Experimental and Numerical Investigation on Non-Newtonian Nanofluids Flowing in Shell Side of Helical Baffled Heat Exchanger Combined with Elliptic Tubes
Abstract
:1. Introduction
2. Experimental Method
2.1. Sample Preparation and Measurements
2.2. Experimental System
2.3. Data Reduction
3. Mathematical Modeling
3.1. Physical Model
3.2. Governing Equations and Numerical Method
3.3. Boundary Conditions
- (1)
- The inlet of shell side used the mass flow inlet boundary condition as follow:
- (2)
- The outlet shell side used the pressure outlet boundary condition as follow:
- (3)
- The adiabatic wall boundary conditions were adopted for the shell walls and baffle walls:
3.4. Grid Generation and Independence
4. Results and Discussion
4.1. Thermal-Physical Properties of Non-Newtonian Nanofluids
4.2. Overall and Shell-Side Heat Transfer Coefficient
4.3. Nusselt Number and Friction Factor
4.4. Euler Number
4.5. Correlations
4.6. Comprehensive Performance
5. Conclusions
- (1)
- Experiment results have proven that the accuracy of numerical simulation model is satisfactory. Good agreements exist between experimental and numerical data. The single-phase flow model can simulate the flow and heat transfer characteristic of non-Newtonian nanofluids at low concentration.
- (2)
- The heat transfer is significantly enhanced by adding nanoparticle compared to base fluid. The overall and shell-side heat transfer coefficients of nanofluids are higher than those of base fluid at the same Reynolds number. The enhancement in heat transfer coefficient increases with the increasing in the weight fraction of MWCNTs.
- (3)
- The Nuo, fo, Euo increase with the increasing in the weight fraction of nanoparticle at the same Reynolds number. In the whole range of volume flow rate, the TPF of nanofluids are all higher than 1.0. The changes in flow and heat characteristic of nanofluids can be attributed to the enhanced thermal conductivities and viscosities.
- (4)
- Correlations for predicting the shell-side Nusselt number, friction factor and Euler number of non-Newtonian nanofluids in the helically baffled heat exchanger with elliptic tubes were obtained based on experimental results, and fitted the data very well.
Acknowledgments
Author Contributions
Conflicts of Interest
Nomenclature | |
a, b, c | coefficients in corrections |
A | surface area (m2) |
B | baffle spacing (m) |
C1, C2 | coefficients in k-ε turbulence model |
Eu | Euler number |
f | friction factor |
FT | correction factor |
j | j-factor |
k | turbulent fluctuation kinetic energy (m2·s−2) |
K | consistency index (Pa·sn) |
l | length of tube (m) |
M | mass flow rate (kg·s−1) |
n | power law index |
Nu | Nusselt number |
P | pressure (Pa) |
Pr | Prandtl number |
r | effect variable |
R | thermal resistance (m2·K−1·W−1) |
Re | Reynolds number |
T | temperature (K) |
TPF | thermal performance factor |
u, v, w | velocity (m·s−1) |
Uo | overall heat transfer coefficient based on Ao (W·m−2·K−1) |
V | volume flow rate (m3·s−1) |
xn | effect variable |
x, y, z | coordinate (mm) |
y+ | dimensionless distance from the wall |
Greek Symbol | |
ρ | density (kg·m−3) |
η | dynamic viscosity (Pa·s) |
ν | kinematic viscosity (m2·s−1) |
λ | thermal conductivity (W·m−1·K−1) |
τ | turbulent kinematic viscosity (m2·s−1) |
ε | turbulent kinetic energy dissipation rate (m2·s−3) |
δ | wall thickness (mm) |
σk | Prandtl number for k |
σε | Prandtl number for ε |
γ | shear rate (s−1) |
ζ | heat balance deviation |
ϕ | weight fraction of nanoparticle |
Δ | difference |
Subscripts | |
bf | base fluid |
f | non-Newtonian fluid |
i | inside |
in | inlet |
max | maximum |
nf | nanofluid |
o | outside |
wall | tube wall |
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Fluid | Correlations (298.15 K < T < 338.15 K) | ||||
---|---|---|---|---|---|
K (m2·sn) | n | λ (W·m−1·K−1) | ρ (kg·m−3) | cp (kJ·kg−1·K−1) | |
Base fluid | −0.0131T + 4.6322 (R2 = 0.999) | 0.0043T − 0.9469 (R2 = 0.988) | 0.0043T − 0.6265 (R2 = 0.979) | −0.0073T2 + 4.2840T + 382.8 (R2 = 0.991) | −2.7149 × 10 − 5T2 − 0.01189T + 4.8763 (R2 = 0.996) |
0.2 wt % MWCNTs/XG | −0.0124T + 4.4211 (R2 = 0.999) | 0.0040T − 0.8517 (R2 = 0.989) | 0.0035T − 0.4168 (R2 = 0.987) | −0.0067T2 + 3.8902T + 451.2 (R2 = 0.991) | −5.4948 × 10 − 5T2 + 0.04071T − 3.5919 (R2 = 0.991) |
0.5 wt % MWCNTs/XG | −0.0111T + 4.1513 (R2 = 0.992) | 0.0025T − 0.3962 (R2 = 0.982) | 0.0026T − 0.1468 (R2 = 0.995) | −0.0052T2 + 2.9004T + 611.5 (R2 = 0.990) | −3.9137 × 10 − 5T2 + 0.03135T − 2.3183 (R2 = 0.998) |
1.0 wt % MWCNTs/XG | −0.0130T + 4.8356 (R2 = 0.996) | 0.0021T − 0.3016 (R2= 0.998) | 0.0025T − 0.1473 (R2 = 0.988) | −0.0016T2 + 0.6362T + 965.2 (R2 = 0.987) | 6.9542 × 10 − 5T2 − 0.04154T + 9.6727 (R2 = 0.972) |
Non-Dimensional Number | Fluid | Average Deviation |
---|---|---|
Nuo | Base fluid | 5.11% |
0.2 wt % MWCNTs/XG | 5.63% | |
0.5 wt % MWCNTs/XG | 1.17% | |
1.0 wt % MWCNTs/XG | −1.14% | |
fo | Base fluid | 0.25% |
0.2 wt % MWCNTs/XG | 0.60% | |
0.5 wt % MWCNTs/XG | −0.62% | |
1.0 wt % MWCNTs/XG | −5.06% |
Correlation | a | b | c | Maximum Deviation |
---|---|---|---|---|
Equation (15) | 0.0284 | 0.8692 | 0.3081 | 9.62% |
Equation (16) | 4.8456 | −0.4650 | 0.4484 | 4.04% |
Equation (17) | 310.17 | −0.4694 | 0.4364 | 4.66% |
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Ling, Z.; He, Z.; Xu, T.; Fang, X.; Gao, X.; Zhang, Z. Experimental and Numerical Investigation on Non-Newtonian Nanofluids Flowing in Shell Side of Helical Baffled Heat Exchanger Combined with Elliptic Tubes. Appl. Sci. 2017, 7, 48. https://doi.org/10.3390/app7010048
Ling Z, He Z, Xu T, Fang X, Gao X, Zhang Z. Experimental and Numerical Investigation on Non-Newtonian Nanofluids Flowing in Shell Side of Helical Baffled Heat Exchanger Combined with Elliptic Tubes. Applied Sciences. 2017; 7(1):48. https://doi.org/10.3390/app7010048
Chicago/Turabian StyleLing, Ziye, Zhenbin He, Tao Xu, Xiaoming Fang, Xuenong Gao, and Zhengguo Zhang. 2017. "Experimental and Numerical Investigation on Non-Newtonian Nanofluids Flowing in Shell Side of Helical Baffled Heat Exchanger Combined with Elliptic Tubes" Applied Sciences 7, no. 1: 48. https://doi.org/10.3390/app7010048
APA StyleLing, Z., He, Z., Xu, T., Fang, X., Gao, X., & Zhang, Z. (2017). Experimental and Numerical Investigation on Non-Newtonian Nanofluids Flowing in Shell Side of Helical Baffled Heat Exchanger Combined with Elliptic Tubes. Applied Sciences, 7(1), 48. https://doi.org/10.3390/app7010048