Impact of baffle on forced convection heat transfer of CuO/water nanofluid in a micro-scale backward facing step channel

Numerical simulations have been carried out to investigate the thermal-hydraulic characteristics using water-based CuO nanofluid with volume fraction ( ϕ ) = 0 – 5% and fixed nanoparticle size ( d p ) = 20 nm at Reynolds numbers (Re) = 100 – 389 in a microscale backward facing step channel with and without a baffle using finite volume method. The flow is steady, laminar, and incompressible. The channel has an expansion ratio (ER) = 1.9423with a fixed step height (S) of 490 µm . To study the effect of the baffle, different geometrical configurations have been developed by varying its height and location. The height of the baffle is varied as H b = 160 – 640 µm . The baffle is stationed on the upper wall of the channel at a dimensionless distance (D) = 1, 2, 3 and 4. The upstream, step and upper walls are thermally insulated while the lower wall downstream of the step is under a constant heat flux (q s ") = 20000 W/m 2 . The parameters of interest for analysis are Nusselt number, skin friction coefficient and velocity distribution under different flow conditions. Results indicate that the rise in volume fraction and Reynolds number enhances the Nusselt number, indicating improved heat transfer. However, the skin friction coefficient decreases with the increment in Reynolds number. The increase in baffle height causes the Nusselt number and skin friction coefficient to rise. As the baffle is moved away from the step, the Nusselt number tends to decrease. In comparison to water, the heat transfer improved by about 164% using CuO nanofluid at Re = 389 with ϕ = 5% in the presence of the baffle with H b = 640 µm and D = 1. However, the heat transfer enhancement has been achieved at the cost of higher pumping power requirements.


INTRODUCTION
Sudden expansion occurs in many engineering applications such as microelectronics, gas turbines, combustion chambers, heat exchangers, etc. [1]. The prominent features of sudden expansion problems are the occurrence of flow separation and subsequent reattachment. Channels with a backward facing step (BFS) configuration are one of the widely investigated topics in fluid mechanics. In such geometries, the occurrence of flow separation leads to generation of turbulence in the recirculation zone which enhances mixing between fluids, and consequently improves heat transfer.
Over the years, heat transfer augmentation has been achieved by implementing several active and passive techniques such as geometry modifications, use of ribs and baffles, use of nanoparticles, etc. Among these techniques, nanofluids are considered to be one of the effective methods of enhancing the thermal performance of engineering systems. The prominent characteristic of such fluids is their enhanced thermophysical properties which facilitate heat transfer. The preparation of these fluids requires the suspension of nanoparticles into the conventional base fluids such as water, ethylene glycol, etc. [2].
In the past two decades, rapid progress has been made regarding heat transfer enhancement using nanofluids. Guo [3] provided a comprehensive review of the implementation of nanofluids for heat transfer enhancement. There have been massive numerical and experimental studies on heat transfer augmentation using nanofluids in different geometrical configurations with applications to different thermal systems. Abu-Nada et al. [4] numerically investigated the effect of nanofluids on heat transfer characteristics over a backward facing step using the finite volume method. Kherbeet et al. [5] utilized the finite volume method to study the mixed convection heat transfer over a microscale backward facing step under a constant heat flux condition using nanofluids with volume fractionsin the range of 1 -4 % and nanoparticle size (d p ) = 25 -70 nm. They found that SiO 2 nanofluid has the highest Nusselt number and Nusselt number increases with decreasing nanoparticle diameter. Ekiciler [6] performed a numerical investigation regarding laminar forced convection heat transfer utilizing Al 2 O 3 /water nanofluid in a duct having a single backward facing step configuration. He found that the Nusselt number increases with the rise in nanoparticle volume fraction and Reynolds number. Abdulvahitoglu [7] implemented an analytic hierarchy process to evaluate the performance of different nanofluids (Cu-water, NiO-water, and CuO-water) for engine cooling systems. He concluded that the Cu-water nanofluid is the most suitable coolant in terms of thermophysical properties as compared to the other nanofluids. Kilic et al. [8] numerically investigated the combined effect of the use of different working fluids(pure water, Al 2 O 3 / water, Cu/water, and TiO 2 /water) and swirling jets on heat transfer in a rectangular channel of a vehicle radiator. They found that the average Nusselt number increased by 51.3% with the rise in Reynolds number from 12000 to 21000. The CuO/water nanofluid registered increments on the average Nusselt number by 3.6%, 7.6%, and 8.5% as compared to Ti/ water, Al 2 O 3 /water, and pure water respectively.
Along with the utilization of nanofluids, researchers have also integrated the use of obstacles such as ribs, baffles, etc. to facilitate heat transfer in backward and forward facing steps. Heshmati et al. [9] numerically studied the forced convection heat transfer in a channel having backward facing steps with different expansion ratios in the presence of solid or slotted baffles at Re = 100 -400. They concluded that the geometry with an expansion ratio of 2 and solid baffle has the highest Nusselt number compared to other geometries. They also found that a slotted baffle installed at the top wall instead of a solid baffle reduced the average Nusselt number. Alawi et al. [10] carried out a numerical study of laminar mixed convection flow using nanofluids (Al 2 O 3 , CuO, ZnO, SiO 2 ) with ϕ = 1 -4 % and nanoparticle diameter in the range of 25 -80 nm over a backward facing step with a vertical baffle under a constant heat flux condition in the range of 10 -70 W/m 2 . Their results indicated that the SiO 2 nanofluid has the highest Nusselt number in comparison to other nanofluids. The effects of baffle height, width, and distance on heat transfer characteristics are substantial.
The survey of existing literature suggests that no studies have been carried out to investigate the effects of a vertical baffle in a micro-scale backward facing step under a constant heat flux boundary condition utilizing CuO nanofluid. Hence, the current work aims to perform a thorough investigation of the effects of the vertical baffle on the laminar flow and heat transfer characteristics of water-based CuO nanofluid with ϕ = 0 -5% and d p = 20 nm at Re = 100 -389. This work will further supplement our understanding of the flow and heat transfer characteristics of nanofluids in facing step channels. From design and application perspectives, our findings will be useful in the augmentation of heat transfer in thermal systems. Lastly, the results are presented in terms of Nusselt number, skin friction coefficient, and velocity contours for different Reynolds numbers and volume fractions.

Physical Model
Two-dimensional laminar forced convection heat transfer of water-based CuO nanofluid in a micro-scale backward facing step (MBFS) channel in the presence of a thin solid baffle is numerically investigated. A baffle is installed on the upper wall of the channel at a dimensionless distance (D = d/H) away from the step. A diagrammatic representation of the physical model is shown in Figure 1

Governing Equations
Two-dimensional, steady, laminar and incompressible flow is considered. Accordingly, the continuity, momentum and energy equations can be expressed as [11]: • Continuity equation: • Momentum equation: • Energy equation: where υ represents the kinematic viscosity and α is the thermal diffusivity.
The Reynolds number has been expressed in terms of hydraulic diameter as follows: where ℎ is the hydraulic diameter equal to twice the channel inlet height and is the fluid viscosity. Similarly, the Nusselt number (Nu) can be calculated as: where h is the heat transfer coefficient and k is the thermal conductivity of the working fluid. The skin friction coefficient (C f ) can be computed as: where τ w is the wall shear stress.

Thermophysical Properties of Nanofluids
The thermophysical properties of interest for CuO nanofluid are density, dynamic viscosity, specific heat capacity and thermal conductivity. The following theoretical relations have been utilized to approximate the effective properties of the CuO nanofluid: The effective thermal conductivity can be calculated from the following relation [12]: The effective viscosity has been determined from the empirical correlation provided by [13]: where µ eff and µ f are the viscosities of the nanofluid and the base fluid respectively. Similarly, ϕ is the nanoparticle volume fraction, d p is the nanoparticle diameter and d f is the diameter of the base fluid molecule. The equivalent diameter of base fluid molecule (d f ) can be expressed as follows: where M is the molecular weight of the base fluid, N is the Avogadro number and subscripts f and p refer to the base fluid and nanoparticle respectively. Here, ρ f 0 is the mass density of basefluid taken at reference temperature, T 0 = 273 K.
The effective density of the nanofluid can be approximated by the following correlation as follows [13]: (11) where ρ f and ρ p are the densities of the basefluid and nanoparticles respectively. The effective heat capacity of the nanofluid can be expressed as follows [14]: where (ρC p ) f and (ρC p ) eff are the heat capacities of the base fluid and the nanoparticles respectively. Table 1 provides the thermophysical properties of water and CuO at T = 300 K.

Grid Independence Study
To obtain a grid independent solution, nine progressively refined grids were generated using ICEM CFD software. The grid structure for the geometrical model without and with baffle is illustrated in Figures 2 (a-b). All the grids have expansion factors of 1.03 and 1.1 in the x-and y-directions respectively. The grid sizes range from 4×10 3 to 1.6×10 5 elements. Employing water as the working fluid, numerical simulations were carried out at Re = 100 for the Table 1. Thermophysical properties of water and CuO at T = 300 K  grid without baffle and the variation in the values of average Nusselt number and skin friction coefficient with increasing grid densities were obtained. Figures 3(a-b) present the variation in the values of average Nusselt number and skin friction coefficient respectively. With the increase in the grid size from 5×10 4 to 1.6×10 5 elements, it is observed that the changes in the values of average Nusselt number and skin friction coefficient are 2.2% and 1.77% respectively. Consequently, the grid containing 5×10 4 elements has been selected in terms of solution accuracy and computational time.

Model Validation
The present numerical solutions have been validated against the experimental and numerical results of Armaly et al. [15]. The validation of the current model has been done in terms of the non-dimensionalised values of reattachment point and velocity distribution. In their study, they considered air as the working fluid. The present numerical solutions have been validated for Re = 100 and 389 using water as the working fluid. Table 2 Figures 4 (a-d). Results indicate that the average deviations of x-velocity against the published literature at Re = 100 at x/S = 2.55 and 4.8 are 4.1% and 3.65% respectively. Similarly, the present results regarding the x-velocity at Re = 389 at x/S = 2.55 and 4.8 deviated by 2.38% and 2.25% respectively. Hence, our computational model demonstrates a good agreement with the published data.

Numerical Procedures
A finite volume method has been implemented in order to solve Equations (1)-(4) using commercially available ANSYS FLUENT software. The Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm has been employed to couple the pressure and velocity fields. For spatial discretization, the second-order upwind scheme has been used for continuity, momentum and energy equations. The residual for solution convergence has been set to 10 -8 for continuity, momentum and energy equations.

RESULTS AND DISCUSSION
This section deals with the impact of the vertical baffle on thermal-hydraulic characteristics using CuO nanofluid in the MBFS channel. The parameters of interest for analysis are Nusselt number, skin friction coefficient, and velocity distributions for different volume fractions and Reynolds numbers.

Effect of Volume Fraction Nusselt number
The effect of volume fraction on Nusselt number has been studied at Re = 389 with ϕ = 0 -5%. Figure 5 illustrates the distribution of local Nusselt number along the heated wall with increasing volume fraction. The results indicate that the heat transfer is augmented with the rise in volume fraction. This can be attributed to the fact that the thermal conductivity of the fluid is enhanced with increasing volume fraction. Due to the addition of nanoparticles, the rate of exchange of energy is enhanced due to their irregular and random motions in the fluid and thus contributes to more heat transfer [16].

Effect of Reynolds Number Skin friction coefficient
The effect of Reynolds number on skin friction coefficient has been investigated at Re = 100 -389 with ϕ = 5% and a fixed baffle height (H b ) = 640 µm installed at D = 1. Figure 6 (a) presents the distribution of local skin friction coefficient along the heated wall with increasing Reynolds numbers. It can be observed that the skin friction coefficient decreases with the rise in Reynolds number. The reason is that the skin friction coefficient is inversely proportional to Reynolds number.

Nusselt number
The distribution of Nusselt number with increasing Reynolds number has been studied. Figure 6 (b) shows the    Figures 7 (a-e) depict the flow structures at Re = 389 with ϕ = 5%.In the absence of baffle, a primary recirculation zone is formed behind the step due to negative pressure gradient arising due to sudden expansion as shown in Figure 7 (a).The reattachment of the main flow occurs at x/S = 8.08. Additionally, a secondary recirculation zone of small size and strength is also present close to the lower corner between the step and the heated wall. With the insertion of baffle, the flow dynamics is significantly altered as shown in Figures 7  (b-e).A drastic change in the flow structures even with a short baffle of H b = 160 µm is observed as shown in Figure 7 (b).The main flow is directed towards the lower section of the channel, forming a densely packed region due to contraction caused by the baffle. It can be noticed that there is a reduction in the size of the primary recirculation zone near the step. This causes shifting of the reattachment point of the main flow towards the step direction.
Meanwhile, on the upper section of the channel near the baffle, the appearance of the second secondary recirculation zone consisting of counter-clockwise vortices takes place. When the baffle is elongated to H b = 320 µm as shown in Figure 7 (c), a peculiar development in the flow structures occurs inside the channel. There is a re-separation of the flow on the heated wall, creating a new secondary recirculation zone in the channel. Also, the primary recirculation zone near the step gets further reduced in size. With further extension of the baffle up to H b = 640 µm, the primary recirculation region significantly shrinks in size,

Nusselt number
The effect of increasing baffle height from H b = 160 µm to 640 µm on thermal characteristics has been investigated at Re = 389 with ϕ = 5 and D = 1. Figure 9 (a) shows the distribution of local Nusselt number along the heated wall for the cases with no baffle and aforementioned baffle heights. In the case without baffle, the Nusselt number steeply rises, and reaches the maximum peak near the reattachment point of the primary recirculation region behind the step. Then it slowly decreases downstream of the heated wall due to the thickening of thermal boundary layer and almost a fixed shape is attained. With the addition of baffle, the distribution of Nusselt number is strongly affected. When a short baffle with H b = 160 µm is installed, the local Nusselt number increases and its peak value is enhanced by about 1.6  of local Nusselt number appears at the reattachment point of the secondary recirculation zone formed downstream of the lower wall. The growth in size and strength of the secondary recirculation zone helps the mixing process, thereby enhancing the heat transfer. Results indicate that for baffle heights in the range of H b = 160 -480 µm, the location of their maximum peak valuesof Nusselt number is observed outside and slightly away from the compressed primary recirculation zone. For the longest baffle with H b = 640 µm, the highest value of local Nusselt number occurs slightly away from the baffle side wall after the flow leaves the contracted primary recirculation zone. Figure 9 (b) shows the variation of average Nusselt number at Re = 100 -389 for the cases with and without baffle. It is clear that the average Nusselt number increases with Reynolds number for all baffle heights, with the maximum value attained at Re = 389 and H b = 640 µm. Calculations show that the average Nusselt number increased by 164% as compared to the case without baffle.

Skin friction coefficient
The effect of baffle height on skin friction coefficient has been studied. Figure 10 shows the trend of local skin friction coefficient at Re = 389 with ϕ = 5% in the presence of a baffle stationed at D = 1 with increasing heights i.e. H b = 160 -640 µm. It is seen that the behavior of local skin friction coefficient is significantly affected with the addition of baffle. In the case of a short baffle with H b = 160 µm, two peaks of local skin friction coefficient appear due to times the maximum peak Nusselt number for the case without baffle. This is because the presence of baffle leads to the increase in temperature gradient arising due to the thinning of thermal boundary layer [17]. With a further increase in baffle height, the local Nusselt number drastically increases. When the baffle is elongated from H b = 160 µm to 640 µm, the peak Nusselt number significantly increases by about 2.4 times the case with H b = 160 µm. On the other hand, for the case with H b = 640 µm, a noticeable second peak  the effect of baffle. The minimum peak of local skin friction coefficient corresponds to the compressed primary recirculation zone while the maximum peak is observed outside and slightly away from the compressed primary recirculation zone. With a gradual increase in the baffle height from 160 µm to 640 µm, it can be noticed that the two peaks of the skin friction coefficient rise and is shifted towards the step direction. The rise in skin friction coefficient can be attributed to the fact that the velocity gradient in the flow substantially increases with the increase in baffle height.
For the longest baffle with H b = 640 µm, the maximum peak value of local skin friction coefficient is seen and is located near the baffle side wall after the flow exits the compressed primary recirculation region.

Effect of Baffle Distance Flow structures
In this section, the influence of baffle distance on flow structures has been investigated for different baffle positions i.e. D = 1, 2, 3 and 4 on the upper wall of the channel. To

Skin friction coefficient
The distribution of local skin friction coefficient with increasing baffle distance i.e. D = 1, 2, 3 and 4 at Re = 389 investigate the flow structures inside the channel, the baffle with a fixed height of H b = 640 µm is moved away from the step i.e. with the increase in D. Results are presented at Re = 389 with ϕ = 5% for geometrical configurations mentioned above as shown in Figures 11(a-e). Figure 11(a) shows the regular flow structure for the case without baffle. When the baffle is located at D = 1, there is the formation of the three recirculation zones at different channel locations as shown earlier in Figure 8. With a gradual movement of the baffle from D = 1 to 4, it can be observed that the size of the primary recirculation zone near the step increases while the secondary recirculation zones at the upper and lower walls shrink in size. Such flow behavior continues to occur when the baffle is placed further away from the step i.e. D = 2 to 4. Figure 12 demonstrates the effect of baffle distance (D = 1, 2, 3 and 4) on local Nusselt number along the heated wall at Re = 389 with ϕ = 5% and a fixed height of H b = 640 µm. Figure 12(a) clearly shows that there is a gradual decrease in local Nusselt number with movement of the baffle away from the step. For all baffle positions, the maximum peak of Nusselt number is attained slightly away from the baffle side wall. Figure 12   with ϕ = 5% and a fixed height of H b = 640 µm is shown in Figure 13. It is observed that when the baffle is gradually displaced away from the step, there is decrement in the peak local skin friction coefficient which is located slightly away from the baffle side wall. The maximum peak of local skin friction coefficient is obtained when the baffle is placed at D = 1 and the average skin friction coefficient increased by about 291% as compared to the case without baffle.

CONCLUSION
Numerical investigations were carried out to study the flow and thermal characteristics using water-basedCuO nanofluid at different Reynolds numbers and volume fractions in a micro-scale backward facing step (MBFS) channel with and without baffle. Different geometrical configurations of the MBFS channel were created by changing the baffle height and distance on the upper wall to study their effects on parameters such as velocity distribution, Nusselt number and skin friction coefficient. The conclusions of the present study are as follows: • The increase in volume fraction and Reynolds number leads to the enhancement of Nusselt number. But the skin friction coefficient decreases with the rise in Reynolds number. • The analysis of the effects of baffle height and location suggests that there exists an optimum position and height of the baffle under certain flow conditions at which the heat transfer is drastically improved. • The baffle height has a significant influence on flow and heat transfer. As the baffle is elongated, the Nusselt number is gradually enhanced. Also, the elongation of the baffle causes the primary recirculation zone formed behind the step to decrease, while the secondary recirculation region behind the baffle tends to increase in size. • The position of the baffle also presents dramatic effects on thermal-hydraulic characteristics. With the increase in the distance between the baffle and the step, the Nusselt number tends to decrease, while the primary recirculation region increases in size. • The heat transfer increased by 164% when the baffle of height of 640 µm is placed near the step. But the average skin friction coefficient showed increment by 291% as compared to case without baffle. This suggests that an improvement in heat transfer has been achieved with the penalty of increased pumping power requirements.

DATA AVAILABILITY STATEMENT
The authors confirm that the data that supports the findings of this study are available within the article.
Raw data that support the finding of this study are available from the corresponding author, upon reasonable request.

CONFLICT OF INTEREST
The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

ETHICS
There are no ethical issues with the publication of this manuscript.