T. Sathish
OPEN ACCESS
Base fluids like water, ethylene glycolandengineoilare conventionally used as a heat transfer medium. The performance of heat transferred is improved in the conventional fluids with the addition of Nano particles. Hence, this paper considers the forced conventional flow problem over the base fluid within a uniform heated tube placed on a wall. The analysis of heattransferco-efficientis done through a constant Reynoldsnumberfor both Nano and base fluid with a simulation tool. Further, a comparative analysis is carried out with heat transfer coefficient over the base and various Nano fluids. It is seen that the Nano fluids has a better performance due to its better thermal characteristics under standard conditions.
heat transfer coefficient, CFX simulation, ansys simulation, nano fluid and base fluid
The Nano fluids contains fluid with Nanometer-sized particles [1], which has good stability, increased thermal conductivity even with small suspended Nanoparticles and heat transferring performance. The Nano fluidmaterials vary based on metal oxides, chemically stable metals, metal carbides, oxide ceramics etc. However, most literatures focus on single-particle based Nano fluids to test the thermal characteristics [2]. The thermal fluids like oil, water and ethylene glycol plays a major role in cooling process in many power applications. However, these fluid contains poor thermal properties and the properties of heat transfer rate is affected. Hence, to heat transfer coefficient is improved with the help of extended surface channels, surface vibration and fluid injection. The use of new technology is being an enhancing factor to improve the thermal properties of such substance [3].
The main advantage of Nano fluids include ling term stability, superior thermal conductivity and reduced drop in pressure, when compared with mm and μm sized particle. The materials like metal carbides, oxide ceramics, metals, nitrides, nonmetals, carbon Nanotubes and Nanoparticles is used to form the Nano fluid. A synthesis optimization is used to make the suspensions of Nanoparticle to be stable inside the base fluid.
In order to improve the thermal properties, several combinations of base fluid with Nano particle is possible. Also, the Nano fluids are produced using a single step or two step method, where the former one uses formation and dispersion of Nanoparticles within the base fluid, using several experimental procedures [4]. Hence, the use of storage, drying, transportation and dispersion is avoided with such method.
The solid substance possesses better thermal conductivities than other substances. Most researches concentrated on the thermal properties associated with the suspension of solid particles in conventional fluids. Such dispersed particles vary from mm to μm size over the base fluid and this leads to change in thermo-physical properties of such fluid and that results in enhancing the heat transfer ratio. The main disadvantage of such mm to μm sized particle leads to poor stability and suspension and this results in channel clogging. However, recent advances with the help of new materials improves the thermal properties of the fluid than the conventional fluids [5]. From conventional studies, it is seen than the thermal conductivity of the Nano fluids is found higher than base fluid [6-8].
Out of which, water is used as a base fluid, where a rod and spherical shaped TiO2 [9] Nanoparticles are dispersed in water. The use of aqueous/non-aqueous solution as base fluid is used with metal oxide particles of varying shapes and concentration [10]. The water is further used with Al2O3 [11, 12], Fe3O4 [13], NH3 [14], Al2O3and TiO2 [15], MgO [16], COOH [17], to measure the pH effect with varying thermal conductivity. With different fractional weights, the copper based water base fluid is used to measure the pH rate with sodium dodecyl benzene sulfonate surfactant [18]. Also, water is used with carbon Nano tubes and TiO2 [19] with carbon Nano tubes measures the time and temperature [20] variations and Nanodiamond particle with deionized fluid measures varying loads [21]. Nanoparticlesgraphene [22], Nanoshell [23], graphene oxide Nanosheets [24] and Nano diamond [25] with water as base fluids.
The use of Ethylene Glycol as base fluid is experimented in several researches, which includes: synthetic EG multiwalled carbon Nanotubes [26], ZnO-EG Nano fluids [27, 28], Al-Zn with EG Nanoparticles [29], graphene Nanosheets with EG [30], Aluminum nitride with EG Nanoparticle [31], Al2Cu and Ag2Al with EG Nanoparticles [32], Al2O3, CuO, ZnO with EG [33], TiO2Nanoparticles with EG [34], CuO Nanoparticles [35], Cu Nanoparticles [36], α-SiC Nano fluids [37], spherical ZnO Nanoparticles [38], Al2O3 with EG and water [39, 40].
The increased techniques to improve the heat transfer coefficients suffer majorly the important strategy required to achieve effective heat transfer over conventional base fluid. Hence, the heat transfer is intensified with the suspension of Nanoparticles with the use of base fluid. In the proposed work, we considered the problem of improving the heat transfer coefficient by the use of Nano fluids. Here, base fluids like engine oil, ethylene glycol and water and the Nanoparticles of gold, copper, aluminum and silver is used. Empirical relations are used to calculate the properties of the Nano fluids. Further, the thermo-physical properties of ethylene glycol, water, copper, engine oil, gold, aluminum and silver is calculated to find the Nano fluid properties. The heat transfer rate of the Nano and base fluid is analysed with the use of CFX simulation tool under a constant Reynolds number. Finally, comparative analysis is carried between the thermal conductivity models namely, Maxwell, Hamilton and Crosser, and Davis models [41, 42].
The outline of the paper is mentioned as follows: Section 2 provides the proposed model to analyse the flow rate in base and Nano fluid analysis. Section 3 provides the experimental method for finding the thermo-physical properties. Section 4 provides the evaluation on different combinations of Nano fluids with base fluid. Section 5 concludes the paper.
Figure 1. Experimental Setup
Figure 2. Geometry of Tube
The experimental setup of the proposed method is shown in Figure 1. The system has alooping pipeline flow structure, pumping and copper tube of length1mand diameter 60mm and are servoir tank. Further, the tube is insulated with 25mm glass made of fiber and heat electrically at 5000 W/m2. The tube is coated with nickel chrome wire, which is connected with a 300W DC supply. The tube is installed with four k type tube, where two of which is placed at two end. This is used to measure the temperature of the Nano fluid.
The numerical simulation uses single phase method to find the values of convective heat transfer. Here, the geometry of the tube is shown in Figure 2. The tube allows the Nano fluidto enter at a uniform velocity rate (U1)and the rate of temperature(T1).The condition of full development is assumed at the tube end. Based on the tube’s centerline, the assumptions are made symmetrically on thermal and velocity fields. The local heat transfer coefficient rate is hlocal:
${{h}_{local}}=\frac{\left( {{T}_{local}}-{{T}_{input}} \right)\rho CpuD}{4\pi \left( {{T}_{w}}-{{T}_{input}} \right)}$ (1)
The averagerate of heattransferco-efficient is given as have:
${{h}_{ave}}=\frac{1}{L\int_{0}^{L}{h\left( z \right)dz}}$ (2)
The Average Nusselt number is then given by:
$N{{u}_{ave}}=\frac{{{h}_{ave}}D}{{{K}_{af}}}$ (3)
Heat transfer(Q)
$Q=\sqrt{\frac{{{C}_{d}}{{a}_{1}}{{a}_{2}}\left( 2g{{h}_{a}} \right)}{\left( a_{1}^{2}-a_{2}^{2} \right)}}$ (4)
The measuring the thermal conductivity of the Nano fluid use heat transfer coefficient, both in forced and natural fluid flow. The main limitation involves thermal characteristics of the Nanoparticles without changing the phase. The proposed model uses two phase systems for finding the heat transfer ratio of particles in the Nano fluid. Here, the coefficient of heat transfer rate depends on thermal conductivity, density, specific heat ratio and dynamic viscosity of particles in the Nano fluid. The properties of particles in the Nano fluid at normal temperature is shown in Table 1 and the properties of base fluid at normal temperature is shown in Table 2.
Table 1. Nano particles Properties
|
Property |
Copper |
Gold |
Silver |
Aluminum |
|
Thermal conductivity (KS)W/mK |
401 |
317 |
429 |
237 |
|
Density (ρp)kg/m3 |
8933 |
19300 |
10500 |
2702 |
|
Specific heat (CP) J/kg K |
385 |
129 |
235 |
903 |
Table 2. Base Fluid Properties
|
Property |
Water |
E. glycol |
Engine Oil |
|
Thermal conductivity (Kf)W/mK |
0.613 |
0.252 |
0.145 |
|
Density (ρf)kg/m3 |
996.5 |
1114.4 |
884.1 |
|
Specific heat (Cf)J/kgK |
4179 |
2415 |
1909 |
|
Dynamic viscosity (µf) Kg/ms |
0.000855 |
0.0157 |
0.486 |
3.1. Density Estimation
The Nanofluiddensity is calculatedwith massbalance, which is given as:
ρnf=(1-φS)ρf+φSρp (5)
The particles present in the Nano fluid has a volume fraction < 1% and the changeof <5%fluiddensityis thus expected. Further, the density for 1% particles with copper mix and water as base fluid, the Nano fluid density is found to be 1075.865Kg/m3. From Eq. (5), the Nano fluid density for different % mixes i.e. 1,3,5,...,25, various combinations are calculated, which is shown in Table.3. The different mixture of Nano fluids include: copper as base fluid with water as Nano fluid, gold as base fluid with water as Nano fluid, silver as base fluid with water as Nano fluid, aluminum as base fluid with water as Nano fluid, copper as base fluid with ethyleneglycol as Nano fluid, gold as base fluid and ethyleneglycol as Nano fluid, silver as base fluid with ethyleneglycol as Nano fluid, aluminum as base fluid with ethyleneglycol as Nano fluid, copper as base fluid with engine oil as Nano fluid, gold as base fluid with engine oil as Nano fluid, silver as base fluid with engine oil as Nano fluid and finally aluminum as base fluid with engine oil as Nano fluid. The density of these base fluid and Nano fluid mixtures are shown in Table 3.
Table 3. Various Nano fluid Density (in Kg/m3)with different base fluid combinations
|
Volume fraction (%) |
copper- water |
gold- water |
silver-water |
aluminum - water |
copper-Ethylene glycol |
gold-Ethylene glycol |
silver-Ethylene glycol |
aluminum-Ethylene glycol |
copper-Engine Oil |
gold-Engine Oil |
silver-Engine Oil |
aluminum- Engine Oil |
|
1 |
1075.865 |
1179.535 |
1091.535 |
1013.555 |
1192.586 |
1296.256 |
1208.256 |
1130.276 |
964.589 |
1068.259 |
980.259 |
902.279 |
|
3 |
1234.595 |
1545.605 |
1281.605 |
1047.665 |
1348.958 |
1659.968 |
1395.968 |
1162.028 |
1125.567 |
1436.577 |
1172.577 |
938.637 |
|
5 |
1393.325 |
1911.675 |
1471.675 |
1081.775 |
1505.33 |
2023.68 |
1583.68 |
1193.78 |
1286.545 |
1804.895 |
1364.895 |
974.995 |
|
7 |
1552.055 |
2277.745 |
1661.745 |
1115.885 |
1661.702 |
2387.392 |
1771.392 |
1225.532 |
1447.523 |
2173.213 |
1557.213 |
1011.353 |
|
9 |
1710.785 |
2643.815 |
1851.815 |
1149.995 |
1818.074 |
2751.104 |
1959.104 |
1257.284 |
1608.501 |
2541.531 |
1749.531 |
1047.711 |
|
11 |
1869.515 |
3009.885 |
2041.885 |
1184.105 |
1974.446 |
3114.816 |
2146.816 |
1289.036 |
1769.479 |
2909.849 |
1941.849 |
1084.069 |
|
13 |
2028.245 |
3375.955 |
2231.955 |
1218.215 |
2130.818 |
3478.528 |
2334.528 |
1320.788 |
1930.457 |
3278.167 |
2134.167 |
1120.427 |
|
15 |
2186.975 |
3742.025 |
2422.025 |
1252.325 |
2287.19 |
3842.24 |
2522.24 |
1352.54 |
2091.435 |
3646.485 |
2326.485 |
1156.785 |
|
17 |
2345.705 |
4108.095 |
2612.095 |
1286.435 |
2443.562 |
4205.952 |
2709.952 |
1384.292 |
2252.413 |
4014.803 |
2518.803 |
1193.143 |
|
19 |
2504.435 |
4474.165 |
2802.165 |
1320.545 |
2599.934 |
4569.664 |
2897.664 |
1416.044 |
2413.391 |
4383.121 |
2711.121 |
1229.501 |
|
21 |
2663.165 |
4840.235 |
2992.235 |
1354.655 |
2756.306 |
4933.376 |
3085.376 |
1447.796 |
2574.369 |
4751.439 |
2903.439 |
1265.859 |
|
23 |
2821.895 |
5206.305 |
3182.305 |
1388.765 |
2912.678 |
5297.088 |
3273.088 |
1479.548 |
2735.347 |
5119.757 |
3095.757 |
1302.217 |
|
25 |
2980.625 |
5572.375 |
3372.375 |
1422.875 |
3069.05 |
5660.8 |
3460.8 |
1511.3 |
2896.325 |
5488.075 |
3288.075 |
1338.575 |
3.2. Specific heat estimation
The estimation of specific heat of Nano fluids with mass balance is calculated as:
(1-φS)ρfCf+φSρpCP (6)
where, Cnf=ρnf, a small reduction over the Nano particle’s specific heat while the dispersion of solid particle in liquid is estimated using following calculations. Further, the specific heat for 1% particles with aluminum oxide mix and water as base fluid, the Nano fluid density is found to be 3863.981J/KgK. The specific heat for other Nano-fluid mixes for different percentage is shown in Table 4.
Table 4. Nano fluid Specific Heat Capacity (inJ/KgK) with different base fluid combinations
|
Nano particle % |
copper- Water |
gold-Water |
silver-Water |
Aluminum -Water |
copper-Ethylene glycol |
gold-Ethylene glycol |
silver-Ethylene glycol |
aluminum-Ethylene glycol |
copper- Engine Oil |
gold-Engine Oil |
silver-Engine Oil |
aluminum- Engine Oil |
|
1 |
3863.981 |
3516.324 |
3799.608 |
4091.666 |
2262.944 |
2074.637 |
2225.553 |
2378.855 |
1767.863 |
1587.411 |
1729.69 |
1878.874 |
|
3 |
3355.447 |
2661.827 |
3209.622 |
3925.529 |
2011.711 |
1617.639 |
1923.083 |
2309.527 |
1546.146 |
1191.586 |
1459.298 |
1822.123 |
|
5 |
2962.78 |
2134.589 |
2772.032 |
3769.869 |
1812.674 |
1324.912 |
1692.316 |
2243.887 |
1379.913 |
957.3103 |
1265.104 |
1769.604 |
|
7 |
2650.429 |
1776.822 |
2434.545 |
3623.725 |
1651.097 |
1121.377 |
1510.457 |
2181.649 |
1250.653 |
802.4449 |
1118.877 |
1720.861 |
|
9 |
2396.039 |
1518.129 |
2166.337 |
3486.251 |
1517.314 |
971.6587 |
1363.448 |
2122.554 |
1147.266 |
692.4656 |
1004.798 |
1675.501 |
|
11 |
2184.847 |
1322.363 |
1948.061 |
3356.697 |
1404.722 |
856.9054 |
1242.147 |
2066.37 |
1062.69 |
610.3278 |
913.315 |
1633.184 |
|
13 |
2006.711 |
1169.052 |
1766.962 |
3234.398 |
1308.656 |
766.1491 |
1140.353 |
2012.888 |
992.2192 |
546.6472 |
838.32 |
1593.613 |
|
15 |
1854.433 |
1045.737 |
1614.287 |
3118.762 |
1225.725 |
692.5751 |
1053.71 |
1961.916 |
932.5968 |
495.8309 |
775.7238 |
1556.53 |
|
17 |
1722.763 |
944.3986 |
1483.83 |
3009.257 |
1153.408 |
631.7257 |
979.0705 |
1913.284 |
881.4968 |
454.3383 |
722.6865 |
1521.707 |
|
19 |
1607.784 |
859.6432 |
1371.071 |
2905.41 |
1089.79 |
580.5627 |
914.1013 |
1866.832 |
837.2137 |
419.8191 |
677.1738 |
1488.943 |
|
21 |
1506.511 |
787.708 |
1272.637 |
2806.792 |
1033.391 |
536.9437 |
857.0375 |
1822.417 |
798.4687 |
390.6516 |
637.6904 |
1458.062 |
|
23 |
1416.631 |
725.8888 |
1185.962 |
2713.019 |
983.0471 |
499.3146 |
806.519 |
1779.909 |
764.2841 |
365.6807 |
603.1126 |
1428.904 |
|
25 |
1336.324 |
672.1919 |
1109.057 |
2623.742 |
937.8336 |
466.521 |
761.4806 |
1739.187 |
733.8995 |
344.0615 |
572.5798 |
1401.331 |
3.3. Velocity of Nano Fluid
The input parameter for the simulation model is the velocity of Nano fluid possessing its own materialistic properties. Initially, the co-efficient for heat transfer rate is estimated for base and Nano fluid using constant Reynold number, where Re = udρ/μ = 2000.The velocity of the water is found as 0.29m/s, and for ethylene glycol =4.7m/s and engine oil is 183m/s. Further, the velocity of different Nano-fluid mixes for different percentage is shown in Table 5.
Table 5. Velocity (in m/s) of Different Nano fluid mixtures
|
Nano particle % |
copper-Water |
gold-Water |
silver-Water |
aluminum -Water |
copper-Ethylene glycol |
gold-Ethylene glycol |
silver-Ethylene glycol |
aluminum-Ethylene glycol |
copper-Engine Oil |
gold-Engine Oil |
silver-Engine Oil |
aluminum- Engine Oil |
|
1 |
0.264903 |
0.241621 |
0.2611 |
0.281188 |
4.388223 |
4.037268 |
4.331312 |
4.630138 |
167.9472 |
151.6486 |
165.2624 |
179.5454 |
|
3 |
0.230845 |
0.184394 |
0.222377 |
0.272034 |
3.879538 |
3.152671 |
3.748892 |
4.503621 |
143.9275 |
112.7681 |
138.1572 |
172.5907 |
|
5 |
0.204547 |
0.149084 |
0.193657 |
0.263456 |
3.476536 |
2.586048 |
3.30454 |
4.383834 |
125.9186 |
89.75591 |
118.6904 |
166.1547 |
|
7 |
0.183628 |
0.125124 |
0.171506 |
0.255403 |
3.149381 |
2.192071 |
2.954362 |
4.270254 |
111.9153 |
74.544 |
104.032 |
160.1815 |
|
9 |
0.16659 |
0.107799 |
0.153903 |
0.247827 |
2.878504 |
1.902267 |
2.671289 |
4.162411 |
100.7149 |
63.74111 |
92.59624 |
154.6228 |
|
11 |
0.152446 |
0.094688 |
0.139577 |
0.240688 |
2.650533 |
1.680142 |
2.437719 |
4.059881 |
91.55237 |
55.67299 |
83.42564 |
149.437 |
|
13 |
0.140516 |
0.084421 |
0.127691 |
0.233949 |
2.456021 |
1.504468 |
2.241709 |
3.962281 |
83.91795 |
49.41786 |
75.90784 |
144.5877 |
|
15 |
0.130317 |
0.076162 |
0.11767 |
0.227577 |
2.288106 |
1.362053 |
2.074875 |
3.869263 |
77.45878 |
44.42634 |
69.63294 |
140.0433 |
|
17 |
0.121499 |
0.069375 |
0.109108 |
0.221542 |
2.141682 |
1.244268 |
1.931154 |
3.780513 |
71.92287 |
40.35067 |
64.31626 |
135.7758 |
|
19 |
0.113798 |
0.063699 |
0.101707 |
0.21582 |
2.012872 |
1.145234 |
1.806053 |
3.695742 |
67.12547 |
36.95997 |
59.75388 |
131.7608 |
|
21 |
0.107016 |
0.058881 |
0.095247 |
0.210386 |
1.898676 |
1.060802 |
1.696174 |
3.61469 |
62.92804 |
34.09493 |
55.7959 |
127.9763 |
|
23 |
0.100996 |
0.054741 |
0.089558 |
0.205218 |
1.796743 |
0.987964 |
1.598898 |
3.537116 |
59.22466 |
31.64213 |
52.32969 |
124.4032 |
|
25 |
0.095618 |
0.051145 |
0.08451 |
0.200299 |
1.705197 |
0.924487 |
1.512174 |
3.462802 |
55.93295 |
29.51855 |
49.26895 |
121.0242 |
3.4. Viscosity of Nano fluids
The Nano fluid viscosity is estimated using 2 phase mixtures,
µ=µ0(123φS2+7.3φS+1) (7)
Further, the viscosity of 1% particles with copper mix and water as base fluid, the Nano fluid density is 0.000928kg/ms. The combination of Nano fluid with water, ethylene glycol and engine oil is estimated and shown in Table 6.
Table 6. Nano fluid Viscosity (in kg/ms) with water, ethylene glycol and engine oil
|
Nanoparticle % |
Nanoparticle-Water |
Nanoparticle- Ethyleneglycol |
Nanoparticle- Engineoil |
|
1 |
0.000928 |
0.017039 |
0.527456 |
|
3 |
0.001137 |
0.020876 |
0.646234 |
|
5 |
0.00143 |
0.026258 |
0.812835 |
|
7 |
0.001807 |
0.033185 |
1.027258 |
|
9 |
0.002269 |
0.041657 |
1.289504 |
|
11 |
0.002814 |
0.051673 |
1.599572 |
|
13 |
0.003444 |
0.063235 |
1.957462 |
|
15 |
0.004157 |
0.076341 |
2.363175 |
|
17 |
0.004955 |
0.090992 |
2.81671 |
|
19 |
0.005837 |
0.107189 |
3.318068 |
|
21 |
0.006803 |
0.12493 |
3.867248 |
|
23 |
0.007854 |
0.144215 |
4.46425 |
|
25 |
0.008988 |
0.165046 |
5.109075 |
3.5. Nano fluid Thermal Conductivity
TheNano fluid contains smaller particles with high thermal conductivity than the base fluid. The thermal conductivity depends entirely on particle volume fraction for its better enhancement. The thermal conductivity of the Nano fluids are estimated using three models, which depends entirely on the particle shape:
3.5.1. Maxwell Model
This model considers the spherical Nano particle and the relation is given by,
$K={{K}_{L}}\frac{{{K}_{S}}+2{{K}_{L}}+2\left( {{K}_{S}}-{{K}_{L}} \right){{\phi }_{S}}}{{{K}_{S}}+2{{K}_{L}}-\left( {{K}_{S}}-{{K}_{L}} \right){{\phi }_{S}}}$ (8)
3.5.2. Hamilton and Crosser Model
This model considers the non-spherical Nanoparticle and the relation is given by,
$K={{K}_{L}}\frac{{{K}_{S}}+\left( n-1 \right){{K}_{L}}-\left( n-1 \right)\left( {{K}_{L}}-{{K}_{S}} \right){{\phi }_{S}}}{{{K}_{S}}+\left( n-1 \right){{K}_{f}}-\left( {{K}_{L}}-{{K}_{S}} \right){{\phi }_{S}}}$ (9)
where n totally depends on the shape of particleand KS/KL,Also,nis 3/ψ∀KS/KL>100 and the value of n is 3forothercases
3.5.3. Davis Model
This model considers the tubularNanoparticle and the relation is given by,
$K={{K}_{L}}\times 1+\frac{3\left( \frac{{{K}_{S}}}{{{K}_{L}}-1} \right)\left[ {{\phi }_{S}}+f.\phi _{S}^{2}+O\left( \phi _{S}^{3} \right) \right]}{\left( \frac{{{K}_{S}}}{{{K}_{L}}+2} \right)-\left( \frac{{{K}_{S}}}{{{K}_{L}}-1} \right){{\phi }_{S}}}\times {{K}_{L}}$ (10)
Table 7(a). Nano fluid thermal conductivity
|
Nano particle % |
Water & Copper |
Ethylene glycol & Copper |
Engine oil & Copper |
||||||
|
Maxwell |
Hamilton and crosser |
Davis |
Maxwell |
Hamilton and crosser |
Davis |
Maxwell |
Hamilton and crosser |
Davis |
|
|
1 |
0.63149 |
0.619042 |
0.631677 |
0.259622 |
0.25449 |
0.259699 |
0.149389 |
0.146434 |
0.149433 |
|
3 |
0.669608 |
0.630775 |
0.671357 |
0.275336 |
0.259326 |
0.276057 |
0.158439 |
0.149219 |
0.158854 |
|
5 |
0.709324 |
0.642063 |
0.714381 |
0.291711 |
0.263978 |
0.293795 |
0.167869 |
0.151898 |
0.169069 |
|
7 |
0.750739 |
0.652931 |
0.761056 |
0.308788 |
0.268457 |
0.313041 |
0.177704 |
0.154476 |
0.180153 |
|
9 |
0.793966 |
0.663402 |
0.811718 |
0.326615 |
0.272771 |
0.333934 |
0.187971 |
0.156961 |
0.192186 |
|
11 |
0.839125 |
0.673497 |
0.866735 |
0.345241 |
0.276931 |
0.356625 |
0.198699 |
0.159355 |
0.205255 |
|
13 |
0.88635 |
0.683237 |
0.926505 |
0.364721 |
0.280943 |
0.38128 |
0.209919 |
0.161665 |
0.219456 |
|
15 |
0.935785 |
0.692638 |
0.991466 |
0.385116 |
0.284816 |
0.408079 |
0.221667 |
0.163895 |
0.234892 |
|
17 |
0.98759 |
0.70172 |
1.062096 |
0.406492 |
0.288556 |
0.437221 |
0.23398 |
0.166049 |
0.251678 |
|
19 |
1.041938 |
0.710498 |
1.138921 |
0.428921 |
0.292172 |
0.468923 |
0.246901 |
0.16813 |
0.26994 |
|
21 |
1.099022 |
0.718986 |
1.222521 |
0.452483 |
0.295667 |
0.503426 |
0.260474 |
0.170143 |
0.289816 |
|
23 |
1.159054 |
0.7272 |
1.313533 |
0.477266 |
0.29905 |
0.540994 |
0.274752 |
0.17209 |
0.311459 |
|
25 |
1.222269 |
0.735151 |
1.412665 |
0.503368 |
0.302324 |
0.58192 |
0.289791 |
0.173975 |
0.335038 |
Table 7(a). Nano fluid thermal conductivity (continued)
|
Nano particle % |
Water & Gold |
Engine oil & Gold |
Ethylene glycol & Gold |
||||||
|
Maxwell |
Hamilton and crosser |
Davis |
Maxwell |
Hamilton and crosser |
Davis |
Maxwell |
Hamilton and crosser |
Davis |
|
|
1 |
0.631467 |
0.619035 |
0.631654 |
0.188879 |
0.146434 |
0.149432 |
0.259618 |
0.254489 |
0.259695 |
|
3 |
0.669538 |
0.630754 |
0.671285 |
0.192767 |
0.149218 |
0.15885 |
0.275324 |
0.259323 |
0.276045 |
|
5 |
0.709201 |
0.64203 |
0.714251 |
0.19682 |
0.151896 |
0.169062 |
0.29169 |
0.263973 |
0.293773 |
|
7 |
0.75056 |
0.652886 |
0.760863 |
0.201046 |
0.154474 |
0.180142 |
0.308758 |
0.268449 |
0.313009 |
|
9 |
0.793725 |
0.663346 |
0.811454 |
0.205458 |
0.156957 |
0.192171 |
0.326574 |
0.272762 |
0.333889 |
|
11 |
0.838817 |
0.673431 |
0.86639 |
0.210068 |
0.159352 |
0.205236 |
0.345188 |
0.276919 |
0.356567 |
|
13 |
0.885969 |
0.683161 |
0.926069 |
0.21489 |
0.161661 |
0.219431 |
0.364656 |
0.28093 |
0.381206 |
|
15 |
0.935325 |
0.692554 |
0.990926 |
0.219938 |
0.16389 |
0.234861 |
0.385038 |
0.284801 |
0.407987 |
|
17 |
0.987043 |
0.701628 |
1.06144 |
0.225229 |
0.166044 |
0.251641 |
0.406399 |
0.288541 |
0.437109 |
|
19 |
1.041297 |
0.710398 |
1.138135 |
0.230781 |
0.168125 |
0.269896 |
0.428812 |
0.292155 |
0.46879 |
|
21 |
1.098278 |
0.71888 |
1.221587 |
0.236613 |
0.170137 |
0.289764 |
0.452357 |
0.295649 |
0.503267 |
|
23 |
1.158196 |
0.727087 |
1.312432 |
0.242748 |
0.172084 |
0.311397 |
0.47712 |
0.299031 |
0.540807 |
|
25 |
1.221286 |
0.735033 |
1.411375 |
0.249209 |
0.173968 |
0.334965 |
0.503201 |
0.302304 |
0.581701 |
Table 7(b). Nano fluid thermal conductivity
|
Nano particle % |
Water & Silver |
Ethylene glycol & Silver |
Engine oil & Silver |
||||||
|
Maxwell |
Hamilton and crosser |
Davis |
Maxwell |
Hamilton and crosser |
Davis |
Maxwell |
Hamilton and crosser |
Davis |
|
|
1 |
0.631496 |
0.619044 |
0.631682 |
0.259623 |
0.254491 |
0.2597 |
0.149389 |
0.146434 |
0.149434 |
|
3 |
0.669626 |
0.63078 |
0.671375 |
0.275339 |
0.259327 |
0.27606 |
0.15844 |
0.149219 |
0.158855 |
|
5 |
0.709354 |
0.642072 |
0.714413 |
0.291716 |
0.26398 |
0.293801 |
0.16787 |
0.151898 |
0.169071 |
|
7 |
0.750783 |
0.652943 |
0.761103 |
0.308796 |
0.268459 |
0.31305 |
0.177706 |
0.154477 |
0.180156 |
|
9 |
0.794025 |
0.663416 |
0.811784 |
0.326625 |
0.272774 |
0.333945 |
0.187974 |
0.156961 |
0.19219 |
|
11 |
0.839201 |
0.673514 |
0.86682 |
0.345253 |
0.276933 |
0.35664 |
0.198703 |
0.159356 |
0.20526 |
|
13 |
0.886444 |
0.683255 |
0.926613 |
0.364737 |
0.280946 |
0.381298 |
0.209924 |
0.161666 |
0.219462 |
|
15 |
0.935899 |
0.692659 |
0.991599 |
0.385136 |
0.284819 |
0.408101 |
0.221673 |
0.163896 |
0.234899 |
|
17 |
0.987725 |
0.701743 |
1.062257 |
0.406515 |
0.28856 |
0.437248 |
0.233988 |
0.16605 |
0.251687 |
|
19 |
1.042096 |
0.710522 |
1.139115 |
0.428948 |
0.292176 |
0.468956 |
0.246909 |
0.168132 |
0.269951 |
|
21 |
1.099206 |
0.719012 |
1.222751 |
0.452514 |
0.295672 |
0.503465 |
0.260485 |
0.170144 |
0.289829 |
|
23 |
1.159266 |
0.727227 |
1.313805 |
0.477302 |
0.299054 |
0.54104 |
0.274764 |
0.172091 |
0.311474 |
|
25 |
1.222511 |
0.73518 |
1.412984 |
0.503409 |
0.302329 |
0.581974 |
0.289804 |
0.173976 |
0.335055 |
Table 7(b). Nano fluid thermal conductivity (continued)
|
Nano particle % |
Water & Aluminum |
Ethylene glycol & Aluminum |
Engine oil & Aluminum |
||||||
|
Maxwell |
Hamilton and crosser |
Davis |
Maxwell |
Hamilton and crosser |
Davis |
Maxwell |
Hamilton and crosser |
Davis |
|
|
1 |
0.631431 |
0.619023 |
0.631617 |
0.259612 |
0.254487 |
0.259689 |
0.149386 |
0.146433 |
0.14943 |
|
3 |
0.669424 |
0.630721 |
0.671167 |
0.275305 |
0.259317 |
0.276025 |
0.158428 |
0.149216 |
0.158843 |
|
5 |
0.709003 |
0.641976 |
0.714043 |
0.291656 |
0.263964 |
0.293738 |
0.167851 |
0.151893 |
0.16905 |
|
7 |
0.750271 |
0.652813 |
0.760553 |
0.308709 |
0.268437 |
0.312956 |
0.177677 |
0.15447 |
0.180125 |
|
9 |
0.793337 |
0.663256 |
0.811029 |
0.326508 |
0.272747 |
0.333817 |
0.187935 |
0.156952 |
0.192147 |
|
11 |
0.838323 |
0.673325 |
0.865834 |
0.345104 |
0.276901 |
0.356472 |
0.198653 |
0.159346 |
0.205204 |
|
13 |
0.885358 |
0.68304 |
0.925367 |
0.364552 |
0.280909 |
0.381086 |
0.209863 |
0.161654 |
0.219391 |
|
15 |
0.934586 |
0.692419 |
0.99006 |
0.384912 |
0.284779 |
0.40784 |
0.221599 |
0.163883 |
0.234813 |
|
17 |
0.986165 |
0.70148 |
1.060387 |
0.40625 |
0.288516 |
0.43693 |
0.2339 |
0.166035 |
0.251582 |
|
19 |
1.040267 |
0.710238 |
1.136872 |
0.428637 |
0.292128 |
0.468575 |
0.246806 |
0.168116 |
0.269825 |
|
21 |
1.097081 |
0.718709 |
1.220086 |
0.452153 |
0.29562 |
0.503012 |
0.260365 |
0.170127 |
0.289679 |
|
23 |
1.156817 |
0.726906 |
1.310663 |
0.476886 |
0.299 |
0.540506 |
0.274626 |
0.172073 |
0.311297 |
|
25 |
1.219707 |
0.734842 |
1.409303 |
0.502932 |
0.302272 |
0.581348 |
0.289646 |
0.173957 |
0.334848 |
Further, the thermal conductivity of 1% particles with copper mix and water as base fluid is 0.63149 using Maxwell model, 0.619042 suing Hamilton and crosser model, and 0.631677 using Davis model. The thermal conductivity of different Nano particle mixtures for all the three models is given in Table 7(a) and Table 7(b).
From the results, it is found that the Maxwell model provides a better results with regular variation and the mean values has better values than the other two models. Since, most of the particles in the Nano fluid possess spherical in shape.
This research considers the problem related to convection flow of Nano particles in a tube, which is heated uniformly. The chosen measurements for the study includes 6mm diameter and length of 170mm and the simulation analysis is carried out in Ansys Workbench tool.
The proposed tubular module is connected to a constant and uniform heat flux at the wall of the chamber. The analysis to find the heat transfer rate is analysed on base and Nano fluid with constant Reynolds number.
(a) Modeling after symmetry; (b) Modeling after meshing
Figure 3. 3D modelling of uniform heated tube
Figure 4. CFX Modelling
Table 8. Heat transfer co-efficientof Water, Ethylene glycol (E.GL) and Engine oil (E.Oil) with Nanoparticles at 333K
|
Nano particle % |
H2O + Cu |
H2O +Au |
H2O + Ag |
H2O + Al |
E.Gl + Cu |
E.Gl + Au |
E.Gl + Ag |
|||
|
CFX |
Experimental |
CFX |
Experimental |
CFX |
Experimental |
|||||
|
1 |
13540 |
13689.4 |
13610.8 |
13553.1 |
13493.3 |
13520.36 |
3935.24 |
4018.2 |
3963.36 |
3940.53 |
|
3 |
14533.5 |
14628.3 |
14681.2 |
14564.6 |
14412.6 |
14530.42 |
4262.92 |
4325.8 |
4351.45 |
4280.27 |
|
5 |
15542.4 |
15722.6 |
15584.3 |
15367.1 |
4613.62 |
4766.56 |
4644.98 |
|||
|
7 |
16572.7 |
16762.8 |
16621 |
16357.2 |
4985.12 |
5204.62 |
5032.2 |
|||
|
9 |
17629.6 |
17816.8 |
17681.4 |
17384.1 |
5376.37 |
5662.75 |
5440.7 |
|||
|
11 |
18719 |
18894 |
18772 |
18451.3 |
5788.12 |
6140.56 |
5870.95 |
|||
|
13 |
19846.1 |
20003.9 |
19898.5 |
19562.8 |
6222.22 |
6638.89 |
6324.61 |
|||
|
15 |
21014.9 |
21159.9 |
21065.5 |
20722.4 |
6680.16 |
7158.86 |
6802.98 |
|||
|
17 |
22230.6 |
22366.3 |
22278 |
21933.7 |
7163.46 |
7701.48 |
7307.41 |
|||
|
19 |
23497.6 |
23629.5 |
23543.2 |
23200.6 |
7673.6 |
8267.87 |
7839.16 |
|||
|
21 |
24821.8 |
24951.6 |
24869.8 |
24527 |
8212.31 |
8859.32 |
8399.79 |
|||
|
23 |
26213.4 |
26335.6 |
26261.3 |
25918.9 |
8782.36 |
9478.35 |
8991.85 |
|||
|
25 |
27675.5 |
27784.7 |
27725.1 |
27381.1 |
9385.15 |
10126.3 |
9616.54 |
|||
Table 8. Heat transfer co-efficientof Water, Ethylene glycol (E.GL) and Engine oil (E.Oil) with Nanoparticles at 333K (continued)
|
Nano particle % |
E.Gl + Al |
E.Oil+Cu |
E.Oil +Au |
E.Oil +Ag |
E.Oil +Al |
|||
|
CFX |
Experimental |
CFX |
Experimental |
CFX |
Experimental |
|||
|
1 |
3919.66 |
4022.3 |
2063.1 |
2098.13 |
2611.27 |
2063.21 |
2062.78 |
2125.35 |
|
3 |
4212.63 |
4275.7 |
2203.46 |
2258.93 |
2685.83 |
2203.89 |
2202.32 |
2428.8 |
|
5 |
4523.97 |
2351.2 |
2763.99 |
2352.03 |
2349.1 |
|||
|
7 |
4851.74 |
2505.11 |
2843.93 |
2506.48 |
2493.56 |
|||
|
9 |
5195.2 |
2664.68 |
2924.94 |
2666.71 |
2659.89 |
|||
|
11 |
5555.59 |
2830.4 |
3007.39 |
2833.25 |
2823.93 |
|||
|
13 |
5934.99 |
3003.09 |
3092.09 |
3006.93 |
2994.63 |
|||
|
15 |
6335.11 |
3183.36 |
3179.35 |
3188.41 |
3172.65 |
|||
|
17 |
6757.88 |
3372.03 |
3269.79 |
3378.49 |
3358.75 |
|||
|
19 |
7205.07 |
3569.77 |
3363.77 |
3577.91 |
3553.57 |
|||
|
21 |
7678.88 |
3777.6 |
3461.99 |
3787.74 |
3758.06 |
|||
|
23 |
8182.34 |
3996.7 |
3565.12 |
4009.16 |
3973.32 |
|||
|
25 |
8717.26 |
4229.73 |
3673.56 |
4243.13 |
4200.22 |
|||
Figure 5. Heat transfer co-efficient of water at 333K
Figure 6. Heat transfer co-efficient of Water with Nano particles at 333K
Figure 7. Heat transfer co-efficient of ethyleneglycolat333K
Figure 8. Heat transfer co-efficient of Ethylene glycol with Nano particles at 333K
Figure 9. Heat transfer co-efficient of engineoil at 333K
Figure 10. Heat transfer co-efficient of Engineoil with Nanoparticles at 333K
The analytical work is carried out with a CFX11.0 module inside the tubular structure, as shown in Figure 4. The modeling is done in Ansys Workbench 11.0 and imported into CFX11.0 software to analyse the flow and finding the heat transfer co-efficient of water.
From the analysis, it is found that the heat transfer coefficient (Figure 5) for water is 13048.1 W/ m2K at 333K. From Table 7 or Figure 6, it is seen that the Nano fluids other than copper, gold, silver and aluminum Nanoparticles mixture with water proves a higher heat transfer rate than water in both experimental and simulation method. Likewise, it is found that the heat transfer coefficient (Figure 7) for ethylene glycol is 3781.16 W/ m2K at 333K.
From Table 8 or Figure 8, it is seen that the Nano fluids other than copper, gold, silver and aluminum Nanoparticles mixture with ethylene glycol proves a higher heat transfer rate than ethylene glycol in both experimental and simulation method. Also, it is found that the heat transfer coefficient (Figure 9) for engine oil is 1996.36 W/ m2K at 333K. From Table 7 or Figure 10, it is seen that the Nano fluids other than copper, gold, silver and aluminum Nanoparticles mixture with ethylene glycol proves a higher heat transfer rate than engine oil in both experimental and simulation method.
This paper solves the convective heat transfer problem using a heated tube at 333K over base and Nano fluids and that includes: water, ethylene glycol and engine oilas base fluids and Water/ Nano particles of Copper, Gold, Silver and Aluminum, Ethyleneglycol/ Nanoparticles of Copper, Gold, Silver and Aluminum, Engineoil/ Nanoparticles of Copper, Gold, Silver and Aluminum as Nano fluid combination. The performance results prove that the Nano fluids possess higher heat transfer coefficient than the base fluid under constant Reynolds number. The Nanoparticles suspended in the base fluid increases constantly the performance of convective heat transfer rate and it could further be concluded that with constant Reynolds number, the heat transfer coefficient has increased with its associated particle volume fraction.
vi [ms-1] velocity in ith position
tmax [min] maximal time limit
T0 [K] initial temperature
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