NUMERICAL INVESTIGATION OF LAMINAR HEAT TRANSFER AND PRESSURE DROP IN NANOFLUID FLOW IN COILED HELICAL DUCT

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1 International Journal of Mechanical Engineering and Technology (IJMET) Volume 9, Issue 13, December 2018, pp , Article ID: IJMET_09_13_125 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed NUMERICAL INVESTIGATION OF LAMINAR HEAT TRANSFER AND PRESSURE DROP IN NANOFLUID FLOW IN COILED HELICAL DUCT Nabil Jamil Yasin Engineering Technical College-Baghdad, Middle Technical University, Baghdad, Iraq Kadhum Audaa Jehhef Department of Power Mechanics, Institute of Technology, Middle Technical University, Baghdad, Iraq, ABSTRACT Heat transfer enhancement in horizontal annuli using variable nanoparticles concentrations of Al 2 O 3 -water nanofluid is investigated. A numerical simulation on pressure drop and heat transfer of vertical rectangular helical coiled duct by utilizing nanofluid as the test fluid is presented. The nanofluid suspensions is water-al 2 O 3 with volume of fraction of 0.5, 1, 2 and 3 % vol. was examined in this study. Steady state laminar flow of a single phase nanofluid in helical duct was solved by the computational fluid dynamics (CFD) approach presented by finite volume method. In this study, the nanofluid thermo-physical properties are formulated as functions of nanoparticle volumetric fraction. The heat transfer and flow behavior performance of these nanofluid suspensions were studied as a function of various parameter such as rectangular tubes aspect ratio, radius of coil, number of turns, Reynolds number and Dean number. The results indicate that the heat transfer performance improves significantly when using volume fraction up to 0.5 % vol. Also, the pressure drop increases with increasing the duct aspect ratio and coil radius ratio but it decreases with increasing pitch ratio of the coiled duct. Moreover, there is a significant enhancement in the Nusselt number when increasing the duct aspect ratio and coil radius ratio as well as with increasing the Reynolds and Dean number for water and nanofluid. Finally, the improvement in Nusselt number was obtained by (68 %) at Dean number of 590 and particle concentration of 3.0% vol., but, the minimum enhancement in the Nusselt number was obtained by (31 %) at Dean number of 65 and particle concentration of 0.5 % vol. Key words: Nanofluids, Coiled Duct, Dean Number, Helical Tubes editor@iaeme.com

2 Numerical Investigation of Laminar Heat Transfer and Pressure Drop in Nanofluid Flow in Coiled Helical Duct Cite this Article: Nabil Jamil Yasin and Kadhum Audaa Jehhef, Numerical Investigation of Laminar Heat Transfer and Pressure Drop in Nanofluid Flow in Coiled Helical Duct, International Journal of Mechanical Engineering and Technology 9(13), 2018, pp INTRODUCTION The helical coiled tube have several application in engineering system such as nuclear reactor, power generation plant, heat recovery system, food industry and refrigeration. Due to the high heat transfer coefficient and compact structure, the heat exchangers of helical coil type are widely used [1]. In order to prevent the overheating of equipments such as transportation and other electronic devices, a heat transfer fluid or a coolant is used. However, water or ethylene glycol of conventional heat transfer fluid basically has low thermal properties. Thus, many researches used high thermal conductivity small particles in the conventional heat transfer fluid, in order to obtain high thermal properties nanofluids to enhance the thermal properties of the heat exchange systems. It has been widely reported in literature that heat transfer rates in helical coils are higher as compared to a straight tube. [2], used laminar flow of Al 2 O 3 and CuO-water was flowed in coiled square tubes, e.g., in-plane spiral, conical spiral, and helical spiral. The results indicated that using volume fraction nanoparticles up to 1% will enhance the overall performance of heat transfer. Moreover, CuO nanofluid performed fewer enhancements in heat transfer performance than Al 2 O 3 nanofluid that flowed in coiled tubes. Also, the in-plane spiral tubes give better performance than other coiled tubes for nanofluids. The heat transfer enhancement is higher at high Reynolds number due to increase the heat transfer coefficient. The maximum pressure drop was obtained with higher volume concentration [3]. [4] studied the nanofluid heat transfer in helically coiled tubes at constant heat flux. The higher heat transfer enhancement was given by helical tube with large curvature ratio. The maximum enhancement in the heat transfer can be obtained in shell and helical tube heat exchanger when nanofluid used as reported by [5]. However, the increase of nanoparticles volume concentration leads to Nusselt number increase and the reduction of the entropy generation due to heat transfer effect as reported by [6] who used the entropy generation analyses to study heat transfer of nanofluid flow in heat exchanger of helical coiled tube. The results of 2% vol. CuO-water nanofluid, it showed that the rate of heat transfer was 14 % greater than the pure water, but this improvement will decrease because the higher viscosity due to the higher particle concentration. Also, [7] investigated the thermal and hydraulic performance of aqueous Multi-wall carbon nanotubes (MWCNT) in double helical coil heat exchanger. The enhancement of the heat transfer was come from the thermal conductivity by MWCNT and due to the centrifugal force in the helical tube caused by secondary flow intensity. [8] investigated the thermal performance of the hybrid nanofluid used in coiled heat exchanger. Their results indicated that the increase in Nusselt number is accompanied by increasing concentration of nanoparticle. Also, the pressure drop increased as the concentration of particle and Reynolds number increased. Moreover, [9] studied the flow characteristics and heat transfer in helical duct plate heat exchanger using in a series arrangement in counter flow of water as the test fluid. Their results showed that the aspect (width-to-height) ratio and pitch ratio variation has effect on heat transfer rate enhancement and pressure drop reduction. Also, [10] indicated that the Nusselt number increased with increase the Dean number, due to formation of stronger secondary flow, thinning boundary layer and increasing fluid thermal conductivity. However, the pressure drop was increased with increasing the Dean number as well as particle concentration. [11] studied the enhancement of heat transfer by using CuO-water mixture that flows in the heat exchanger of editor@iaeme.com

3 Nabil Jamil Yasin and Kadhum Audaa Jehhef type helical coil at laminar flow regime. Their results showed that the enhancement in the heat transfer coefficient was increased with increasing the CuO nanoparticles in base fluid. [12] investigated the enhancement of the heat transfer by using Fe 2 O 3, Al 2 O 3 and CuO non- Newtonian nanofluids that flows in a shell and helical coil heat exchanger. They used non- Newtonian nanofluids with the concentration range of wt % in aqueous carboxymethyl cellulose (CMC) base fluid. They showed that the Nusselt number increased with increasing volume fraction, Dean number (coil-side water flow rate), shell side fluid temperature and stirrer speeds. Also, the better heat transfer nanofluid was CuO/CMC-based nanofluid as compared with the other two kinds of fluid. The heat transfer enhancement by PANI (polyaniline) water based nanofluid in heat exchanger with vertical helically coiled tube was investigated experimentally by [13]. They found that the heat transfer coefficient increased with an increase in the volume fraction in nanoparticles and Reynolds number. As a result, this work introduced various configurations of the special type of helical coiled duct in order to enhance the heat transfer rate by using Al 2 O 3 -water nanofluid with various volume fractions. In this study, three dimensional computational domain was solved by simulation model of heat transfer and nanfluid flow in the in a vertical rectangular helical duct with different duct cross section aspect ratio, different helical pitch, different coil radios and various inlet Reynolds number and Dean number. 2. PROBLEM FORMULATION 2.1. Mathematical Modeling The Computational Fluid Dynamics (CFD) applied using ANSYS-Fluent V.16.2 software based on finite volume method to study the flow and heat transfer characteristics in vertical rectangular helical duct. In the finite volume method, the flow domain discretized into a finite set of control volumes called mesh or cells as a computational domain, and then the governing convection equations, momentum and energy applied on each cell Physical Model The computational domain and physical problem of the vertical coiled helical duct is shown in Figure. 1. The computational domain consists of the inlet section with various inlets Reynolds number and Dean number and at constant inlet temperature. Figure 1 Physical model problem geometrey and dimenssions of the present study editor@iaeme.com

4 Numerical Investigation of Laminar Heat Transfer and Pressure Drop in Nanofluid Flow in Coiled Helical Duct The outlet fluid section was considered with fixed atmospheric pressure boundary condition of zero pressure outlet. Also, the constant uniform heat flux q'' in W/m 2 is applied on the wall of the helical duct. In the present study, the square and rectangular cross sections of the helical coiled duct with different coiled duct cross section aspect ratio, different helical pitch, different coil radios, all these design and configuration parameters was listed in Table.1. Table 1 Different design parameters employed in this study. Parameter Symbol Units Values Width b mm 10 Length a mm 10, 20, 30 and 40 Duct Aspect Ratio (a/b) , 0.3, 0.5 and 1 Pitch p mm 40, 32, 26 and 21 Pitch Ratio (p/b) , 0.31, 0.38 and 0.47 Coil Radius R mm 10, 20, 30 and 40 Radios ratio (R/b) - 1, 2, 3 and 4 Number of Turns n - 10, 12, 14 and 16 Reynolds Number Re Dean Number De Volume Fraction ф % Assumption When the nanofluid flows through the helical coiled duct test section, it extracted the heat from the heat sources of the applied heat flux on the duct wall. Thus, the following assumptions are applied in this work: A three-dimensional computational domain; The thermal conductivity walls does not change with temperature; Laminar, single phase, steady-state and fully-developed fluid flow; Incompressible and Newtonian nanofluid; Thermal equilibrium state for fluid phase and the nanoparticles; The slip velocity between the solid and the fluid phases is ignored because the nanoparticles are so small in sizes, so Governing Equations In this study, the heat transfer and fluid flow are described by the 3D steady-state governing equations such as continuity, momentum, and energy equations with constant thermo-physical properties [14]. The equation of continuity is: The equation of momentum is: (1) [ ] (2) The equation of energy given by: (3) editor@iaeme.com

5 Nabil Jamil Yasin and Kadhum Audaa Jehhef Where the thermal diffusivity Γ is molecular given by: (4) 2.5. The Key Parameters of Flow and Heat Transfer The inlet nanofluids flows with uniform constant average velocity of (U av ), thus the inlet Reynolds number can be defined as: In coil tubes, to determine the flow is laminar or turbulrnt, the critical Reynolds number may be determined using the correlation by using [15] (5) [ ] (6) And Prandtl number given by: Similar to Reynolds number for flow in pipes, Dean number is used to characterize the flow in a helical pipe. The Dean number (De) is defined as: Where D h is the hydraulic diameter and given by. (7) (8) The numerical heat transfer coefficients of the nanofluid and water and Dean number are computed from the following equations. Heat flux in the test section is determined as follows: Also, the heat transfer coefficient of the base fluid and nanofluid can be calculated as follows: Also, the Nusselt number can be defined as [16]: (9) (10) (11) 2.6. Pressure Drop and Friction Factor The Poiseuille equation is used for laminar flow regime (Re < 2300), is given by: For coiled tubes, the friction factor involves the pressure drop across the working length of coil and the friction factor given by: (12) [ ] (13) Where the pressure drop was computed from the numerical results as: Thus, it can be determined the fluid pumping power (P p ) as: editor@iaeme.com

6 Numerical Investigation of Laminar Heat Transfer and Pressure Drop in Nanofluid Flow in Coiled Helical Duct (14) 2.7. Boundary Conditions Based on the previous assumptions, the assigned boundary conditions as plotted in Figure.2 are the following: (a) At the inlet boundary: (b) At the heated wall boundary of the coiled helical duct: (e) At the outlet boundary: Figure 2 Boundary conditions of the computational domain used in the present analysis Thermophysical Properties of Nanofluids Introducing the Nanofluid volume fraction (ф), the thermophysical properties of the Nanofluid, namely the density and heat capacity, have been calculated from Nanoparticle and the pure fluid properties at the ambient temperature as follows. The nanofluids thermophysical properties used in the present study are formulated for mixture of the pure water and Al2O3 nanoparticles only is used, these properties are listed in Table. 2. Table 2 The thermophysical properties of water and nanoparticle at T=298 K. Thermo-physical properties Water Al 2 O 3 Density, ρ (kg/m 3 ) Specific heat C p (J/Kg K) Thermal conductivity, k (W/m K) Dynamic viscosity, µ (Ns/m 3 ) In this work, to model the nanofluids flow in a vertical helical duct, the single-phase model is considered, thus the thermal physical properties equations are used as following editor@iaeme.com

7 Nabil Jamil Yasin and Kadhum Audaa Jehhef Density: Equation used to compute the effective density for a classical two-phase mixture given by [17]: (15) Specific heat: Calculation of the effective specific heat of nanofluid is straight forward. It can be based on the physical principle of the mixture. The specific heat is calculated for a classical two-phase mixture as follow [18]: Thermal expansion: Equation of the effective thermal expansion at the reference temperature (T in ) for a classical two-phase mixture given by [19]: Dynamic viscosity: The effective viscosity is calculated with the Einstein equation [20] which is applicable to spherical particles in volume fractions of less than 5.0 vol.% and is defined as follows [21]: Thermal conductivity: For particle fluid mixtures, numerous theoretical studies have been conducted dating back to the classical work of [22]. For the two component entity of spherical-particle suspension, the determined by Maxwell-Garnett s (MG model) given by: (16) (17) (18) [ ] (19) Maxwell s formula shows that the effective thermal conductivity of nanofluids relies on the thermal conductivity of the spherical particle, the base fluid and the volume fraction of the solid particles Numerical Solution The Finite Volume Method (FVM) is used to solve and discretize the physical governing equations along the computational domain of the helical coiled duct with specific boundary conditions. To couple the pressure-velocity system, SIMPLE algorithm was utilized. The second order upwind scheme is selected for the convective terms in order to achieve a more precise numerical solution. The appropriate convergence criteria are obtained. The convergence criteria for the continuity, momentum, and energy equations are 10-6, 10-6, and 10-8, respectively. It is assumed that the inlet fluid flow is laminar. The governing equations are iteratively solved until the set residuals are obtained Mesh Generation To perform the simulation of the present compositional channel of the helical rectangular duct domain on a computer as presented in Figure.3, the PDEs need to be discretized, resulting in a finite number of points in space. In the present study the ANSYS-Fluent-v.16.2 meshing software starts with advanced SOLIDWORKS 2016 x64 Edition reading, after drawing all the geometrical details, and generates the mesh of annular channel in the Design Modular. The meshing procedure start with face mesh and continue to the whole volume using volume mesh editor@iaeme.com

8 Numerical Investigation of Laminar Heat Transfer and Pressure Drop in Nanofluid Flow in Coiled Helical Duct to have the whole 3D model of annular channel of the double pipe heat exchanger for further simulation. Figure 3 Meshed computational domain Grid Independent Test Before conducting the simulation, the computational domain presented in above is tested for grid independence test for better result accuracy as well as time effectiveness. In the present paper, four different mesh size models were modeled using Design Modular and only one suitable mesh will be selected for simulation model. The model with very fines mesh size will be taken as reference for the other models. To make sure that the results are due to the boundary conditions and physics used, not the mesh resolution, mesh independence should be studied in CFD. The standard method to test for grid independence is to increase the resolution and repeat the simulation. If the results do not change appreciably, the original grid is probably adequate. Computations have carried out for four selected node sizes (i.e., 73801, , and ). Table 3 presented grid independence summary of the test results. The results showed that the nodes given ad and produce almost identical results with a percentage error of 0.02%. Thus, a computational domain with nodes of was chosen to increase the computational accuracy and to reduce the computations time. Table 3 Grid independent test Mesh Type Number of Nodes Average Nusselt number of heated wall Difference with previous coarse mesh (%) Course Medium Fine Very Fine Model results validation To ensure the reliability of the numerical simulation code used in this study, in the laminar range flow, the numerical results of friction factor were compared with the correlation proposed by [23] for the water flows in a helical coiled duct, as follows: (20) editor@iaeme.com

9 Nabil Jamil Yasin and Kadhum Audaa Jehhef The present results of the numerical simulation are gave a good agreement with the correlation of [23], within maximum deviation 5.6% as shown in Figure. 4. Therefore, the numerical methods adopted in this study for pressure drop predictions were judged to be reliable. Also, the heat transfer coefficients for the present numerical data were compared with the [2] numerical results for laminar flow in coil ducts as plotted in Figure Friction factor, f Guo, et al., (2001) Present Numerical Work (water) Re Figure.4 Comparison of friction factor coefficient between present simulation and numerical data given by [23] for water Heat Transfer 400 Coefficient, W/m.K Sasmito, et al. [5] Re Figure.5 The present results of heat transfer coefficient as compared with the data given by [2] for water flow. 3. RESULTS AND DISCUSSION 3.1. Pressure Drop and Friction Factor The effect of duct dimensions on the pressure drop can be showed clearly an in Figure. 6 a and b, that present the pressure drop of water for duct with aspect ratio of 1 and editor@iaeme.com

10 Numerical Investigation of Laminar Heat Transfer and Pressure Drop in Nanofluid Flow in Coiled Helical Duct respectively. The pressure drop results indicated that as the aspect ratio of coiled duct decreases, the pressure drop across the water flow duct decreases for all pitch ratios. a) Ar=1 b) Ar=0.25 Figure.6 Comparison of pressure drop between two aspect ratio numerical data for water Effect of Geometry (Aspect Ratio) In this section, the effect of cross-sectional of the duct geometry was considered; due to it has significant effects on the performance of heat transfer. In this study, it was used four different square cross section tubes geometries according to the aspect ratio of the duct such as 0.25, 0.3, 0.5 and 1 by increasing the width of the duct and remained at constant height with water as the base working fluid. To investigate the flow patterns inside the helical ducts, it can be noted that the convective heat transfer is directly affected by the flow behavior inside the helical coiled ducts. From the previous literature studies, showed that the in the case of using helical coiled ducts the presence of centrifugal force due to curvature that can generate significant radial pressure gradients in flow core region. However, the axial velocity and the centrifugal force will approach zero. Therefore, a secondary flow should develop along the outer wall in order to balance the momentum transport. As showed in Figure7a for square duct (Ar=1), the secondary flow with higher velocities is generated along the outer wall of the helical duct, and the secondary flows appear as one-pair. But when decreasing the aspect ratio editor@iaeme.com

11 Nabil Jamil Yasin and Kadhum Audaa Jehhef of the duct to 0.5, 0.3 and 0.25, the secondary flow with higher velocities began to stretch along the width of the duct and become more and more until to reach the inner wall of the duct, due to increasing the flow area of the duct. The high velocities secondary flow with is affected on the heat transfer rate inside the helical duct. Figure 8 presents the temperature contours over the cross sections of various duct aspect ratios. In general, the temperatures separated in two heated zone in the upper and lower region of the duct. But when decreasing the aspect ratio in coiled duct, it was showed that the deference in temperature becomes stronger between the two regions, and it appeared cold regions in the upper and lower temperatures. A mixed region in the middle of the duct was become as separator between the two cold regions. The temperature of the upper region increased with decreasing the duct aspect ratio. This phenomenon indicates that the coiled ducts have higher rate of heat transfer with low aspect ratio when compared to that of high aspect ratio or square ducts that caused by the secondary flows. Also, the results of this study concluded that there is a higher intensity of secondary flow in the case of using rectangular coiled ducts, and this lead to increase the rate of the heat transfer. a) Ar=1 b) Ar=0.5 c) Ar= editor@iaeme.com

12 Numerical Investigation of Laminar Heat Transfer and Pressure Drop in Nanofluid Flow in Coiled Helical Duct d) Ar=0.25 Figure.7 Velocity profiles of water flow in rectangular helical spiral vertical duct at L c = 500 mm, R h =40 mm and n=10. a) Ar=1 b) Ar=0.5 c) Ar= editor@iaeme.com

13 Nabil Jamil Yasin and Kadhum Audaa Jehhef d) Ar=0.25 Figure. 8 Temperatures profiles of water flow in rectangular helical spiral vertical duct at L c = 500 mm, R h =40 mm and n= Effect of Radius of coil As indicated before, the duct with rectangular cross sectional area have significant heat transfer area as compared with square duct, thus in this study it is benefits to discuss the parameters that can effects on the velocity field and heat transfer rate in the rectangular coiled ducts, one of these parameters is radios coil as presented Figures 9 and 10 respectively. The Figure showed that the core of the maximum velocities was transferred from the lower corner to upper corner along the inner wall as decreasing the radios coil ratio. The effect of radios coil ratio on the temperatures distribution was presented in Figure10. The hot plume was increased in the middle of the duct began from the inner duct, and the temperatures of the upper zone of the duct increased with increasing the ratio of the radios coil for the case of water as working fluid. Also, the cold layers transferred from upper to lower region when increasing this ratio. a) R/b=1 b) R/b= editor@iaeme.com

14 Numerical Investigation of Laminar Heat Transfer and Pressure Drop in Nanofluid Flow in Coiled Helical Duct c) R/b=3 d) R/b=4 Figure. 9: Velocity profiles of water flow in rectangular helical spiral vertical duct at L c = 500 mm, Ar=0.25 mm and n=10. a) R/b=1 b) R/b= editor@iaeme.com

15 Nabil Jamil Yasin and Kadhum Audaa Jehhef c) R/b=3 d) R/b=4 Figure. 10: Temperatures profiles of water flow in rectangular helical spiral vertical duct at L c = 500 mm, Ar=0.25 mm and n= Effect of Number of Turns Increasing the number of coil turns will cause to lead lo create a small maximum velocity near the outer wall as showed in Figure 11 the results indicated that the maximum velocity of the secondary flow was reduced when increasing the number of coil turns of the rectangular duct when used the water and at L c = 500 mm, Ar=0.25 mm and R h =40 mm. In addition to the upper and lower longitude cold zones in the coiled duct, there is a small cold zone was appeared near the outer wall when increased the number of turns from 14 to 16 as presented in Figure 12. Also, the increasing the coil turns lead to increasing the temperatures of the upper zone of the duct. a) n= editor@iaeme.com

16 Numerical Investigation of Laminar Heat Transfer and Pressure Drop in Nanofluid Flow in Coiled Helical Duct b) n=12 c) n=14 d) n=16 Figure. 11: Velocity profiles of water flow in rectangular helical spiral vertical duct at L c = 500 mm, Ar=0.25 mm and R h =40 mm. a) n= editor@iaeme.com

17 Nabil Jamil Yasin and Kadhum Audaa Jehhef b) n=12 c) n=14 d) n=14 Figure 12: Temperatures profiles of water flow in rectangular helical spiral vertical duct at L c = 500 mm, Ar=0.25 mm and R h =40 mm Effect of Volume Faction The main aim of this study is studying the effect of the nanoparticles amount that adding to the water that used as a base fluid in this study. These nanoparticles affected on the determining of the performance of the heat transfer. Intuitively, to increase the thermal conductivity of the nanofluid it was needed to add larger amount of nanoparticles in the basefluid; but this leads to increase the fluids friction factor. In this study, it was used four different volume fraction 0, 0.5, 1, 2, and 3% of Al 2 O 3. Figure. 13 showed the velocity contours for the rectangular vertical coiled duct for various volume fractions. Interestingly, the results showed that the velocity distribution has less affected when using low volume fractions. But when increasing the volume fractions to 0.5% editor@iaeme.com

18 Numerical Investigation of Laminar Heat Transfer and Pressure Drop in Nanofluid Flow in Coiled Helical Duct vol., the core maximum velocity increased by 1.1 %; whereas, at 3% Al2O3 concentration, the core maximum velocity increased by 8.2 % due to the secondary flow appears in twopairs as compared to that in one-pair at lower nanoparticle concentrations, because the stronger effect of the nanofluid suspension. Conversely, the thermal conductivity of the nanofluid has significant effects on the thermal behavior of the fluids, as showed in Figure.14, due to the small amount of nanoparticle (0.5%) were added to the water will changes the distributions of the temperature inside the helical coiled duct. The hot zone in the temperature of the upper of the rectangular duct was increased from 305 to 307 K when increased the volume fraction from 0% to 0.5 %. But when using higher amount of nanoparticle concentration such as (2 and 3% vol.), it can be showed that the temperatures also slightly change, but they also mainly affected by the nanofluid hydrodynamics and when create the (secondary flows) inside the helical coiled duct. a) Water b) Al 2 O 3 Nanofluid 0.5% c) Al 2 O 3 Nanofluid 1.0 % editor@iaeme.com

19 Nabil Jamil Yasin and Kadhum Audaa Jehhef d) Al 2 O 3 Nanofluid 2.0 % e) Al 2 O 3 Nanofluid 3.0 % Figure.13: Velocity profiles of Al 2 O 3 Nanofluid with various volume fraction flows in rectangular helical spiral vertical duct at L c = 500 mm, Ar=0.25 mm, R h =40 mm and n=10. a) Water b) Al 2 O 3 Nanofluid 0.5% editor@iaeme.com

20 Numerical Investigation of Laminar Heat Transfer and Pressure Drop in Nanofluid Flow in Coiled Helical Duct c) Al 2 O 3 Nanofluid 1.0 % d) Al 2 O 3 Nanofluid 2.0 % e) Al 2 O 3 Nanofluid 3.0 % Figure.14: Temperature distribution of Al 2 O 3 Nanofluid with various volume fraction flows in rectangular helical spiral vertical duct at L c = 500 mm, Ar=0.25 mm, R h =40 mm and n= Pressure drop and Nusselt number The effect of three parameters of coiled duct includes aspect ratio, coil radius ratio and pitch coil radius on the pressure drop was plotted in Figure 15. The results showed that the pressure drop trend is the same for both aspect and coil radius ratios, where the pressures drop increased with them. But pressure drop will decreasing with Pitch coil radius. Also, in general the pressure drop increased with increasing Reynolds number. For water flow in helical duct, the pressure drop increased with increasing the Reynolds number. As plotted in Figure 15a, the minimum pressure drop was obtained is 561 N m -2 at Re = 160 with aspect ratio of0.25. But, the maximum one was obtained is 665 N m -2 at Re = 1500 with aspect ratio of 1. So based on these results, it can be noted that as the aspect ratio increases the pressure drop increases. Figure.16 presented the effect of aspect ratio, coil radius ratio and pitch coil radius on the Nusselt number. The result showed that the using ducts with high aspect ratio will become good choose in order to increasing the heat transfer rate and then increase the Nusselt number. The Nusselt number by 43% by using duct with aspect ratio of a/b=1 instead of duct of aspect ratio of a/b=0.25. And it increased by 21% by using duct with aspect ratio of R/b=4 instead of editor@iaeme.com

21 Nabil Jamil Yasin and Kadhum Audaa Jehhef duct of radius ratio of R/b=1, but, it decreased by -28% by using duct with Pitch ratio of p/b=0.25 instead of duct of aspect ratio of p/b=0.47at Re=1500. The Dean number (De) is varied from 65 to 590 for water, where water is considered as reference fluid in this study. Variations of pressure drop versus Dean number for various duct aspect ratios are shown in Figure. 17. It is seen that the increase in Dean number increases the pressure drop, and it can be noted that when the Dean number is increased, the secondary flow is intensified. And the effect of Dean number on heat transfer rate and on the Nusselt number for water is predicted in Figure. 18. It can be showed that Nusselt number significantly increases with increase the Dean number with similar trend. In laminar regime due to the curvature of the tubes centrifugal force is generated. This centrifugal force developed secondary flow. Due to effect of secondary flow there is higher heat transfer coefficient and high Nusselt number. The heat transfer enhancement is more in vertical position due to rapid developments of secondary flow. The pressure drop was observed to be increase with increase particle concentration as well as Dean number as shown in Figure 19 due to the increased density and viscosity at higher particle nanoparticles concentration. Also, the results indicated that the Nusselt number to be increase with increasing the particle concentrations as well as Dean number as shown in Figure 20. The results concluded that the nanoparticles concentration will lead to increase the maximum Nusselt number enhancement in by (68 %) was obtained at Dean number of 590 and particle concentration of 3.0%but, the minimum enhancement in Nusselt number by (31 %) was obtained at Dean number of 65 and particle concentration of 0.5%. The Nusselt number increasing with increasing the Dean number due to as the secondary flow formation increased and this lead to increase the boundary layer thinning. The decreasing thermal boundary thickness and increasing nanofluid conductivity are the main reason for enchantment the coefficients of the nanofluids heat transfer in coiled duct when a nanofluid is passing through the coiled tube Pressure 640 Drop, ΔP, 620 pa Re= Re= Re= Re= Aspect Ratio, (a/b) a) Aspect ratio editor@iaeme.com

22 Numerical Investigation of Laminar Heat Transfer and Pressure Drop in Nanofluid Flow in Coiled Helical Duct Pressure 640 Drop, 620 ΔP, pa 600 Re= Re= Re=1000 Re= Coil Radius Ratio, (R/b) Pressure 750 Drop, 700 ΔP, pa b) Radius ratio Pitch Ratio, 0.4 (P/b) c) Pitch ratio Figure. 15 Pressure drop of the water pitch coil radius ratio with various Reynolds numbers Nusselt 15 Number, Nu 10 5 Re=160 Re=500 Re=1000 Re=1500 a) Aspect ratio Re=160 Re=500 Re=1000 Re= Aspect Ratio, (a/b) editor@iaeme.com

23 Nabil Jamil Yasin and Kadhum Audaa Jehhef Re= Nusselt 10 Number, Nu 8 6 Re=500 Re=1000 Re= Coil Radius Ratio, (R/b) 5.2 b) Coil radius ratio Nusselt Number, 10 Nu 5 Re=160 Re=500 Re=1000 Re= Pitch Ratio, (P/b) 0.6 c) Pitch coil radius Figure. 16: Nusselt number of the water against coil radius ratio with various Reynolds numbers. 640 Pressure Drop, ΔP, pa Ar=1 660 Ar= Ar=0.3 Ar= Dean Number, De Figure. 17: Pressure drop of the water against Dean number ratio with various aspect ratio editor@iaeme.com

24 Numerical Investigation of Laminar Heat Transfer and Pressure Drop in Nanofluid Flow in Coiled Helical Duct Nusselt 20 Number, Nu 15 Ar=1 Ar= Dean Number, De Figure. 18: Nusselt number of the water against Dean number ratio with various aspect ratio Pressure 600 Drop, ΔP, pa 580 ϕ=0 % ϕ=0.5 % ϕ=1.0 % ϕ=2.0 % ϕ=3.0 % De Figure. 19: Pressure drop of the water against Dean number ratio with various nanoparticle volume fractions. 30 ϕ=0 % 25 ϕ=0.5 % ϕ=1.0 % Nusselt 20 Number, Nu ϕ=2.0 % ϕ=3.0 % De Figure. 20: Nusselt number of the water against Dean number ratio with various nanoparticle volume fractions editor@iaeme.com

25 Nabil Jamil Yasin and Kadhum Audaa Jehhef 3.8. Performance Evaluation Criterion (PEC) In order to evaluation the thermal performance of any system of fluid flowing, it can be used the PEC as defined below [24]: A Performance Evaluation Criterion (PEC) is adopted in order to compare the thermal and fluid-dynamic performance of the triangular-corrugated channels with different design factors. The variation of performance evaluation criteria (PEC) versus Reynolds number is shown in Figure. 21 for different nanoparticles concentrations. It is seen that the PEC value increases with the increase of Reynolds number, and then it decreases with further increase of the Reynolds number. The maximum value of PEC was 3.4 in the case of using volume fraction of 3% vol. and at Re=1000. It is clearly seen that when the Reynolds number is small, a better thermo-hydraulic performance can be achieved. Thus, to achieve a relatively good thermo-hydraulic performance over the tested Reynolds number range, the best parameter combination should be Re=1000 and φ=3 % vol. 4 Performance 3.5 Evaluation Criterion 3 (PEC) 2.5 (21) ϕ=0 % (water) 2 ϕ=0.5 % ϕ=1.0 % ϕ=2.0 % 0.5 ϕ=3.0 % Re Figure. 21: variation of PEC of the water and nanofluid against Reynolds number ratio with various nanoparticle volume fractions. 4. CONCLUSIONS In this study the laminar flow of the Al 2 O 3 -water nanofluid with various nanoparticles volume fraction flows in the vertical helical coiled duct with various aspect ratio for constant heat flux applied on the walls of the duct has been investigated numerically. The parameters was studied in this work incluies volume fraction of nanoparticles, Reynolds number, Dean number, aspect ratio, and radius ratio. The results showed that the pressure drop increases with increasing the aspect and coil radius ratios but it decreases with increasing pitch ratio. Also, there is a significant enhancement in the Nusselt number when increasing the duct aspect ratio and coil radius ratio as well as with increasing the Reynolds and Dean number for water and nanofluid. Finally, the results concluded that the Nusselt number get a maximum enhancement by (68 %) was obtained at Dean number of 590 and particle concentration of 3.0 %but, the minimum enhancement in Nusselt number by (31 %) was obtained at Dean number of 65 and particle concentration of 0.5 % editor@iaeme.com

26 Numerical Investigation of Laminar Heat Transfer and Pressure Drop in Nanofluid Flow in Coiled Helical Duct ACKNOWLEDGEMENTS The authors would like to thank to the Institute of Technology, Middle Technical University for their support to accomplish this work in the computer center of the Institute. NOMENCLATURES a coiled duct width, m b coiled duct higth, m p coil pitch, m R coil Radius, m n number of turns, - L coil length, m Re Reynolds number, - De Dean number, - Pr Prandtl number,- x i axial distance in x-direction, m x j axial distance in y-direction, m u i velocity in x-direction, m/s u j velocity in y-direction, m/s u' fluctuated velocity, m/s p fluid static pressure, Pa T temperature, K Uav average inlet velocity, m/s D h hydraulic diameter, m P cross section perimeter, m A c duct cross section area, m 2 A s heat transfer area, m 2 Cp Specific heat, J/kg.K h heat transfer coefficient, [W/m 2.K] k thermal conductivity, [W/m.K) m mass flow rate, kg/s V' volumetric flow rate, m 3 /s T in inlet temperatures, K T out outlet temperatures, K Tw local wall temperature, K Tf bulk fluid wall temperature, K ΔP pressure drop, Pa f friction factor, - Greek letters μ dynamic viscosity, Pa.s δ internal tube radius di/mean coil radius D editor@iaeme.com

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