Numerical and experimental investigations on the heat transfer enhancement in corrugated channels using SiO2-water nanofluid

In this paper, convective heat transfer of SiO2-water nanofluid flow in channels with different shapes is numerically and experimentally studied over Reynolds number ranges of 400-4000. Three different channels such as trapezoidal, sinusoidal and straight were fabricated and tested. The SiO2-water nanofluid with different volume fractions of 0%, 0.5% and 1.0% were prepared and examined. All physical properties of nanofluid which are required to evaluate the flow and thermal characteristics have been measured. In the numerical aspect of the current work, the governing equations are discretized by using the collocated finite volume method and solved iteratively by using the SIMPLE algorithm. In addition, the low Reynolds number k-ε model of Launder and Sharma is employed to compute the turbulent non-isothermal flow in the present study. The results showed that the average Nusselt number and the heat transfer enhancement increase as the nanoparticles volume fraction increases, however, at the expense of increasing pressure drop. Furthermore, the trapezoidal-corrugated channel has the highest heat transfer enhancement followed by the sinusoidal-corrugated channel and straight channel. The numerical results are compared with the corresponding experimental data, and the results are in a good agreement.


Introduction
In spite of using corrugated channels to provide a significant enhancement in thermal performance of the compact heat exchangers, this improvement was insufficient to meet all the industrial requirements. Therefore, research on enhancement technique in such channels have become very prominent. For this purpose, using nanofluids as a cooling fluids in corrugated channels instead of traditional fluids can enhance thermal conductivity of the base fluids and thereby a further improvement in thermal performance of heat exchangers with a more compact design. *Corresponding author Tel: +6 0108985308 Email: moh0891@yahoo.com, mohammed.ahmed@uoanbar.edu.iq Nusselt number for CuO-water nanofluid was higher than the Al 2 O 3 and TiO 2 -water but the shear stress was higher as well. Bianco et al. [11] have numerically studied on the turbulent forced convection of Al 2 O 3 -water nanofluid flow in a circular tube. The study was conducted for Reynolds number range of 10 4 -10 5 and particles volume fraction of 1%, 4% and 6%. Results showed that the heat transfer coefficient for nanofluid was higher than that of the base fluid. The enhancement in heat transfer increased with Reynolds number and particles volume fraction. Namburu et al. [12] have investigated numerically the turbulent convective heat transfer of nanofluids in a circular tube. To the best knowledge of authors, all the numerical studies on the convective heat transfer of nanofluids in corrugated channels were only focused on the laminar flow regime. In addition, the convective heat transfer of nanofluid in trapezoidal-corrugated channels has never experimentally studied. Therefore, this paper aims to investigate numerically and experimentally the turbulent forced convection flow of SiO 2 -water nanofluid in corrugated channels.

Nanofluid preparation
In this paper, nanoparticles of SiO 2 with the average diameter of 30 nm (Purchased from Beijing Deke Daojin Science And Technology Co., Ltd.) was used to prepare the nanofluid. The scanning electron microscope (SEM) of SiO 2 nanoparticles is depicted in Fig. 1 [20].

Thermophysical properties of nanofluids
The properties of nanofluids such as density, viscosity, thermal conductivity and the specific heat were measured in present study. Therefore, the thermal conductivity and the viscosity of the nanofluids were measured using KD2 Pro thermal properties analyzer (Decagon devices, Inc., USA) and Brookfield LVDV-III Ultra Rheometer, respectively. Furthermore, the density was measured using density meter (DA-130N, Kyoto Electronics). Moreover, a differential scanning calorimeter (PerkinElmer model DSC 4000) was used to measure the specific heat of nanofluids. All the measured properties of nanofluids and their base fluid are presented in Table 1. In experiments, when the flow reached a steady state condition, the pressure drop across the test section, the flow rate, the bulk fluid temperature at the inlet and the outlet of the test section as well as the wall temperature of the test section were recorded. After performed the experiments for nanofluid with one volume fraction, the system was washed (cleaned) with the pure water, in order to completely remove the nanofluid from system.

Test section
It consists of the top and bottom (main) walls and two side walls. The top and bottom (corrugated) walls of test section were fabricated from copper plates with dimensions of 8 mm thick, 50 mm wide and 240 mm long. However, the form of corrugations were accomplished by using wire electrical discharge machining (WEDM). The side walls of test section were fabricated from acrylic, 8 mm thick, to reduce heat losses to the environment. Each of them has two axial grooves (along the length of side wall) to prevent the fluid leakage from the test section. The test section was assembled and corrugated wall-side wall junction were sealed using thermal epoxy. Three different shapes of channels such as trapezoidal, sinusoidal and straight channels were fabricated and tested in this study, as shown in Fig.3. However, the average spacing, H av , between the top and bottom wall was 10 mm, the width of channel, W, was 50 mm, the axial length of the test section was 240 mm, the wavelength of corrugated channels, L w , was 20 mm and the amplitude of corrugated channel was 2.0 mm. Two adiabatic straight ducts, which are upstream acrylic duct of 800 mm and downstream acrylic duct of 200 mm length, were used in order to create appropriate conditions for the inflow and outflow of the test section.

Data reduction
The heat received by the nanofluids from the test section can be determined as follows [19]: Therefore, the average heat transfer coefficient can be expressed as follows [19]: Then, the average Nusselt number is calculated as follows [21]: Where h D is the hydraulic diameter of corrugated channel which can be defined as [9]: The frication factor ) ( f can be expressed as [20]:

Uncertainty analysis
The experimental uncertainties of dependent parameters, such as Reynold number, friction factors and Nusselt number, were estimated in current study based on the Kline and McClintock method [19]. For example, given a dependent parameter, R , as: Where 2 1 , X X and n X are independent measured parameters. Therefore, the uncertainty of R can be calculated as follows:

Problem description
The basic channels used in present study are trapezoidal, sinusoidal and straight channels, as depicted in Fig.3. The top and bottom walls of these channels are subjected to uniform heat flux conditions.
The average spacing between these walls is H av . The corrugated channel consists of ten corrugation units with amplitude of a and the wavelength of L w. . It is assumed that the flow is steady, fully developed, incompressible and two-dimensional. Furthermore, it can also be assumed that the mixture of base fluid (water) and the nanoparticles (SiO 2 ) are in thermal equilibrium and they flow at the same velocity. The mixture is also assumed as Newtonian fluid.

Governing equations
In this study, the single-phase approach has been used in the modeling of nanofluid. Therefore, the two-dimensional governing for steady, incompressible flow in terms of Cartesian coordinates are [22]: v-momentum equation: Energy equation: (11) In order to determine the turbulent dynamic viscosity (µ t ), the Launder-Sharma k-ε model is adopted in this study as follows: Turbulent kinetic energy equation [23]: Where the dissipation rate at the wall ( w  ) is given by: Turbulent kinetic energy dissipation equation [23]: Where In the above equations, the production rate of the turbulent kinetic energy ( k p ) is defined as: Also, the turbulent eddy viscosity is given by [23]: The empirical constants as well as the turbulent Prandtl number that appear in the above equations are defined as [23]: Furthermore, the wall-damping functions can be defined as [24]: And, the turbulent Reynolds number is given by: The above governing equations are transformed from Cartesian coordinate system ) , ( y x into bodyfitted coordinate system ) , (   due to the complex geometry used in this study. So, the transformed governing equations can be written in general form as follows: Where q 11 , q 12 and q 22 are geometry factors, J is the Jacobian of the transformation these factors can be defined as: And c U and c V are the contravariant velocity components in x and y direction, these velocities can be defined as [25]: In above equations, is the general variable,   is the diffusion coefficient and ) , (    S is the source terms. All of these parameters are defined in Table 2.

Boundary conditions
In order to solve the governing equations, appropriate boundary conditions for all dependent variables must be prescribed on all the boundaries of the computational domain. These boundary conditions are presented as follows [8]: ii. At the outlet section: 25) iii. At the walls of channel:

Implementation of numerical solution
In this study, the finite volume method method (FVM) is used for discretization of governing equations. The upwind scheme is used to discretise the convection terms of governing equations, while diffusion terms were discretised using the central differencing scheme. The SIMPLE algorithm was used, for coupling of the velocity and pressure equations, to determine pressure field [27]. The collocated grid arrangement was used in current study, in which all dependent variables are stored at the same control volume. This results in a weak coupling between the velocity components and the pressure. Therefore, Rhie and Chow momentum interpolation method [26] was used to provide a direct link between the velocity and the pressure nodes to avoid the unreal pressure oscillation.
Moreover, Poisson equations are employed to develop the computational mesh of the present study.
In order to achieve a better convergence behavior, under-relaxation is applied. The computation is terminated when the sum of absolute residual for each variables over computational domain is less than 1×10 -5 .

Validation of numerical methods and grid independence test
In order to validate the results obtained from CFD code developed in present study, the average Nusselt number for turbulent convective heat of air flow in triangular-corrugated channel are calculated and compared with the previous experimental results of Elshafei et al. [7] as shown in Fig.   4(a). According to this figure, the results are in good agreement. Moreover, the average Nusselt number for copper-water nanofluid flow in sinusoidal channel was compared with the numerical results of Heidary and Kermani [14]. From Fig. 4(b), it is found that the present results are very close to the previous results. To estimate the required grid size of the present study, the non-dimensional temperature and streamwise velocity at the trough of the eighth wave of the sinusoidal channel have been investigated for different grid sizes at Re=2000 and % 1   , as depicted in Fig. 5. It is found that the grid size of 995×101 ensures the grid-independent solution. the core (cold) fluid. As a results, the thermal boundary layer in corrugated channels is thinner than that for the straight channel and hence the temperature gradients near the heated-walls is higher, as shown in Fig. 6 (b).

Results and discussion
The average Nusselt number versus Reynolds number for trapezoidal and sinusoidal-corrugated channels at different volume fractions (0, 0.5 and 1%) is shown in Fig. 7. As expected, the average Nusselt numbers for both trapezoidal and sinusoidal channels increase with increasing Reynolds number, at a given volume fraction. Also, it is found that the average Nusselt number increases as the volume fraction of nanoparticles increase due to the addition naonparticles to the base fluid which can improve thermal conductivity of base fluid (hence heat transfer rate). Furthermore, it is found that for trapezoidal and sinusoidal-corrugated channels, the average deviation between numerical and experimental results are approximately 7.8% and 7.3%, respectively, which display good agreement between these results. The ratio of the average Nusselt number of nanofluid flow in corrugated channels to that of the distilled water ( % 0   ) flow in straight channel at different Reynolds numbers and volume fractions is given in Fig. 9. It should be noted that at % 0   , the enhancement ratio for both trapezoidal and sinusoidal channels increase with increasing Reynolds number because the fluid mixing in corrugated channels strongly depends on Reynolds number. Also, it can be clearly seen that enhancement ratio increases with the volume fraction of nanoparticles due to enhance the thermal conductivity of the base fluid. Therefore, at % 1   , both trapezoidal and sinusoidal channels display the highest enhancement in heat transfer over Reynolds number range.  Furthermore, the trapezoidal channel has the greatest pressure drop followed by the sinusoidal channel due to intensity of the re-circulation regions that appear in such channels in addition to the effect of the sharp edges of the corrugated channel. Also, it found that the straight channel has the lowest pressure drop because of there is no reverse flow in such channel. . It can be observed that the enhancement ratio for all shapes of channels increase with Reynolds number up to 3000. While, the enhancement ratio is slightly decrease when Reynolds number is beyond 3000. It is also found that the trapezoidal-corrugated channel provides the highest enhancement ratio followed by sinusoidal and straight channels. Therefore, the peak values of the enhancement ratio for trapezoidal channel obtained from computation and experiment are 5.5 and 5.8, respectively.

Conclusion
In