3D Numerical simulation of turbulent heat transfer and Fe3O4/nanofluid annular flow in sudden enlargement

In this paper, 3D Simulation of turbulent Fe3O4/Nanofluid annular flow and heat transfer in sudden expansion are presented. k-ε turbulence standard model and FVM are applied with Reynolds number different from 20000 to 50000, enlargement ratio (ER) varied 1.25, 1.67, and 2, , and volume concentration of Fe3O4/Nanofluid ranging from 0 to 2% at constant heat flux of 4000 W/m. The main significant effect on surface Nusselt number found by increases in volume concentration of Fe3O4/Nanofluid for all cases because of nanoparticles heat transport in normal fluid as produced increases in convection heat transfer. Also the results showed that suddenly increment in Nusselt number happened after the abrupt enlargement and reach to maximum value then reduction to the exit passage flow due to recirculation flow as created. Moreover the size of recirculation region enlarged with the rise in enlargement ratio and Reynolds number. Increase of volume Fe3O4/nanofluid enhances the Nusselt number due to nanoparticles heat transport in base fluid which raises the convection heat transfer. Increase of Reynolds number was observed with increased Nusselt number and maximum thermal performance was found with enlargement ratio of (ER=2) and 2% of volume concentration of Fe3O4/nanofluid. Further increases in Reynolds number and enlargement ratio found lead to reductions in static pressure.


Introduction
Due to annular fluid flow and heat transfer characteristics are commonly used in condensers, heat exchangers, nuclear reactors, evaporator,..etc therefore, many experimental and numerical investigation have been achieved to improve efficiency of thermal and cooling systems. Sudden expanding or contracting in cross sectional area of flow passage is one of the important technique for enhancing thermal performance. Biswas et al. [1] conducted study on influence step height of backward-facing step on characteristics of fluid flow and get that increase in separation length non-linearly and acceptable with Armaly et al. [2] because increase in step height. Also Augmentation in heat transfer was noticed by effect of contraction ratio and maximum improvement was found at contraction ratio of 1 as described by Hakan et al. [3]. Modification in transport pipeline has significant effect on thermal performance such as expanding or contracting in passage, ribbed channel, and used fins are examined in numerous numerical and experimental researches [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. In the last two decades, many researches are used nanofluids as alternative fluids due to it have been greater thermal conductivity compared to normal fluids [19][20][21][22][23][24][25][26][27][28]. Kherbeet et al. [29,30] have experimentally and numerically investigated on effect using nanofluids * Corresponding author: htokan_2004@yahoo.com; hussein-tokan@utq.edu.iq flow in forward facing channel where determined the highest Nusselt number was about 30.6% at 1% SiO2 nanofluid. Moreover, Togun et al. [31,32] employed K-E model for analysis heat transfer characteristic and nanofluids flow through a channel with forward facing step. The results found that increase in Nusselt number with increased of volume concentrations of nanofluids, step height, and Reynolds number. However Safaei et al. [33] applied shear stress transport K-ω model to study thermal performance by using (FMWCNT) nanofluids flow over FFS. They noticed that increases in Reynolds number and volume fractions lead to rises in heat transfer coefficient. From the previous researches, few studies adopted effects volume fractions of nanofluids with enlargement ratio and Reynolds number in annular flow passage on enhancement heat transfer rate. Therefore, the purpose of the current research is to investigate numerically the enrichment of heat transfer in abrupt enlargement of annular flow passage and the influences of volume concentrations of nanofluids, Reynolds numbers and enlargement ratio on thermal performance.

2.1Physical Model and boundary conditions
The physical model of current paper is presented in Fig.  1A. Create geometry and meshing process by Ansys software in three dimensional as shown in Fig. 1B. The boundary condition is represented by inner pipe is insulted and has constant diameter (di) of 25 mm and length 2500 mm) while outer pipe divided into two section the inlet pipe is insulated and has different diameters (De) of 80, 60, 50 mm and length (a) of 1500 mm) while the exit pipe is heated with a constant diameter (Dt) of 100 mm and of length (b) of 1000 mm. In this simulation, the set of parameters applied to run the summations are presented in Table 1. In addition to that assumes there is no slip conditions occur between them at thermal equilibrium. Fully developed velocity was considered with hydrodynamic steady. .

Physical properties of the nanofluid
In order to compute physical properties of the nanofluid specific correlations are applied. The current density of nanofluid (ૉ ‫ܖ‬ is calculated by eq. (1), [34] ρ ୬ = (1 − ϕ)ρ + ϕρ ୬୮ (1) Where ρ and ρ ୬୮ are define the density of the normal fluid and the solid nanoparticles respectively. The specific heat of the nanofluid is found by eq. (2), [34], are define the heat capacities of the normal fluid and the solid nanoparticles respectively. Effective thermal conductivity of nanofluids determined by Wasp model [35] and [36]: The effective dynamic viscosity found by eq. (4) [37] ߤ = ߤ × (1 + 2.5 × ߶) (4)

Governing equations
The set equations of continuity, momentum and energy are used in three dimension form and solved based on control volume method [38] ப ப୶ = 0 To compute Reynolds stresses and heat fluxes the eqs.8 and 9 are used: In the current study k-ε turbulence standard model are applied based on the turbulence kinetic energy and energy dissipation [39].
According to hydraulic diameter the Reynolds number are considered by equation (14) ܴ݁ To achieve satisfy simulation results the standard kɛ turbulence model was certain, 2 nd scheme with join between pressure and velocity is applied at SIMPLE algorithm. Every iteration and the convergence condition in the remaining calculation was calculated and arranged where fewer than 10 -6 for the continuity, and lesser than 10 -7 for the momentum and energy equations.

Mesh-Independent and code validation
In order to get mesh independent five sizes of mesh were considered as shown in Table 2. Fourth mesh is selected as mesh independent due to the change in average Nusselt number between the fourth and fifth mesh was less than 1%. In this simulation the results of nanofluid flow and heat transfer over backward-facing step channel [40] were adopted for confirmation of the current model. The results from fig. 2 showed the good agreement between results of current model and results of Al-aswadi et al. [40].  Distributions of local Nusselt number at different Reynolds number with enlargement ratio of 2 are presented in Figs. 4A and 4B for water and 2% of Fe3O4 nanofluid respectively. Increases in Reynolds number observed effect on increases of local Nusselt number due to increases flow rate and the peak of profile Nusselt number noticed nearer to corner of abrupt enlargement results of separation flow as created. Fig. 5 shows that the effect of volume concentrations of Fe3O4 nanofluid on local Nusselt number at enlargement ratio of 2 and Reynolds number of 50000. Increase in volume concentration Fe3O4/nanofluid observed lead to enhance the Nusselt number due to nanoparticles heat transport in base fluid which raises the convection heat transfer rate. The findings denoted that the highest of Nusselt number was happened at 2% volume concentration of Fe3O4 nanofluid and Reynolds number of 50000. For more explanation the profile of static pressure at different Reynolds number and enlargement ratios are presented in Fig 6 and 7 respectively. For all cases reduction in local static pressure at entry section of abrupt enlargement and then suddenly augmented to converge near the exit for all cases. It can be seen from the result increases in Reynolds number and enlargement ratio lead to decreases in static pressure and the local static pressure have been same trends and the lowest static pressure detected at enlargement ratio 2 and Reynolds number 50000.