Reg is the vapor Reynolds number, G is mass velocity (kg/m2s), and μ is dynamic viscosity. Zhang et al. [18] changed Chen’s [15] original F=f(X) to F=f(Ø), proposing a relation between the Reynolds number, factor F, and a two-phase frictional multiplier, Ø2. The equation for the two-phase frictional multiplier is as follows:

$${\phi}_f^2=1+\frac{C}{X}+\frac{1}{X^2}$$
(7)

where Ø is a two-phase multiplier, C is the Chisholm parameter which is a constant value for a specific liquid-vapor flow condition, and X is the Lockhart–Martinelli’s parameter. Lockhart and Martinelli [19] introduced the equations for X as follows:

$$X={\left(\frac{f_f}{f_g}\right)}^{0.5}{\left(\frac{\rho_g}{\rho_f}\right)}^{0.5}\left(\frac{1-x}{x}\right)$$
(8)

where X is a Lockhart–Martinelli’s parameter, f is friction factor, ρ is density (kg m−3), and x is vapor quality. The subscript f and g refers to the liquid and vapor state, respectively. The friction factor in Eq. (8) is captured by the flow conditions of laminar-turbulent flows which is f = 16Re−1 for laminar flow Re < 2300 or f = 0.079Re−0.25 for turbulent flow when Re > 3000.

The S and F equations for the Mohd-Yunos et al. [13] correlation referred to Choi et al. [10] correlation where the initial correlation was developed from Jung et al. [20] and Zhang et al. [18], respectively. Coefficients and exponents in the S and F correlations developed by Mohd-Yunos et al. [13] was obtained using genetic algorithm (GA) as an optimization tool. They developed three new correlations for three conditions of vapor quality but their correlation for pre-dryout at x = 0.6 was selected in this study which is

$${\displaystyle \begin{array}{c}S=0.8{\left({\phi}_f^2\right)}^{0.124}{Bo}^{0.093}\\ {}F=\mathit{\operatorname{MAX}}\left[\left(1.226{\left({\phi}_f^2\right)}^{0.107}-0.28\right),1\right]\end{array}}$$
(9)

where Bo is the boiling number expressed as

$$Bo=\frac{q}{Gi_{fg}}$$
(10)

where q is heat flux (W m−2), i is enthalpy (J kg−1). The accuracy of the correlation is based on the minimization of the MAE:

$$MAE=\frac{1}{n}{\sum}_{i=1}^n\frac{\left|{h}_{tp,{pred}_i}\left.-{h}_{tp,{\exp}_i}\right|\right.}{h_{tp,{\exp}_i}}\times 100$$
(11)

where n is number of experimental data points, htp,pred is predicted heat transfer coefficient, and htp,exp is experimental heat transfer coefficient.

A total of 831 experimental data points of heat transfer coefficient were extracted using Grabit, a tool in MATLAB R2018a and collected from 7 sources for pre-dry out data only. The collected experimental data was chosen on the basis of a narrow channel and the R290 was used as the refrigerant. Note that 135 data points (16%) utilized in this study have not been used by [13] in developing their correlation. The range of saturation temperature, mass flux, and heat flux for the data points in the current study is also smaller. Table 1 lists the selected experimental data used in this study. All of Dth, Tsat, G, q, and xd value are taken based on the experimental works by authors as listed in Table 1.

Table 1 List of selected experimental data released
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Table 2 shows the number of data points collected at pre-dryout condition for each author. The data points collected for pre-dry out conditions were based on their experimental work and the dry out condition were then set up at vapor quality, x, of 0.4, 0.5, 0.6, 0.7, and 1.0. The programming code was used to identify the data points up to x of 0.4, 0.5, 0.6, 0.7, and 1.0. Note that the majority of data points are for below the vapor quality of 0.7. Consequently, the MAE for the predicted heat transfer coefficient is expected to be high if all the data points are used to generate a predicted correlation for 0 ≤ x ≤ 1.

Table 2 Number of data points collected at pre-dryout condition for each author
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The predicted heat transfer coefficient, htp,pred, and mean absolute error, MAE, were calculated using MATLAB R2018a software with the modified programming code from Mohd-Yunos et al. [13]. Figure 1 indicates the distribution of the relation between the extracted experimental data and the expected data using their correlation. The correlation of Mohd-Yunos et al. [13] had an MAE of 21.84% for pre-dryout data collected for this study. This MAE value can be considered as a low value. This might be due to 84% of the collected experimental data from several authors for this study were the same as those utilized by Mohd-Yunos et al. [13] which was from [5, 8,9,10]. However, the MAE value is expected to be further reduced after the optimization process using single-objective genetic algorithm (SOGA).

Fig. 1
figure 1

Comparison of experimental data with correlation of Mohd-Yunos et al. [13]

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There are a total of six variables in Eq. (12) namely as b1, b2, b3, b4, b5, and b6. These new series of variables were generated from the GA optimization based on the smallest MAE value that can be achieved given by Eq. (11). The new series of constants found were used in Eq. (12), S and F equations. The new correlation is then correlated with the experimental data extracted from previous published studies as well as the Mohd-Yunos et al. [13] correlation to determine if the accuracy has improved.

$${\displaystyle \begin{array}{c}S={b}_1{\left({\phi}_f^2\right)}^{b_2}{Bo}^{b_3}\\ {}F=\mathit{\operatorname{MAX}}\left[\left({b}_4{\left({\phi}_f^2\right)}^{b_5}-{b}_6\right),1\right]\end{array}}$$
(12)

The genetic algorithm is a tool based on natural selection, the mechanism that causes biological evolution, for resolving both constrained and unconstrained optimization problems. It repeatedly changes the population of individual solutions. The genetic algorithm chooses individuals from the existing population to be parents at variance at each point and uses them to generate better off-springs for the next generation. In this case, the better solutions for the variables bn are generated through the selection, crossover and mutation steps to fulfill the minimization of the objective function, the MAE. In SOGA, the variables are optimized while trying to achieve a minimum or maximum condition of the objective function. Here, the objective function to be minimized is the mean absolute error (MAE);

$$\operatorname{Minimize}\ f\left({x}_i\right)=\textrm{MAE}$$
(13)

where the MAE is written as Eq. (11). In this proposed approach, the respective coefficients, bn imbedded in Eq. (12) were obtained using the optimization method of SOGA. The objective function for Eq. (13) is subjected to the design variables of bn and can be written as;

$${\displaystyle \begin{array}{c}\textrm{Design}\ \textrm{variables},{x}_i=\left\{{b}_1,{b}_2,\dots ..,{b}_n\right\}\\ {}\textrm{Subjected}\ \textrm{to}\ \left\{\ {b}_{n,\mathit{\min}}<{b}_n<{b}_{n,\mathit{\max}}\right.\end{array}}$$
(14)

where bn,min and bn,max are the design variable lower and upper search boundaries respectively. Detail of the GA process can be retrieved from Mohd-Yunos et al. [13]. Previously, Picanto et al. [22] and Porto et al. [23, 24] have demonstrated the use of genetic algorithm in developing heat transfer correlation, which were applied for macrochannel data.

3 Results and discussion

The optimization has been undertaken to select a more accurate heat transfer coefficient correlation for pre-dry out condition of R290 in terms of a reduced MAE from the original selected correlation. Five new correlations have been generated based on the fixed dry out conditions and data for vapor quality, x ≤ 0.4, 0.5, 0.6, 0.7, and 1.0 to see which of the five new correlations is applicable at most dry out conditions. For all variables, the lower and upper search boundaries were specified to be – 1 < bn < 2. These bounds were chosen based on the average variable values in the S and F equations in Eq. (9). The cycle was stopped when it exceeded the stopover condition, where the limit generation number was set at 100 × number of variables, b. In the present condition, the population number was 200. Optimization was repeated three times and the optimized variables, b, in the S and F equations for pre-dry out correlations are shown in Table 3.

Table 3 New variables in S and F equation after optimization
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Each new correlation was then tested with the data up to vapor quality, x, of 0.4, 0.5, 0.6, 0.7, and 1.0, and the MAE was each calculated between the new predicted value and experimental data up to vapor quality, x of 0.4, 0.5, 0.6, 0.7, and 1.0. For the comparison, the reduction of the MAE, ∆MAE, between the new correlation and Mohd-Yunos et al. [13] correlation (htp,pred) was observed and one new correlation was chosen for the analysis of heat transfer in this study based on the ∆MAE as shown in Table 4. The higher the ∆MAE means the higher the improvement obtained. From the observation, the best correlation applicable to dryout condition is the correlation with selected quality x ≤ 0.4, least ∆MAE when tested. Thus, it is chosen to be further analyzed.

Table 4 MAE between Mohd-Yunos et al. [13] and optimized correlations for x = 0.4, 0.5, 0.6, 0.7, and 1.0
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The MAE value after the optimization process is 17.02% which is reduced by 4.88% from the original value. Figure 2 shows the graph comparison between experimental data (htp,exp) and new optimized heat transfer coefficient (htp,new) for pre-dry out condition of R290 selected at x = 0.4. More data are closer to the 45° reference line for the new optimized correlation compared to the original correlation. This shows a good prediction of the pre-dry out data.

Fig. 2
figure 2

Comparison of heat transfer coefficients for experimental data and predicted optimized correlation

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The new optimized pre-dryout heat transfer coefficient was compared with several data points from several separate sources at various q and G. A total of 84 data points were extracted from Citarella et al. [21]. Figure 3 shows the comparison between three different values of heat transfer coefficient, which is htp,exp, htp,pred, and htp,new, at the constant mass flux of 220 kg/m2s, various heat flux, q, (a) 10 kW/m2 (b) 40 kW/m2, at the saturation temperature, Tsat 25 °C, and diameter, D 6.0 mm. Figure 3a shows the last point at x = 0.85 since from the collected experimental data points, the htp starts to drop which is called dry out incipience, so that the predicted and new heat transfer coefficient was observed at x ≤ 0.85 which is the exact pre-dryout condition. From the experimental data in Fig. 3b, the last point is at x = 0.63 since from the collected experimental data points, the dry out incipience was at quality of 0.63. The dry-out phenomena occured at a lower x, from 0.85 to 0.63 when the q is increased from 10 to 40 kW/m2. The htp,new value was predicted to follow the pattern of htp,pred since the correlation was developed following the same approach by means of genetic algorithm (GA) to minimize the error of each data point. The new correlation has managed to improve htp,pred by Mohd-Yunos et al. [13] by 5%.

Fig. 3
figure 3

Graph of htp versus x at constant G = 220 kg/m2s and various q a 10 kW/m2, b 40 kW/m2

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Figure 4 shows the comparison of htp from Allymehr et al. [6] at constant q = 23 kW/m2 and various G (a) 252 kg/m2s, (b) 500 kg/m2s, Tsat 5 °C, and D 4.1 mm. Both Fig. 4 a, b has no dryout occurrence based on the 51 experimental data points from [6]. The pattern of htp,exp in Fig. 4a increases from 0.3 to 0.83 vapor quality, but at x = 0.45, a small drop occurred while in Fig. 4b, htp,exp increases from 0.15 to 0.88 vapor quality but at x = 0.27, a small drop of htp,exp occured. For htp,pred, it shows the data points are far off from the htp,exp compared to the htp,new. The htp,new in Fig. 4b are increasing significantly at higher vapor quality. The composed pre-dryout experimental data sets for heat transfer in small channel are showing the increasing trend as the vapor quality is increasing, where a certain data set can significantly increases close to the peak of heat transfer coefficient just before the dryout at a higher vapor quality. In SOGA optimization, the optimization process is trying to balance the error produced between the experimental and predicted data set from the optimized model. Therefore, this significant increasing trend at a higher quality is expected for the predicted data sets, while the optimization is trying to best fit all data.

Fig. 4
figure 4

Graph of htp versus x at constant q = 23 kW/m2 and various G a 252 kg/m2s, b 500 kg/m2s

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All the htp, new data points are within 20% of the experimental values except at x = 0.88 in Fig. 4b. Meanwhile, htp,pred are within 20% of the htp,exp only at x = 0.46 in Fig. 4 (a) and at x = 0.15 to 0.33. It shows that the newly optimized correlation created by SOGA well agrees with this chosen data source compared to the original correlation.

4 Conclusion

The occurrence of dryout condition in convection heat transfer of microchannel increases the value of MAE when finding the best developed correlation. Most developed correlations already disagreement issues; compatibility between macro and microchannel experimental data, the emerging of a new alternative refrigerant and the different range of experimental properties among others. The dryout condition shows the sudden drop in the increasing pattern of heat transfer coefficient where some correlations which were developed while considering the linear change of saturation pressure were not able to predict it well at a higher vapor quality.

The objective of this study which was to reduce the MAE of a selected developed heat transfer coefficient correlation for R290 using Single Objective Genetic Algorithm (SOGA), for pre-dry out conditions has been achieved. The new correlation, htp,new, relevant for R290 in a microchannel in an extensive variety of experimental data points was developed by optimizing six variables which appear in the nucleate boiling suppression factor, S, and force convective factor, F of a selected correlation. The MAE value was reduced to 17.02% from 21.84% after the optimization process. Although most of the htp,new are seen to be off from the experimental heat transfer coefficient, htp,exp, by more than 20% at D = 6.0 mm and Tsat = 25 °C, they are better when compared to earlier correlation (htp,pred) at various heat flux. An accurate predicted heat transfer coefficient is important towards savings in refrigerant charge and material and this study has shown that improved accuracy can be achieved with SOGA. With more available data points, it is possible to utilize the same approach in improving the accuracy of correlations that have been developed using the standard regression method on experimental data. The proposed optimization method can be further applied to other types of correlation such as asymptotic as the correlation also consists of the coefficients that were developed through standard regression method.

5 Nomenclature

Greek symbol

𝜌 Density (kg m−3)

μ Viscosity (kg m−1 s−1)

∅ Two-phase multiplier

Subscripts

f Liquid

fo Single-phase liquid

g Vapor

nb Nucleate boiling

tp Two-phase