Heat transfer characteristics of propylene glycolwater based magnesium oxide nanofluid flowing throu

Abstract

Keywords: Magnesium Oxide; Straight Tube; Helical Coil; Convective Heat Transfer Coefficient; Constant Wall Temperature; Nusselt Number

Introduction

Power saving practices and concept of miniaturization of the heat transfer systems motivate many investigators to focus on enhancing the performance of these equipment. Changing the structural configuration of the heat exchanger and enhancing the thermo-physical properties of fluids flowing through these devices lead to enhancement of heat transfer efficiency [1]. Conventional heat transfer fluids with no phase change, like water, refrigerants, engine oil, glycols (ethylene glycol, EG) etc. exhibit poor heat transfer performance because of inherently low thermal conductivity. Introduction of metal and/or metal oxide solid particles into these heat transfer fluid enhances the thermal conductivity of the fluid medium [2]. The size of solid particles in these conventional fluids affects its thermal conductivity. The application of nanoparticles as additives to liquids is more noticeable and currently a large number of researchers are devoted to this subject. Conventional fluids with nanoparticles suspended in them are called nanofluids [3]. Nanofluids are engineered colloidal suspensions of nano particles (of size normally less than 100 nm & in the conc. range of 0 – 5 vol. %), which are more stable than micro particle colloids, with little particle settling, channel erosion and clogging [4]. Nanofluids have interesting properties such as large specific surface area, high thermal conductivity, less erosion and long term stability, thus making them potentially important as heat transfer fluids in heat exchangers, nuclear reactors, electronic cooling, fuel cells, pharmaceutical processes, food industry, etc. [5]. Straight Circular Tubes Various researchers have investigated the flow characteristics and the heat transfer behavior of nanofluids with different types of nanoparticles and base fluids. Pak and Cho [6] studied experimentally the heat transfer performance of Al2O3 and TiO2 nanoparticles dispersed in water under turbulent flow conditions. The results showed that the Nusselt number of nanofluids increased with increasing volume concentration and Reynolds number. However, they reported that the heat transfer coefficient of nanofluid was 12% lower than that of base fluid, when compared under constant velocity conditions. New correlation was proposed for predicting heat transfer coefficient under turbulent conditions. Wen and Ding [7] reported the heat transfer studies on alumina – water based nanofluid under laminar regime in a circular tube under constant heat flux conditions. They reported This paper was recommended for publication in revised form by Regional Editor Kwok-wing Chau 1 Energy Research Centre, Panjab University, Chandigarh, 160014, INDIA 2 Dr. SSB University Institute of Chemical Engineering and Technology, Panjab University, Chandigarh, 160014, INDIA *E-mail address: parminder25@gmail.com Manuscript Received 15 July 2016, Accepted 11 December 2016

Journal of Thermal Engineering, Research Article, Vol. 4, No. 1, pp. 1737-1755, January, 2018 that at the entrance region the increase in heat transfer coefficient is significant and increases with increase in Reynolds number. Heyhat et al. [8] experimentally reported the heat transfer and pressure drop of Al2O3/water nanofluids flowing in a circular tube under fully developed laminar condition with constant wall temperature as a boundary condition. They concluded that the heat transfer coefficient for 2 vol. % nanofluid increased by 32% approximately in comparison to base fluid and increases with increase in Reynolds number and particle concentration. Esfe et al. [9] experimentally studied the heat transfer behavior of MgO – water based nanofluids flowing through circular pipe for volume concentration less than 1 % under turbulent conditions. Results showed an enhancement of 21.8% in Nusselt number for a 0.5% volume fraction at a Reynolds number of 6700. Xie et al. [10] studied the convective heat transfer enhancement of various nanofluids as coolants in laminar flow inside a circular pipe under constant wall temperature conditions. Results showed that Al 2O3, ZnO and MgO showed greater heat transfer enhancement. For Re=1000, MgO having inherently non-corrosive character, showed a high heat transfer enhancement to the extent of 252%. Table 1and 2 summarizes the work of various authors in the area of convective heat transfer of nanofluids. Helical Coils Kubair and Kuloor [24], and Schmidt proposed a correlation to calculate the convective heat transfer for helical coils under constant wall temperature boundary condition while Seban and McLaughlin [26] and Dravid et al. [27] presented the correlation for uniform heat flux boundary condition. Janssen and Hoogendoorn [28] and Manlapaz and Churchill [29] investigated the effect of torsion ratio for laminar flow in helical coils and observed that the torsion ratio can be neglected for lower coil pitch. Cioncolini and Santini [30] studied the effect of pressure drop for laminar, transition and turbulent flow regime in helical coils of different curvature ratios. Jamshidi et al. [31] numerically investigated helical coils for thermal–hydraulic performance by using water and Al2O3/water nanofluid. He suggested that the thermal performance of nanofluids in the helical coils was significantly affected by the coil diameter and coil pitch. Akhavan-Behabadi et al. [32] focused on using vertical helical coils instead of straight tubes because of high heat transfer rates. Also in comparison to base fluid flow, Nusselt number of nanofluids were much on a higher side. Hashemi et al. [33] carried out experimental studies on the heat transfer of oil based CuO nanofluid flowing inside a horizontal helical tube under constant heat flux Table 1. Brief review of experimental work of various authors in the area of convective heat transfer of nanofluids Researcher

Results

Conv. HTC increased with increase in vol. fraction. For Φ = 0.4 wt. %, for Pe = 420000, Nu increased by 132%. Nu number of nanofluid with Φ = 2% was 39% higher than pure water. 8% enhancement in Nu for Φ = 1% at Re = 270. Nu increased with increase in Re. Convective HTC increased by 32% for Φ = 1.8%. HTC enhanced with increase in volume fraction as well as Peclet no. Also Al2O3/water showed more enhancement. HTC showed higher enhancement in the developing region and this increased with increase in volume concentration. HTC in the fully developed region was found to increase by 27% for 6 vol.%Al2O3/water nanofluid.

Table 2. Brief description of various correlations related to heat transfer of nanofluids 1738

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Correlation (Working conditions) 𝑁𝑢 = 0.021𝑅𝑒 0.8 𝑃𝑟 0.5 (Experimental study; Turbulent conditions; Al2O3/water; TiO2/water; Constant heat flux conditions, 0 <Φ < 3.0 vol. %, 6.5 < Pr< 12.3) 𝑁𝑢 = 0.0059(1 + 7.6286𝛷0.6886 𝑃𝑒 0.001 )𝑅𝑒 0.9238 𝑃𝑟 0.4 (Experimental study; Turbulent flow; Cu/water; Constant heat flux conditions, 0 < Φ < 2.0 vol. %) 𝑁𝑢 = 0.4328(1 + 11.285𝛷0.754 𝑃𝑒 0.218 )𝑅𝑒 0.333 𝑃𝑟 0.4 (Experimental study; Laminar conditions; Cu/water; Constant heat flux conditions, 0 < Φ < 2.0 vol. %, Re < 800) 𝑁𝑢 = 0.28𝑅𝑒 0.35 𝑃𝑟 0.35 for constant wall temperature 𝑁𝑢 = 0.086𝑅𝑒 0.55 𝑃𝑟 0.5 for constant wall heat flux (Numerical study; Laminar conditions; Al2O3/water; 0 < Φ < 10 vol. %, Re < 1000) 𝑁𝑢 = 0.074𝑅𝑒 0.707 𝑃𝑟 0.385 𝛷0.074 (Experimental study; Turbulent conditions; TiO2/water; Constant wall temperature,

Materials And Methods

MgO nanoparticles used in this experimental study were procured from Nanoshel. The XRD (X-ray diffraction) pattern of MgO nanoparticles is as shown in Figure1.The X-ray diffractogram shows the crystalline nature of the particles and confirms the presence of MgO. The average particle size of MgO nanoparticles was calculated to be 22 nm using Debye – Scherrer formula [35].Thermo physical properties of MgO nanoparticles are shown in Table 3. Two step method was used for the preparation of MgO – aqueous glycol nanofluids. The required amount of nanoparticles was slowly added to the base fluid with the help of magnetic stirrer followed by homogenization and ultra – sonication. An ultrasonic probe (UP400S, Hielscher GmbH) was used for uniform dispersion of nanoparticles in an aqueous glycol mixture. Two different volume concentrations 0.66% and 0.3% of MgO nanofluids were prepared. No surfactant was added. pH of the nanofluid was maintained at around 10.3, to ensure that the nanoparticles were well dispersed. The nanofluids thus prepared were observed to be stable for at least one week.

Journal of Thermal Engineering, Research Article, Vol. 4, No. 1, pp. 1737-1755, January, 2018

Figure 1. XRD analysis of MgO nanoparticles Table 3. Thermo-physical properties of MgO nanoparticles36 Nanoparticle

Experimental Investigation

Estimation of nanofluid thermo-physical properties All physical properties of base fluid as well as that of nanofluids were measured using calibrated instruments. Density meter(Anton Paar, DMA48), Ubbelohde Viscometer and KD2 Pro thermal properties analyzer (Decagon devices, Inc., USA) were used to measure the density (ρ),kinematic viscosity (µ) and thermal conductivity (k) respectively. Specific heat for base fluid were taken from ASHRAE [37]. Thermo – physical properties of base fluid (20 °C to 40 °C) Density

Thermo – physical properties of nanofluid (20°C to 35°C) Density of MgO / PG – W nanofluid with different volume concentration at different temperature were experimentally determined and were in good agreement with the theoretical equation given by Pak and Cho [6] :

Journal of Thermal Engineering, Research Article, Vol. 4, No. 1, pp. 1737-1755, January, 2018 where ρnf is the density of nanofluid, ɸ is the particle volume fraction, 𝜌𝑝 is the density of nanoparticles, 𝜌𝑏𝑓 is the density of base fluid, i.e., 𝜌𝑃𝐺/𝑊 .

Temp (oC) Figure 2. Density of propylene glycol – water mixture at different temperatures

Temp (0C) Figure 3. Viscosity of propylene glycol – water mixture at different temperatures

Temp (0C) Figure 4. Thermal conductivity of propylene glycol – water mixture at different temperatures

Journal of Thermal Engineering, Research Article, Vol. 4, No. 1, pp. 1737-1755, January, 2018 Figure 5 shows the comparison between experimental and predicted values using equation (5), for both the concentrations of nanofluid. As the particle volume concentration increased, the density of nanofluids also increased. Specific heat The specific heat of nanofluids was estimated by Pak and Cho [6] equation:

Viscosity The viscosity correlation for both the volume concentrations (0.66% & 0.3%) of MgO/PG-W nanofluid in the temperature range of20 0C to 35 0C was given by Sharma et al. [38] : 3259

Thermal Conductivity Thermal conductivity of 0.66 and 0.3 vol. % MgO/PG-W nanofluid was measured using KD2 Pro thermal properties analyzer (Decagon Devices, Inc., USA). After sonicating the fluid for one hour, the thermal conductivity of each sample of different volume concentrations of the nanofluids was measured at a regular time interval. The average of concordant readings was taken as the final thermal conductivity value. Figure 6 shows the measured values of thermal conductivity at different temperatures for both the concentrations of MgO/PG-W nanofluid. 𝑘

The observed data ( 𝑛𝑓= k (T, ) ) was subjected to non-linear regression analysis resulting in the 𝑘𝑏𝑓

= 1 + 0.0838𝜙 0.3372 , where kbf was obtained from Equation (4).

Experimental Setup

Straight tube The test experimental setup for straight tube is shown in Figure 7. It consists of a tank with temperature controller, peristaltic pump, a calming chamber, a test section, a cooling unit, several temperature indicators and a flow measuring unit. The test section was a concentric chamber, consisting of inner copper tube and outer section of stainless steel. Two copper tubes with inner diameters of 12.96 mm and 15.9 mm each and wall thickness of 1.5mm were used as the inner tube of a double pipe heat exchanger. Inner copper tube was surrounded by a stainless steel tube with inner diameter of 38mm. Effective length of each tube was 1.6 m. Hot fluid was passed through the annular section to create a constant wall temperature boundary condition at the outside surface of the inner tube while the test nanofluid was passed through the inner copper tube. To control the temperature of the test fluid, Pak and Cho model 0.66% 0.3%

Temp (0C) Figure 5. Density variation with temperature for both the concentrations of nanofluid. 1742

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Temp (oC) Figure 6. Thermal conductivity variation with temperature for base fluid and both the concentrations of nanofluid. a cooling section was provided after the test section so as to keep the temperature constant at the inlet conditions. Five (K –type) thermocouples are welded on outer surface of copper tube at equal distances so as to record the temperature. Two (K – type) thermocouples were inserted at inlet and outlet of the test section for measuring the bulk temperature of the test fluid. All thermocouples were first calibrated before carrying out the studies on the test fluids. Accuracy of these thermocouples was ± 0.1°C. The volumetric flow rate was measured by noting down the time required to fill a certain volume. The test section was insulated by a thick glass wool followed by aluminum cladding in order to minimize heat loss to the surroundings. Negligible heat loss to the surroundings was assumed.

Journal of Thermal Engineering, Research Article, Vol. 4, No. 1, pp. 1737-1755, January, 2018 Table 4. Geometrical configurations of the helical coils Helical coil

Type of study Boundary Conditions Constant wall temperature Laminar Constant wall temperature Laminar Constant wall temperature

Figure 8. Schematic diagram of helical coil. Helical coils The schematic diagram of the experimental set up for the helical coils is shown in Figure 8. The physical dimension of helical coils used in the present investigation are given in Table 4. An insulated hot water vessel of size 410 mm x 410 mm x 650 mm, with 10 mm thickness of mild steel was used to house the coils. Two electric heaters each of 1.5 kW were used in heating up of liquid surrounding the coils in the vessel. Temperature measurements are done in the same manner as in the case of straight tubes. Six thermocouples (K-type) are mounted at the same position on each alternate coil and two thermocouples (K-type) are inserted at the inlet and outlet of the coil. Data processing Heat transfer coefficient and the Nusselt number for fluid flowing under constant wall temperature conditions are calculated as follows: Rate of heat transfer from hot fluid to the cold fluid (nanofluid) is estimated based on the measurements of the inlet and outlet temperatures along with the volumetric flow rates of the hot fluid and the nanofluid. The following equations were used in calculations.

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Overall and average convective heat transfer coefficients (𝑈 𝑎𝑛𝑑 ℎ𝑒𝑥𝑝 ) can be obtained as: 𝑄𝑎𝑣𝑒𝑟𝑎𝑔𝑒

Conventional heat transfer correlations for straight tube and helical coils are as follows: For straight tube under laminar flow, (Re <2100)(Seider Tate correlation [39]) : 𝑑

where µ𝑤 is fluid viscosity at wall temperature. And for helical coil, (Manlapaz correlation [29]) :

𝑁𝑢𝑐𝑜𝑖𝑙 = {[3.657 + [1+(957⁄𝑃𝑟.𝐻𝑒 2 )]2 ] + 1.158 [ where Reynolds Number 𝑅𝑒 =

Results And Discussion

Straight Tubes The set-up was calibrated using distilled water. The experimental results were in close agreement with Seider-Tate correlation, equation (16), for laminar flow as shown in Figure 9. Figure 10 shows the variation of Nusselt number for the base fluid i.e. PG/water (60:40 by wt.%) with Reynolds number.

As shown in Figure 11 the modified Nusselt number (𝑁𝑢𝑚𝑜𝑑𝑖𝑓𝑖𝑒𝑑 ) of the nanofluids was higher than those of the base fluid (PG/water (60:40 by wt. %)) and it increased with the increase in Peclet number as well as with the particle volume concentration. For 0.66% volume concentration, nanofluid showed an enhancement of 20% in Nusselt number and this enhancement increases to 29% with increase in Peclet number from 44000 to 111400. Whereas for 0.3% volume concentration nanofluid shows an enhancement from 13% to 25% in the above said Peclet number range. One of the reasons for the better thermal performance of these nanofluids is due to combined

Journal of Thermal Engineering, Research Article, Vol. 4, No. 1, pp. 1737-1755, January, 2018 effect of increase in the nanofluid thermal conductivity and the presence of Brownian motion of nanoparticles. Figures 12(a,b,c) show variation in T ,Rate of heat transfer, Q and the heat transfer coefficient, h respectively of the nanofluid flowing through the inner tube of the test section. Significant enhancement of 83.1% and 95.94% in rate of heat transfer, Q , and 30.24% and 70.84% in heat transfer coefficient, h in respect of the base fluid is observed with increase in concentration of MgO from 0.3% to 0.66% in the base fluid respectively at a Reynolds number of 1840. 12 11

Figure 9. Nusselt number versus Peclet number for pure distilled water.

Figure 10. Nusselt number versus Reynolds number for PG/water base fluid. 130 120 110 100 90 80 70 60 50 40 30000

Pe Figure 11. Experimental modified Nusselt number versus Peclet number for PG/water and MgO - PG/water nanofluid.

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(c) Figure 12. (a) Variation of ΔT with Re for base fluid and nanofluid, (b). Variation of Q with Re for base fluid and nanofluid.(c) Variation of h with Re for base fluid and nanofluid.

Journal of Thermal Engineering, Research Article, Vol. 4, No. 1, pp. 1737-1755, January, 2018 Helical coils Figure 13 shows the variation of Nusselt number with Reynolds number for PG/W mixture for a constant pitch ratio and for curvature ratio of 0.0437, 0.0531 and 0.0727. It is clearly evident that the Nusselt number increases with increase in Reynolds number and for a given Reynolds number, Nusselt number is higher for higher curvature ratio. Also the experimental results are in good agreement with the standard available correlation i.e. Manlapaz and Churchill correlation [29]. Further these results show better enhancement in helical coils in comparison to the flow through straight tube. Figure 14 depicts the variation of Nusselt number of PG/water base fluid with respect to Dean Number, which takes into account both the Reynolds number and curvature effect. PG/water base fluid shows higher Nusselt number at higher Dean number. Figure 15 shows the effect of increasing volume concentration of MgO nanoparticles in PG/water mixture for coil – II of curvature ratio 0.0727. It is clear that the Nusselt number increased with the increase in particle volume concentration for a given Dean number. The maximum enhancement in experimental Nusselt number was found to be 19.5 % and 23 % at volume concentration of 0.3%, and 0.66% respectively for a Dean number of 490. 30

Re Figure 13. Experimental Nusselt number versus Reynolds number for PG/water mixture for different curvature ratios

Figure 14. Experimental Nusselt number versus Dean number for PG/water base fluid

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Figure 15. Experimental Nusselt number versus Dean number for MgO - PG/water nanofluid for Coil – II. This is due to the presence of Brownian motion of the nanoparticles and higher enhancement in thermal conductivity of nanofluids. This increase in Nusselt number over Dean number is due to the formation of secondary flow. This flow provides proper mixing and stronger particle migration to enhance heat transfer coefficient. Similar results were obtained for other curvature ratios as well. Data Analysis Base fluid In Helical Coil: Figure 16 shows the variation of Nusselt number ratio of PG/water base fluid w.r.t Dean number. Nusselt number ratio is defined as the ratio of Nusselt number of coil to that of Nusselt number of straight tube. It was observed that the variation of Nusselt number ratio with Dean number can be expressed in the form as 𝑁𝑢

De Figure 16. Nusselt number Ratio (NuCoil/NuST) vs Dean number for PG/water base fluid.

Journal of Thermal Engineering, Research Article, Vol. 4, No. 1, pp. 1737-1755, January, 2018 Using non – linear regression techniques, the correlation constants of equation 19 were obtained as: 𝑎 = 0.060 𝑎𝑛𝑑 𝑏 = 0.484. Different types of statistical parameters like Mean Relative Quadratic Error (MRQE) and Average Relative Error (ARE) were also estimated. experimental − 𝑡ℎ𝑒𝑟𝑜𝑒𝑡𝑖𝑐𝑎𝑙 2 ) 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙

Table 5. Statistical errors for straight tube Correlation New correlation (equation (20)) Sharma and L. Syam [40]

Table 6 shows the values of different statistical errors calculated between the new proposed correlation i.e. equation 19, and the available correlations in the literature. Table 6. Statistical errors for base fluid in helical coils Correlations MRQE 0.016 Proposed correlation (equation (19)) 0.311 Dravid et al. [27] 0.288 Janssen [28] 0.054 Manlapaz [29]

Figure 17 shows the parity plot between the experimental Nusselt number and the predicted Nusselt number for new proposed correlation and Manlapaz and Churchill correlation [29]. It is clearly observed that Manlapaz and Churchill correlation [29] predicted the experimental data within ±15% whereas the new proposed correlation predicted the Nusselt number reasonably well within ±4%. Nanofluid Based on the experimental data of both the volume concentrations of MgO nanofluid, new correlations for straight tube and for helical coils have been proposed. For straight tube: Proposed model is 40

Nu_experimental Figure 17. Mean deviation between predicted and experimental Nusselt number for proposed correlation and Manlapaz correlation 29.

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Using non – linear regression techniques, m & n were obtained as m =4.900 and n = 0.576. Statistical parameters like MRQE and ARE were also estimated. Various available correlations in literature were also compared with the new proposed correlation. Table 6 shows the comparison based on statistical errors. Also as seen in Figure 18, the proposed correlation predicted the experimental data well within ±5%. For helical coils: Proposed correlation for nanofluids flowing through helical coil is represented in the similar way as represented for base fluids i.e. 𝑁𝑢𝑅𝑎𝑡𝑖𝑜 =

where 𝑁𝑢𝑆𝑇_𝑚𝑜𝑑𝑖𝑓𝑖𝑒𝑑 is given in equation 20. Using non – linear regression techniques, constants were calculated as A = 0.052 & B = 0.515. Different statistical errors were also calculated. The proposed correlation gave MRQE = 0.029 and ARE = 2.230% for the present experimental data. Figure 19 shows that the proposed correlation predicted the experimental data well within ±5%. 120

Nu_experimental Figure 18. Parity plot between Nu_predicted and Nu_experimental for straight tube. 2,5

Nu_experimental Figure 19. Parity plot between Nu_predicted and Nu_experimental for helical coils.

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Conclusion

Forced convective heat transfer studies for laminar flow of MgO/PG-W nanofluid for volume concentrations of 0.66% and 0.3% in straight tube and helical coils were conducted.  Thermal conductivity and viscosity of MgO/PG-W based nanofluids were experimentally determined in the required temperature range of 20 to 35 °C.  Experimental results showed the maximum thermal conductivity enhancement of 7.5 % and 10.5 % for a volume conc. of 0.3% and 0.66% respectively of MgO/PG-W at a temperature of 33°C.  In straight tubes, convective heat transfer coefficient of 0.66 vol. % MgO/PG-W nanofluid was found to be 24 % higher as compared to that of PG/W base fluid.  Significant enhancement of 83.1% and 95.94% in rate of heat transfer, Q , and 30.24% and 70.84% in heat transfer coefficient, h in respect of the base fluid is observed with increase in concentration of MgO from 0.3% to 0.66% in the base fluid respectively at a Reynolds number of 1840  The increase in heat transfer characteristics of MgO/PG-W nanofluid could be due to: (i) increase in, the surface area per unit volume provided by the nanoparticles , the heat capacity and the apparent thermal conductivity of the fluid. (ii) local turbulence caused by random interaction and collision among nanoparticles resulting in flattening of local temperature profile within the nanofluid.  In helical coils, the effect of curvature ratio on Nusselt number was studied and experimental results showed that the Nusselt number increased with increase in curvature ratio. For a curvature ratio of 0.0533 and 0.66 vol. % nanofluid, maximum enhancement in heat transfer coefficient was 17.5 %whereas for a curvature ratio of 0.0727, maximum enhancement was 23% for same volume concentration.  A new correlation (equation (20)) has been proposed to estimate the Nusselt number for laminar flow of MgO based nanofluids through straight tubes as a function of particle volume fraction for 0≤ ɸ ≤ 0.66%.  The coil Nusselt number was found to be a function of geometrical parameters of helical coil. A new correlation (equation (21)) to estimate the coil Nusselt number for laminar flow of base fluid as well as MgO nanofluids has been proposed for 0≤ ɸ ≤ 0.66% and 100 ≤ De ≤ 1000.  Effect of further increase in concentration of MgO nanoparticles thereby affecting stability, heat transfer coefficient and Nusselt number under turbulent flow conditions, both in straight tubes and helical coils can be considered for further studies.  Effect of coil geometry, viz. curvature ratio, coil diameter and pitch on convective heat transfer coefficient under turbulent flow conditions need to be studied.

Acknowledgement

One of the authors (Parminder Singh) acknowledges the financial support provided by DST-PURSE-II (Ref. no. 79-81/RPC) as fellowship to carry out his research work. The authors are also thankful to DST-PURSE-II and TEQIP-II, Dr. SSBUICET, PU for providing grants for purchase of chemicals.

Disclosure Statement

No potential conflict of interest was reported by the authors.

Nomenclature

D outside diameter of coil support, m Dc coil diameter, m di inside diameter of the tube, m do tube outer diameter, m Lcoil coil length, m L length of a test section, m N number of turns p coil pitch , m k thermal conductivity, (W/m.K) v fluid velocity, (m/s) Cp specific heat capacity, (J/kg°C) 1752

Journal of Thermal Engineering, Research Article, Vol. 4, No. 1, pp. 1737-1755, January, 2018 Re Reynolds number Pr Prandtl number Nu Nusselt number Pe Peclet number = Re.Pe He Helical number 𝑑

Q Heat transfer rate, W m mass flow rate, kg/s C specific heat, J/kg. °C T temperature of fluid, °C U overall heat transfer coefficient, (W/m2.K) h convective heat transfer coefficient, (W/m2.K) A surface area, m2 C.R curvature ratio = Dc/di P.R pitch ratio = p/di Φ nanoparticle volume fraction µ dynamic viscosity (Pa.s) ρ density (kg/m3) Subscripts c cold fluid h hot fluid o outside i inside p nanoparticle bf base fluid nf nanofluid PG/W mixture of (60:40, by wt. % Propylene glycol and water) SL straight tube, laminar condition ST straight tube LMTD log mean temperature difference exp experimental w tube wall conditions

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