Numerical Study on Convective Heat Transfer Enhancement in Horizontal Rectangle Enclosures Filled with Ag-Ga Nanofluid
- Cong Qi^{1}Email author,
- Liyuan Yang^{1} and
- Guiqing Wang^{1}
Received: 15 February 2017
Accepted: 20 April 2017
Published: 4 May 2017
Abstract
The natural convection heat transfer of horizontal rectangle enclosures with different aspect ratios (A = 2:1 and A = 4:1) filled with Ag-Ga nanofluid (different nanoparticle volume fractions φ = 0.01, φ = 0.03, φ = 0.05 and radiuses r = 20 nm, r = 40 nm, r = 80 nm) at different Rayleigh numbers (Ra = 1 × 10^{3} and Ra = 1 × 10^{5}) is investigated by a two-phase lattice Boltzmann model. It is found that the Nusselt number enhancement ratios of two enclosures (A = 2:1 and A = 4:1) filled with Ag-Ga nanofluid (r = 20 nm) are the same compared with those of the water at the corresponding aspect ratio enclosure. The more flat horizontal rectangular enclosure (A = 4:1) has the higher Nusselt number than the less flat horizontal rectangular enclosure (A = 2:1). It is also found that Nusselt number increases with the decreasing nanoparticle radius. Nusselt number enhancement ratios for every nanoparticle radius reducing by half at high Rayleigh number are higher than those at low Rayleigh number in most cases. The interaction forces between particles are also investigated in this paper. It is found that the Brownian force F _{B} is about two magnitudes greater than that of drag force F _{D}, and the value of driving force F _{S} in A = 4:1 enclosure is about twice the value of driving force F _{S} in A = 2:1 enclosure while other forces are almost the same.
Keywords
Background
Heat transfer enhancement attracts more and more people’s attention. One method is to improve the structure of the heat exchanger, and another method is to find new fluid with higher heat transfer performance instead of the common fluid. People have studied the structures of the heat exchangers for many years. About the heat transfer medium, since the nanofluid with high thermal conductivity is prepared, the thermal properties [1–3] and heat transfer performance [4–9] of nanofluid are studied by more and more researchers.
Natural convection heat transfer is an important heat transfer process. The natural convection heat transfer characteristics of nanofluid have been widely investigated by experimental and numerical methods respectively.
Natural convection heat transfer characteristics of nanofluid are experimentally investigated by many researchers. Ho et al. [10] experimentally investigated the natural convection heat transfer of Al_{2}O_{3}-water nanofluid in different size enclosures respectively, and the effects of nanoparticle volume fraction and Rayleigh number on the natural convection heat transfer of nanofluid are discussed. Heris et al. [11–13] experimentally investigated the laminar flow convective heat transfer of CuO-water, Al_{2}O_{3}-water, and Cu-water nanofluid in a circular tube respectively. Hu et al. [14] experimentally investigated the natural convection heat transfer of TiO_{2}-water nanofluid with different nanoparticle mass fractions, and the effects of Rayleigh number on natural convection heat transfer are discussed. Sommers et al. [15] experimentally investigated the convection heat transfer of Al_{2}O_{3}-propanol nanofluid through a copper pipe, and the effects of heat rate on the convection heat transfer are discussed.
In addition to the experimental method, numerical simulation is also an important method to study the natural convection heat transfer of nanofluid. Many researchers have investigated the natural convection heat transfer of nanofluid by various numerical methods. He et al. [16] investigated the convection heat transfer of TiO_{2}-water nanofluid flowing through a straight tube by a single-phase method and a combined Euler and Lagrange method respectively. The effects of nanoparticle fraction, Reynolds number, and nanoparticle aggregated size on the convection heat transfer are discussed. Bianco et al. [17–19] investigated the convection flow of a circular tube filled with Al_{2}O_{3}-water nanofluid under different conditions respectively. Akbarinia et al. [20–22] investigated the mixed convection of Al_{2}O_{3}-water nanofluid in a horizontal curved tube, annulus and elliptic ducts respectively. Sheikholeslami et al. [23–27] investigated the natural convection heat transfer of various kinds of nanofluid under magnetic field and revealed the heat transfer enhancement mechanism of nanofluid. Qi et al. [28–30] investigated the natural convection heat transfer of Cu/Al_{2}O_{3}-water, Al_{2}O_{3}-water, and Cu-gallium in an enclosure by a lattice Boltzmann method respectively.
The above literatures made a great contribution to the researches on the effects of macro-factors (nanoparticle volume fraction, kinds of nanofluid, and so on) on the heat transfer of nanofluid. The effects of micro-factors (nanoparticle radius) on the heat transfer of nanofluid are needed to be studied. Hence, in our previous published paper [31], the natural convection heat transfer of a vertical rectangle enclosure (the left and the right walls are hot and cold walls, respectively, and other walls are adiabatic) filled with Cu-Ga nanofluid with various radius nanoparticles is investigated. In order to reveal the effects of different laying forms of the rectangle enclosure and different boundary conditions in the natural convection heat transfer of nanofluid with different nanoparticle radiuses, the natural convection of a horizontal rectangle enclosure (the left and right walls are all hot walls, and other walls are all cold walls) filled with Ag-Ga nanofluid with various radius nanoparticles is investigated in this paper.
Methods
The natural convection of the horizontal rectangle enclosure filled with Ag-Ga nanofluid with various radiuses of nanoparticles is simulated by a two-phase lattice Boltzmann model. The two-phase lattice Boltzmann model for nanofluid has been developed by us in the previous published paper [31]. The main basic equations of the two-phase lattice Boltzmann model are given as follows:
The other details of this model can be seen in the previous published paper [31].
Results and Discussion
Thermo-physical parameters. Thermo-physical parameters of liquid metal gallium and silver nanoparticle
Grid independence test. Numerical simulation results at different grids (Ra = 1 × 10^{5}, φ = 0.05)
Grid number | 78 × 39 | 128 × 64 | 198 × 99 | 256 × 128 | 300 × 150 |
---|---|---|---|---|---|
Nu _{avg} | 1.583 | 1.770 | 1.789 | 1.805 | 1.806 |
The reliability and accuracy of the two-phase lattice Boltzmann model have been verified in the previous published paper [31].
Ranges of driving force and interaction forces, A = 2:1. Ranges of driving force and interaction forces between particles in the nanofluid (A = 2:1, Ra = 10^{5}, φ = 0.01)
Forces | r = 20 nm | r = 40 nm | r = 80 nm |
---|---|---|---|
F _{S} | −1.2E−5 ~ 1.2E−5 | −1.2E−5 ~ 1.2E−5 | −1.2E−5 ~ 1.2E−5 |
F _{A} | −3.2E−19 ~ −2E−20 | −8E−19 ~ −5E−20 | −2.8E−18 ~ −2E−19 |
F _{Bx } | −5E−13 ~ 5E−13 | −5E−13 ~ 5E−13 | −5E−13 ~ 5E−13 |
F _{By } | 2E−14 ~ 2E−13 | 2E−14 ~ 2E−13 | 2E−14 ~ 2E−13 |
F _{H} | −9E−19 ~ −1E−19 | −7.5E−18 ~ −5E−19 | −6E−17 ~ −5E−18 |
F _{Dx } | −7E−15 ~ 7E−15 | −1.2E−14 ~ 1.2E−14 | −2E−14 ~ 2E−14 |
F _{Dy } | −8E−15 ~ 7E−15 | −1.4E−14 ~ 1.2E−14 | −2E−14 ~ 2E−14 |
Ranges of driving force and interaction forces, A = 4:1. Ranges of driving force and interaction forces between particles in the nanofluid (A = 4:1, Ra = 10^{5}, φ = 0.01)
Forces | r = 20 nm | r = 40 nm | r = 80 nm |
---|---|---|---|
F _{S} | −2.5E−5 ~ 2.5E−5 | −2.5E−5 ~ 2.5E−5 | −2.5E−5 ~ 2.5E−5 |
F _{A} | −3.2E−19 ~ −2E−20 | −8E−19 ~ −5E−20 | −2.8E−18 ~ −2E−19 |
F _{Bx } | −5E−13 ~ 5E−13 | −5E−13 ~ 5E−13 | −5E−13 ~ 5E−13 |
F _{By } | 2E−14 ~ 2E−13 | 2E−14 ~ 2E−13 | 2E−14 ~ 2E−13 |
F _{H} | −9.5E−19 ~ −5E−20 | −7.5E−18 ~ −5E−19 | −6E−17 ~ −5E−18 |
F _{Dx } | −7E−15 ~ 7E−15 | −1.2E−14 ~ 1.6E−14 | −2.5E−14 ~ 2.5E−14 |
F _{Dy } | −8E−15 ~ 7E−15 | −1.4E−14 ~ 1.2E−14 | −2E−14 ~ 2E−14 |
Rayleigh number | Aspect ratio | Radius | a | b | c | d |
---|---|---|---|---|---|---|
Ra = 10^{3} | A = 2:1 | r = 20 nm | 3.59358 | 0.06429 | −0.01577 | 0.00147 |
r = 40 nm | 3.59358 | 0.04796 | −0.00939 | 7.64995E−5 | ||
r = 80 nm | 3.59358 | 0.03084 | −0.00269 | −2.08674E−5 | ||
A = 4:1 | r = 20 nm | 3.65026 | 0.06397 | −0.01564 | 0.00146 | |
r = 40 nm | 3.65026 | 0.04806 | −0.00941 | 7.68036E−4 | ||
r = 80 nm | 3.65026 | 0.03163 | −0.00299 | 5.39622E−5 | ||
Ra = 10^{5} | A = 2:1 | r = 20 nm | 5.28555 | 0.04797 | −0.00721 | 4.30087E−4 |
r = 40 nm | 5.28555 | 0.00677 | 0.00651 | −8.59108E−4 | ||
r = 80 nm | 5.28555 | −0.00136 | 0.00725 | −8.87629E−4 | ||
A = 4:1 | r = 20 nm | 5.37596 | 0.04436 | −0.00691 | 4.97021E−4 | |
r = 40 nm | 5.37596 | 0.00938 | 0.00406 | −7.42333E−4 | ||
r = 80 nm | 5.37596 | 0.00554 | 0.00195 | −4.0572E−4 |
Nusselt number enhancement ratios. Nusselt number enhancement ratios for every nanoparticle radius reducing by half
A | φ | Ra = 10^{3} | Ra = 10^{3} | Ra = 10^{5} | Ra = 10^{5} |
---|---|---|---|---|---|
\( \frac{N{u}_{r=20}- N{u}_{r=40}}{N{u}_{r=40}} \) | \( \frac{N{u}_{r=40}- N{u}_{r=80}}{N{u}_{r=80}} \) | \( \frac{N{u}_{r=20}- N{u}_{r=40}}{N{u}_{r=40}} \) | \( \frac{N{u}_{r=40}- N{u}_{r=80}}{N{u}_{r=80}} \) | ||
2:1 | 1% | 0.3% | 0.3% | 0.54% | 0.14% |
3% | 0.28% | 0.3% | 0.65% | 0.35% | |
5% | 0.29% | 0.3% | 0.45% | 0.48% | |
4:1 | 1% | 0.29% | 0.29% | 0.47% | 0.10% |
3% | 0.28% | 0.29% | 0.73% | 0.40% | |
5% | 0.28% | 0.29% | 1.0% | 0.56% |
Conclusions
- 1.
Nusselt number increases with the decrease of the nanoparticle radius. The Nusselt number enhancement ratios of two enclosures (A = 4:1 and A = 2:1) filled with Ag-Ga nanofluid (r = 20 nm) are the same compared with those of the water at the corresponding enclosure. For both A = 4:1 and A = 2:1, Ag-Ga nanofluid with the smallest nanoparticle radius (r = 20 nm) can enhance the heat transfer by 3.1 and 2.1% at best compared with water at Ra = 10^{3} and Ra = 10^{5} respectively.
- 2.
The more flat horizontal rectangular enclosure (A = 4:1) has the higher Nusselt number than the less flat horizontal rectangular enclosure (A = 2:1). Nusselt numbers of Ag-Ga nanofluid (r = 20 nm) in the enclosure (A = 4:1) are all 1.5% higher than those in enclosure (A = 2:1) for every nanoparticle volume fraction at Ra = 10^{3}. For Ra = 10^{5}, Nusselt numbers of the enclosure (A = 4:1) are 1.0, 1.1, and 1.6% higher than those in enclosure (A = 2:1) for φ = 1%, φ = 3%, and φ = 5% respectively.
- 3.
Nusselt number enhancement ratios for every nanoparticle radius reducing by half at high Rayleigh number are higher than those at low Rayleigh number in most cases. For the two enclosures (A = 2:1 and A = 4:1), Nusselt number enhancement ratios for every nanoparticle radius reducing by half are all about 0.3% at Ra = 10^{3}, and most of them are 0.35 to 1.0% at Ra = 10^{5}.
- 4.
The Brownian force F _{B} is about two magnitudes greater than the drag force F _{ D }. The value of driving force F _{S} in A = 4:1 enclosure is about twice the value of driving force F _{S} in A = 2:1 enclosure while other forces are almost the same.
Declarations
Acknowledgements
This work is financially supported by the “National Natural Science Foundation of China” (Grant No. 51606214) and “the Fundamental Research Funds for the Central Universities” (Grant No. 2015XKMS063).
Authors’ Contributions
CQ participated in the design of the program, carried out the numerical simulation of the nanofluid, and drafted the manuscript. LYY and GQW participated in the design of the program. All authors read and approved the final manuscript.
Competing Interests
The authors declare that they have no competing interests.
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Authors’ Affiliations
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