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Research Papers

# A Numerical Model for Ammonia/Water Absorption From a Bubble Expanding at a Submerged Nozzle Into a Binary NanofluidOPEN ACCESS

[+] Author and Article Information
Fengmin Su

Institute of Marine Engineering
and Thermal Science,
Dalian Maritime University,
Dalian 116026, China
e-mail: fengminsu@dlmu.edu.cn

Hongbin Ma

Mem. ASME
University of Missouri–Columbia,
Columbia, MO 65211
e-mail: mah@missouri.edu

Yangbo Deng

Institute of Marine Engineering
and Thermal Science,
Dalian Maritime University,
Dalian 116026, China
e-mail: dengyb1970@163.com

Nannan Zhao

Institute of Marine Engineering
and Thermal Science,
Dalian Maritime University,
Dalian 116026, China
e-mail: znn@dlmu.edu.cn

1Corresponding author.

Manuscript received January 19, 2014; final manuscript received July 28, 2014; published online September 15, 2014. Assoc. Editor: Calvin Li.

J. Nanotechnol. Eng. Med 5(1), 010902 (Sep 15, 2014) (5 pages) Paper No: NANO-14-1004; doi: 10.1115/1.4028400 History: Received January 19, 2014; Revised July 28, 2014

## Abstract

An absorber is a major component in the absorption refrigeration systems, and its performance remarkably affects the overall system performance. A mathematical model for ammonia absorption from a bubble expanding at a submerged nozzle into a binary nanofluid was developed to analyze the effects of binary nanofluid on ammonia absorption in the forming process of a bubble. The combined effects of nanoparticles on heat transfer, mass transfer, and bubble size all were considered in the model. The concentration of nanoparticles, the radius of the nozzle, and the flow rate of ammonia vapor were considered as the key parameters. The numerical results showed that the enhancement of binary nanofluid for bubble absorption has the analogous tendency with the mass transfer enhancement of binary nanofluid. The diameter of the nozzle and the flow rate of ammonia vapor hardly affect the enhancement of the binary nanofluid for the absorption of bubble growing stage. The current investigation can result in a better understanding of the absorption process occurring in thermally driven absorption refrigeration systems.

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## Introduction

NH3/H2O absorption refrigeration systems have been the object of an increasing interest in recent years due to the rise of energy price and climate change. The absorber in a NH3/H2O absorption refrigeration system is a critical component, and its performance significantly influences the whole system size and cost. Due to their simple design and high absorbing performance, the bubble absorbers are usually applied in absorption refrigeration system [1]. The most important parameter in an absorber is the absorption rate of the refrigerant vapor. The increase of the absorption rate will directly increase the refrigeration performance and reduce the absorption system size.

Nanofluids, in which nanoparticles (d < 100 nm) are suspended evenly in a base fluid [2], can enhance heat and mass transfer performances of the base fluid [3-7]. Therefore, it can be used to improve the absorption rate in bubble absorption. Because the absorbent of the absorption system is a binary mixture and the nanofluid is considered as a single phase fluid by the definition, the absorption medium with nanoparticles is named as binary nanofluid [8]. Kim et al. [8-10] and Ma et al. [11] found that the binary nanofluids have remarkable enhancement for ammonia bubble absorption rate by experiments. However, few theoretical and analytical investigations about bubble absorption in binary nanofluids are developed at present. Kim et al. [12] developed a differential mathematical model in which the effective absorption ratio which is the ratio of the absorption rate in the case with the addition of nanoparticles to that in the case without any addition is applied simply to express the effect of binary nanofluids. The ratio was from the experimental result. The theoretical investigation about the growing process of the bubble in the binary nanofluids is still vacant.

In this paper, a mathematical model of the growing process of the bubble in the binary nanofluids will be developed, and the effects of the binary nanofluids on the combined heat and mass transfer in the growing process of a bubble are analyzed.

## Theoretical Modeling

In a typical NH3/H2O bubble absorption process, aqueous ammonia solution is used as the absorbent and ammonia vapor as the refrigerant. The refrigerant vapor from the evaporator in absorption refrigeration system at a pressure of P comes into the absorbent in the absorber at initial temperature and concentration of T0 and X0, respectively. The spherical bubble shown in Fig. 1, is formed on the top of the nozzle of the absorber, and grows up gradually. Because the saturated vapor pressure of the absorbent is lower than P, the absorbent absorbs the refrigerant vapor with the bubble growing up. If the interfacial mass transfer resistance is neglected, it can be assumed that the bubble interface is in an equilibrium condition, which corresponds the equilibrium concentration of refrigerant, i.e., Xi. Due to the concentration difference, Xi − X0, the ammonia molecules move from the interface toward the bulk of the absorbent. At one time, the vapor absorbed by the absorbent releases latent heat, which directly increases the interface's temperature, Ti. Due to the temperature difference, Ti− T0, the heat moves into the bulk of the absorbent and is transferred into cooling water. When the size of the bubble becomes larger than the critical volume, the bubble separates with the nozzle. The forming process of a bubble ends.

###### Assumption for the Numerical Model Development.

In order to simplify the system reasonably, the following assumptions are made during the model development:

1. (1)An ammonia bubble in the growing process is spherical in shape all along.
2. (2)The liquid phase around the bubble is static.
3. (3)The pressure of ammonia vapor is constant. The heat rejected in absorption is transferred completely into cooling water and the bulk temperature of the absorbent is constant.
4. (4)Heat and mass transfer of water from liquid to gas phase are neglected. Lee et al. [13] found that mathematical model neglecting the heat and mass transfer of water from liquid to gas phase agrees with the experimental values well.
5. (5)The interfacial mass transfer resistance is neglected. The interface between the vapor and solution is in an equilibrium state. That is, the interfacial concentration of liquid phases is determined from the equilibrium concentrations at the interface temperature.

###### Expression of Critical Volume of a Bubble.

It is well known that there are two stages in the forming process of a bubble: expanded stage and detached stage [14]. In expanded stage, the bubble is affected by four forces: buoyancy, surface tension, inertial force, and viscous force. From the balance of these four forces, the following equation is derived for the bubble size in this stage:Display Formula

(1)$Ve23=11QN2192π(34π)23g+32(34π)13g×μlρlQNVe13+πdoσgρlVe23$

While the rising force is larger than the restricting force, the bubble begins to rise up and comes into the detached stage. Here, the bubble is connected to the nozzle through a thin neck. The bubble grows up unceasingly. When the length of thin neck equals near to the bubble radius in the expanded stage, the bubble will be detached from the nozzle. The bubble size in this stage is expressed byDisplay Formula

(2)$re=B2QN(A+1)(Vb2-Ve2)-(CAQN)(Vb-Ve) -3G2QN(A-13)(Vb23-Ve23)$

whereDisplay Formula

(3)$re=(3Ve4π)13$
Display Formula
(4)$A=1+96π(1.25)reμl11ρlQN$
Display Formula
(5)$B=16g11QN$
Display Formula
(6)$C=16πdoσ11ρlQN$
Display Formula
(7)$G=24μl11(34π)13ρl$

The volume of the bubble at the expanded stage is first calculated with the iterative method and then substituted to Eq. (2). The critical volume of the bubble, Vb, is obtained using the trial and error method.

###### Heat and Mass Transfer in Absorption Process.

According to the assumption of the model, a mass transfer from the interface to the bulk of the absorbent needs only to be considered in the model. For instantaneous ammonia absorption in the liquid phase, Higbie [15] proposed a penetration theory based on the hypothesis of instantaneous gas–liquid contact. In this study, the instantaneous mass transfer coefficient in the static liquid phase, kl, at the gas–liquid contacting time, t, is estimated by Higbie's equationDisplay Formula

(8)$kl=Dlπt$

The instantaneous absorption rate is expressed asDisplay Formula

(9)$N=ρlklAb(Xi-X0)$

Integrating Eq. (9) from 0 to t, the total absorption mass can be obtained asDisplay Formula

(10)$Nt=∫tN(t)dt$

Dividing Eq. (10) by t, the mean absorption rate can be obtained asDisplay Formula

(11)$m=Ntt$

Absorption heat coming from latent heat of the vapor absorbed by the absorbent increases the interface temperature, Ti. Due to the temperature difference, Ti− T0, the heat moves into the bulk of the absorbent by conduction. The instantaneous heat transfer coefficient in the static liquid phase, hl, at the gas–liquid contacting time, t, is expressed as [16]Display Formula

(12)$hl=kρlCp11.45t$

According to heat balance, the absorption heat is expressed asDisplay Formula

(13)$Q=Nhlg=hlAb(Ti-T0)$

The interface temperature, Ti, is given by Eq. (13). According to assumption 5, the interfacial concentration of liquid phases is determined from the equilibrium concentrations at the interface temperature. Figure 2 shows the effect of the equilibrium temperature on the equilibrium concentration of the absorbent at a constant absorption pressure of 0.315 MPa [17]. Using polynomial fitting, an approximate relationship can be determined as

Figure 3 shows a brief flowchart of the model. First, initial conditions, boundary conditions (shown in Table 1), and physical properties (shown in Table 2) of the working pair are given to the model. Second, the critical volume of the bubble is calculated by Eqs. (1)(7). Third, heat and mass coefficient, instantaneous absorption rate, total absorption mass, and mean absorption rate are calculated, respectively, according to initial conditions and boundary conditions when t1 = 0.00001 s. The volume of the bubble here is expressed as

where V0 is the initial volume of the bubble when t0 = 0 s. It is assumed that the volume is the volume of a bubble whose surface area equals to the sectional area of the nozzle. It is expressed asDisplay Formula

(16)$V0=148πd03$

Fourth, the volume of the bubble is compared with the critical volume of the bubble. If it is larger than the critical volume, the calculation ends. If it is smaller, t2 = t1 + 0.00001 s. The results at t1 = 0.00001 s are considered as the initial conditions at t2 = 0.00002 s. Heat and mass coefficient, instantaneous absorption rate, total absorption mass, mean absorption rate, and volume of the bubble are calculated, respectively, again. The process is repeated until the volume of the bubble is larger than the critical volume. The time step size in the calculation is set as 0.00001 s. In the end, the mean absorption rate is given as a result.

## Results and Discussion

The effects of the binary nanofluid on bubble absorption have three factors, according to the investigation of Ma et al. [18]. First, nanoparticles in the binary nanofluid can cause the microconvection in aqueous ammonia because of the Brownian motion of nanoparticles. This microconvection can improve the mass diffusion of ammonia in the binary nanofluid. Second, nanoparticles in the binary nanofluid can enhance the thermal conductivity of aqueous ammonia and the heat transfer in the absorption process. To express the two enhanced effects in the model, the effective mass diffusivity and effective thermal conductivity of binary nanofluid are substituted for those of ammonia solution. Krishnamurthy et al. [7] measured the mass diffusion and thermal conductivity of the nanofluid whose nanoparticles are Al2O3 (their mean diameter is 20 nm) at the same time. The result is shown in Fig. 4 and is used in the model. Except mass diffusivity and thermal conductivity, other physical properties of binary nanofluid, such as surface tension, density, and viscosity, are hardly different with pure ammonia solution [19]. Third, it was found that the bubble size in the binary nanofluid was smaller than that in the absorbent without nanoparticles [8,20]. In order to express the effect in the model, the ratio of the bubble radius in the binary nanofluid and that in absorbent without nanoparticles is defined. According to the experiment of Su et al. [20], it is near a constant when the concentration of nanoparticles is lower than 1% and is 0.95. As presented above, a mathematical model for ammonia absorption from a bubble expanding at a submerged nozzle into a binary nanofluid has been obtained. In this paper, the effects of the volume fraction of nanoparticles, the diameter of the nozzle, and the flow rate of ammonia vapor on mean absorption rate are analyzed using the model.

Figure 5 demonstrates the variation of the mean absorption rates on the volume fraction of nanoparticles. Here, the diameter of the nozzle is 2 mm, and the flow rate is 0.45 l/min. The mean absorption rate increases with the mass fraction of nanoparticles increasing at first and then decreases. To examine the effect of nanoparticles on the mean absorption rate, the effective absorption ratio is defined as

Figure 6 shows the variation of the effective absorption ratio. It reaches the top of 2.26 when the volume fraction of nanoparticles is 0.5 vol. %. Here, the effective mass diffusivity of the binary nanofluid is 12.7 times larger than that of pure ammonia solution, and the effective thermal conductivity is 1.118 times larger. This whole variation is not near that of the effective thermal conductivity of the nanofluid but that of the effective diffusion coefficient shown in Fig. 4. There are two main reasons: one is that the enhancement of nanofluids for mass transfer is obviously more than that for heat transfer [7]; another is that the mass transfer is more dominant than heat transfer in bubble absorption.

Figures 7 and 8 show the effect of the diameter of the nozzle on mean absorption rate and effective absorption ratio, respectively. Here, the volume fraction of nanoparticles is 0.5 vol. %, and the flow rate is 0.45 l/min. The trend of the mean absorption rates in the binary nanofluid is almost same with that in pure absorbent. They all increase with the diameter increasing. The variation of the diameter of the nozzle hardly affects the effective absorption ratio. It equals to 2.26 when the diameter is 1 mm and 2.24 when the diameter is 5 mm. It only decreases 0.02. It demonstrates that the diameter of the nozzle hardly affects the enhancement of the binary nanofluid for the absorption of bubble growing stage.

Figures 9 and 10 show the effect of the flow rate of ammonia vapor on mean absorption rate and effective absorption ratio, respectively. Here, the volume fraction of nanoparticles is 0.5 vol. %, and the diameter of the nozzle is 2 mm. For the binary nanofluid and the pure absorbent, their mean absorption rates all increase with the flow rate increasing. It is parallel with the variation of the nozzle diameter that the flow rate of ammonia vapor hardly affects the effective absorption ratio. It is 2.15 when the flow rate is 0.1 l/min and 2.28 when the flow rate is 0.81 l/min. The difference is only 0.13.

## Conclusion

In this paper, a mathematical model for ammonia absorption from a bubble expanding at a submerged nozzle into a binary nanofluid was obtained. The effects of the volume fraction of nanoparticles, the diameter of the nozzle, and the flow rate of ammonia vapor on mean absorption rate were analyzed using the model. The results show that the enhancement of binary nanofluid for bubble absorption has the analogous tendency with the mass transfer enhancement of binary nanofluid. The diameter of the nozzle and the flow rate of ammonia vapor hardly affect the enhancement of the binary nanofluid for the absorption of bubble growing stage. The current investigation can result in a better understanding of the mechanism of the binary nanofluid enhancing bubble absorption.

## Acknowledgements

The authors are grateful to the financial support provided by National Natural Science Foundation of China (Contract No. 51376027) and the Fundamental Research Funds for the Central Universities (Contract No. 3132013021).

Nomenclature
• Ab =

surface area of bubble (m2)

• Cp =

heat capacity of the absorbent (J/kg °C)

• d0 =

diameter of nozzle (m)

• Dl =

diffusivity of ammonia (m2/s)

• g =

gravity acceleration (m2/s)

• hl =

instantaneous heat transfer coefficient (W/m2 °C

• hlg =

latent heat of ammonia (kJ/kg)

• k =

conductivity of absorbent (W/m °C)

• kl =

instantaneous mass transfer coefficient (m/s)

• m =

mean absorption rate (kg/s)

• mA =

mean absorption rate in pure ammonia solution (kg/s)

• mN =

mean absorption rate in binary nanofluid, (kg/s)

• N =

instantaneous absorption rate (kg/s)

• Nt =

total absorption mass (kg)

• Q =

heat transfer rate (W)

• QN =

flow rate of ammonia vapor (m3/s)

• re =

bubble radius in expanded stage (m)

• RN =

effective absorption ratio

• t =

gas–liquid contacting time (s)

• Ti =

equilibrium temperature in the vapor/liquid interface (°C)

• T0 =

temperature in bulk of absorbent (°C)

• Vb =

critical volume of bubble (m3)

• Ve =

bubble volume in expanded stage (m3)

• Vt =

bubble volume at t (m3)

• V0 =

bubble initial volume at t = 0 s (m3)

• Xi =

concentration of ammonia in the vapor/liquid interface (wt.%)

• X0 =

concentration of ammonia in bulk of absorbent (wt.%)

• μl =

viscosity of absorbent (Pa · s)

• ρg =

density of ammonia vapor (kg/m3)

• ρl =

density of absorbent (kg/m3)

• σ =

surface tension of absorbent (N/m)

## References

Kang, Y. T., Akisawa, A., and Kashiwagi, T., 2000, “Analytical Investigation of Two Different Absorption Modes: Falling Film and Bubble Types,” Int. J. Refrig., 23(6), pp. 430–443.
Choi, U. S., 1995, “Enhancing Thermal Conductivity of Fluids With Nanoparticles,” Development and Application of Non-Newtonian Flows, D. A.Singer, and H. P.Wang, eds., ASME, New York.
Kabelac, S., and Kuhuke, J. F., 2006, “Heat Transfer Mechanism in Nanofluids-Experimental and Theory,” Proceedings of the 13th International Heat Transfer Conference, Sydney, Australia, Aug. 13–18.
Keblinski, P., Eastman, J. A., and Cahill, D. G., 2005, “Nanofluids for Thermal Transport,” Mater. Today, 8(6), pp. 36–44.
Das, S. K., Choi, U. S., and Patel, H. E., 2006, “Heat Transfer in Nanofluids-A Review,” Heat Transfer Eng., 27(10), pp. 3–19.
Choi, U. S., 2007, “Novel Thermal Transport Phenomena in Nanofluids,” The 18th International Symposium on Transport Phenomena, Daejeon, Korea, Aug. 27–30, pp. 182–191.
Krishnamurthy, S., Bhattacharya, P., Phelan, P. E., and Prasher, R. S., 2006, “Enhanced Mass Transport in Nanofluids,” Nano Lett., 6(3), pp. 419–423. [PubMed]
Kim, J. K., Jung, J. Y., and Kang, Y. T., 2006, “The Effect of Nano-Particles on the Bubble Absorption Performance in a Binary Nanofluid,” Int. J. Refrig., 29(1), pp. 22–29.
Kang, Y. T., Kim, H. J., and Lee, K. I., 2008, “Heat and Mass Transfer Enhancement of Binary Nanofluids for H2O\LiBr Falling Film Absorption Process,” Int. J. Refrig., 31(5), pp. 22–29.
Lee, J. K., Koo, J., Hong, H., and Kang, Y. T., 2010, “The Effects of Nanoparticles on Absorption Heat and Mass Transfer Performance in NH3/H2O Binary Nanofluids,” Int. J. Refrig., 33(2), pp. 269–275.
Ma, X. H., Su, F. M., Chen, J. B., and Zhang, Y., 2007, “Heat and Mass Transfer Enhancement of the Bubble Absorption for a Binary Nanofluid,” J. Mech. Sci. Technol., 21(11), pp. 1338–1343.
Kim, J. K., Akisawa, A., Kashiwagi, T., and Kang, Y. T., 2007, “Numerical Design of Ammonia Bubble Absorber Applying Binary Nanofluids and Surfactants,” Int. J. Refrig., 30(6), pp. 1086–1096.
Lee, J. C., Lee, K. B., Chun, B. H., Lee, C. H., Ha, J. J., and Kim, S. H., 2003, “A Study on Numerical Simulations and Experiments for Mass Transfer in Bubble Mode Absorber of Ammonia and Water,” Int. J. Refrig., 26(5), pp. 551–558.
Dai, G. C., and Chen, M. H., 1988, Hydrodynamics in Chemical Engineering, Chemical Industry Press, Beijing, China.
Higbie, R., 1935, The Rate of Absorption of a Pure Gas Into Still Liquid During Short Periods of Exposure, Vol. 31, American Institute of Chemical Engineers, pp. 365–389.
Eckert, E. R. G., and Drahe, R. M., 1987, Analysis of Heat and Mass Transfer, Hemisphere Publishing Corporation, New York, p. 203.
Rizvi, S. S. H., and Hdidemann, R. A., 1987, “Vapor-Liquid Equilibria in the Ammonia-Water System,” J. Chem. Eng. Data, 32(2), pp. 183–191.
Ma, X. H., Su, F. M., Chen, J. B., Bai, T., and Han, Z. X., 2009, “Enhancement of Bubble Absorption Process Using a CNTs-NH3 Binary Nanofluid,” Int. Commun. Heat Mass, 36(7), pp. 657–660.
Su, F. M., Ma, X. H., and Lan, Z., 2011, “The Effect of Carbon Nanotubes on the Physical Properties of a Binary Nanofluids,” J. Taiwan Inst. Chem. Eng., 42(2), pp. 252–257.
Su, F. M., Ma, X. H., and Chen, J. B., 2009, “Effect of Nanoparticles on Forming Process of Bubbles in a Nanofluid,” Proceedings of the ASME 2nd Micro/Nanoscale Heat & Mass Transfer International Conference, Shanghai, China, Dec. 18–21, pp. 425–430.
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## References

Kang, Y. T., Akisawa, A., and Kashiwagi, T., 2000, “Analytical Investigation of Two Different Absorption Modes: Falling Film and Bubble Types,” Int. J. Refrig., 23(6), pp. 430–443.
Choi, U. S., 1995, “Enhancing Thermal Conductivity of Fluids With Nanoparticles,” Development and Application of Non-Newtonian Flows, D. A.Singer, and H. P.Wang, eds., ASME, New York.
Kabelac, S., and Kuhuke, J. F., 2006, “Heat Transfer Mechanism in Nanofluids-Experimental and Theory,” Proceedings of the 13th International Heat Transfer Conference, Sydney, Australia, Aug. 13–18.
Keblinski, P., Eastman, J. A., and Cahill, D. G., 2005, “Nanofluids for Thermal Transport,” Mater. Today, 8(6), pp. 36–44.
Das, S. K., Choi, U. S., and Patel, H. E., 2006, “Heat Transfer in Nanofluids-A Review,” Heat Transfer Eng., 27(10), pp. 3–19.
Choi, U. S., 2007, “Novel Thermal Transport Phenomena in Nanofluids,” The 18th International Symposium on Transport Phenomena, Daejeon, Korea, Aug. 27–30, pp. 182–191.
Krishnamurthy, S., Bhattacharya, P., Phelan, P. E., and Prasher, R. S., 2006, “Enhanced Mass Transport in Nanofluids,” Nano Lett., 6(3), pp. 419–423. [PubMed]
Kim, J. K., Jung, J. Y., and Kang, Y. T., 2006, “The Effect of Nano-Particles on the Bubble Absorption Performance in a Binary Nanofluid,” Int. J. Refrig., 29(1), pp. 22–29.
Kang, Y. T., Kim, H. J., and Lee, K. I., 2008, “Heat and Mass Transfer Enhancement of Binary Nanofluids for H2O\LiBr Falling Film Absorption Process,” Int. J. Refrig., 31(5), pp. 22–29.
Lee, J. K., Koo, J., Hong, H., and Kang, Y. T., 2010, “The Effects of Nanoparticles on Absorption Heat and Mass Transfer Performance in NH3/H2O Binary Nanofluids,” Int. J. Refrig., 33(2), pp. 269–275.
Ma, X. H., Su, F. M., Chen, J. B., and Zhang, Y., 2007, “Heat and Mass Transfer Enhancement of the Bubble Absorption for a Binary Nanofluid,” J. Mech. Sci. Technol., 21(11), pp. 1338–1343.
Kim, J. K., Akisawa, A., Kashiwagi, T., and Kang, Y. T., 2007, “Numerical Design of Ammonia Bubble Absorber Applying Binary Nanofluids and Surfactants,” Int. J. Refrig., 30(6), pp. 1086–1096.
Lee, J. C., Lee, K. B., Chun, B. H., Lee, C. H., Ha, J. J., and Kim, S. H., 2003, “A Study on Numerical Simulations and Experiments for Mass Transfer in Bubble Mode Absorber of Ammonia and Water,” Int. J. Refrig., 26(5), pp. 551–558.
Dai, G. C., and Chen, M. H., 1988, Hydrodynamics in Chemical Engineering, Chemical Industry Press, Beijing, China.
Higbie, R., 1935, The Rate of Absorption of a Pure Gas Into Still Liquid During Short Periods of Exposure, Vol. 31, American Institute of Chemical Engineers, pp. 365–389.
Eckert, E. R. G., and Drahe, R. M., 1987, Analysis of Heat and Mass Transfer, Hemisphere Publishing Corporation, New York, p. 203.
Rizvi, S. S. H., and Hdidemann, R. A., 1987, “Vapor-Liquid Equilibria in the Ammonia-Water System,” J. Chem. Eng. Data, 32(2), pp. 183–191.
Ma, X. H., Su, F. M., Chen, J. B., Bai, T., and Han, Z. X., 2009, “Enhancement of Bubble Absorption Process Using a CNTs-NH3 Binary Nanofluid,” Int. Commun. Heat Mass, 36(7), pp. 657–660.
Su, F. M., Ma, X. H., and Lan, Z., 2011, “The Effect of Carbon Nanotubes on the Physical Properties of a Binary Nanofluids,” J. Taiwan Inst. Chem. Eng., 42(2), pp. 252–257.
Su, F. M., Ma, X. H., and Chen, J. B., 2009, “Effect of Nanoparticles on Forming Process of Bubbles in a Nanofluid,” Proceedings of the ASME 2nd Micro/Nanoscale Heat & Mass Transfer International Conference, Shanghai, China, Dec. 18–21, pp. 425–430.

## Figures

Fig. 1

Physical model of the NH3/H2O bubble absorption

Fig. 2

Solution concentration versus equilibrium temperature (P = 0.315 MPa)

Fig. 3

Flowchart of the model

Fig. 4

Mass diffusion and thermal conductivity enhancement in a nanofluid

Fig. 5

Mean absorption rate versus volume fraction of nanoparticles (d0 = 2 mm and QN = 0.45 l/min)

Fig. 6

Effective absorption ratio versus volume fraction of nanoparticles (d0 = 2 mm and QN = 0.45 l/min)

Fig. 7

Mean absorption rate versus nozzle diameter (CN = 0.5 vol. % and QN = 0.45 l/min)

Fig. 8

Effective absorption ratio versus nozzle diameter (CN = 0.5 vol. % and QN = 0.45 l/min)

Fig. 9

Mean absorption rate versus flow rate of ammonia vapor (CN = 0.5 vol. % and d0 = 2 mm)

Fig. 10

Effective absorption ratio versus flow rate of ammonia vapor (CN = 0.5 vol. % and d0 = 2 mm)

## Tables

Table 1 Operational conditions of bubble absorption
Table 2 Physical properties of pure working pair

## Discussions

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