HEAT TRANSFER AND CU-WATER NANOFLUID FLOW IN A VENTILATED CAVITY HAVING CENTRAL COOLING CYLINDER AND HEATED FROM THE BELOW CONSIDERING THREE DIFFERENT OUTLET PORT LOCATIONS

A numerical study has been performed to investigate mixed convection flow in a vented square cavity with circular cooling obstacle. The governing equations such as two dimensional Navier-Stokes, continuity, and energy balance equations have been solved using a finite volume discretization method with SIMPLE algorithm. The effect of the Richardson number, outlet port location and volume fraction of nanoparticles were studied. The outlet port is varied from top to bottom in order to find the maximum heat transfer rate. The results indicated that by increasing the volume fraction of nanoparticles and reducing Richardson number, the heat transfer rate is enhanced. Moreover, it is found that the best configuration of the system for better heat transfer is obtained when placing the outlet port on the bottom location of the vented cavity.


INTRODUCTION
The knowledge of mixed convection flow in a ventilated cavity is of great interest of the phenomenon in many industrial applications and in the engineering devices such as, cooling of electronic circuit boards, ventilation of rooms with radiators, pollution removal, thermal design of buildings, solar systems, cooling of containers, and heat exchangers. A literature survey shows that a great number of studies on natural and mixed convection of nanofluid in enclosures have been used obstacles with different forms and various thermal conditions. Earlier, natural convection inside the rectangular cavities without and with obstacles were reported by researchers (Guiet et al., (2012); Kolsi et al., (2016); Boulahia et al., (2016); Boulahia and Sehaqui, (2015); Boulahia et al., (2017); Boulahia et al., (2017)a; Boulahia et al., (2017)b; Boulahia et al., (2017)c; Wakif et al., (2017)a; Wakif et al., (2017)b; Wakif et al., (2018)a; Wakif et al., (2018)b; Wakif et al., (2018)c). El Abdallaoui et al., (2015) analyzed numerically the free convection of nanofluid or pure fluid inside a square cavity with decentered and centered triangular heater (El Abdallaoui et al., (2014)) using the lattice Boltzmann method. Their investigations showed that at high Rayleigh, there is an important effect on heat transfer when the triangular block is placed vertically, but at weak values of Rayleigh the heat transfer is more affected for the decentered position of the block. Kalidasan and Kanna, (2017) was concentrated on the effect of natural convection inside the open square enclosure containing a central adiabatic square obstacle. They reported that the heat transfer on the right and left wall changes with increasing the percentage of nanoparticles concentration. AlAmiri et al., (2009) obtained numerical solutions of natural heat transfer convection in square enclosure with a rectangular block placed on the bottom wall. Their investigations showed that increasing the height and width of the * Corresponding author. Email: boulahia.zoubair@gmail.com rectangular hot block enhances the mean Nusselt number. The same study was performed by Varol et al., (2007) and Guiet et al., (2012) for a triangular cavity.
Many studies have been performed on mixed convection of nanofluides in squares cavities ; Khanafer and Aithal, (2013); Boulahia et al., (2016)a; Boulahia et al., (2016)b;Zoubair Boulahia et al., (2016)c). Mehrizi et al., (2012) introduced the effect of volume fraction of nanoparticles on mixed convection in a square enclosure having a central hot obstacle with inlet and outlet ports. They concluded that by increasing the solid volume fraction the heat transfer rate is enhanced at different Richardson numbers and outlet port positions. The heat transfer by mixed convection inside a vented cavity with an internal heated cylinder was studied numerically by Mamun et al., (2010). They founed that the size of the cylinder and the solid-fluid thermal conductivity has significant effect on thermal field. Bahlaoui et al., (2009) used a horizontal ventilated cavity with radiative heated bottom wall having an adiabatic thin partition. They reported that the convective Nusselt number decreases as the radiation effect increases. Kalteh et al., (2014) presented laminar mixed convection of nanofluid in a lid-driven square enclosure with a triangular heated block. They showed that increasing the nanoparticles diameter, the volume fraction and Reynolds leads to an increase in mean Nusselt number. Najam et al., (2004) investigated numerically laminar mixed convection in a ''T'' form cavity with heated obstacles submitted to a vertical jet of fresh air from below. Shahi et al., (2010) numerically studied the mixed convection of copper-water nanofluid inside a ventilated cavity. It was found that the average Nusselt number enhances when the volume faction of nanoparticles increased. Oztop et al., (2009) used a lid driven cavity containing adiabatic, isothermal or conductive circular block. They showed that the position and the size of the inner circular body has an important effect on the heat transfer rate.
2 Rahman et al., (2012) considered an open enclosure with heated circular cylinder. They concluded that by increasing Reynolds number, the Nusselt number increases.
The main objective of the present study is to examine a mixed convection heat transfer inside a vented cavity contains a central cold cylinder and with hot temperature at the bottom wall cavity. The first case under investigation is characterized the numerical models used in our study. The computational procedure elaborated in this study is validated against the numerical results of other researches. The effects of three different outlet port locations on the right wall of cavity are chosen for investigation. Wide range of parameters such as Richardson number (0.1 ≤ Ri ≤ 100), and volume fraction of nanoparticles (0 ≤ ≤ 0.05) have been used. The new models of the thermal conductivity and effective viscosity investigated by Corcione, (2011) are used to estimate themophysical proprieties of the nanofluid. Our numerical results are presented in the form of plots of isotherms, streamlines and mean Nusselt numbers to show the influence of nanofluid and design parameters.

PROBLEM STATEMENT
The problem configurations, coordinate system boundary conditions of the considered ventilated cavity are presented in in Fig. 1. It consists of a ventilated cavity contains a central cold cylinder with diameter (D=0.2) and uniformly heated with a constant temperature, , from its bottom wall while the other parts of the cavity are all thermally insulated. Three cases are considered, i.e., case A where the outlet port is located at the top position of the right wall of the cavity, case B where the outlet port is located at the medium position, and case C where the outlet port is located at the bottom position. The physical system is subjected to an external flow of nanofluid which passes through the vented cavity by injection. The nanofluid enters into the vented cavity from the left opening vertical wall which maintained at cold temperature, , and leaves from the right opening vertical one. The length of these openings have a constant value, 0.1 . It is assumed that the nanofluid is Newtonian, incompressible and laminar i. e, 10 and the base fluid and the nanoparticles are in a thermal equilibrium state. The thermophysical properties of the nanofluid used in this study are evaluated at the average fluid temperature /2 as listed in Table 1.

MATHEMATICAL FORMULATION
The governing equations including the two-dimensional transient equations of the continuity, momentum and energy for an incompressible flow are expressed in the following format: where the nanofluid effective density, heat capacity, thermal expansion coefficient and thermal diffusivity are calculated from the following equations (Haddad et al., (2012); Corcione, (2010)): Corcione models (Corcione, (2010); Corcione, (2011)) for the dynamic viscosity and the thermal conductivity of the nanofluid are given by: 1 4.4 . .
. . (10) The boundary conditions for mixed convection written as: The following dimensionless variables for mixed convection are defined based on properties of pure fluid: where is considered to be for mixed convection. Dimensionless numbers for the system are defined as: . , , The governing equations (1)-(4) are written in the following dimensionless form: 1 .
Dimensionless form of the boundary conditions can be written as: The dimensionless stream function can be written as: , where max The total mean Nusselt number of all cavity's wall is defined as:

NUMERICAL DETAILS
The discretization procedure of the governing equations (Eqs. (17)-(20)) and boundary conditions described by Eq. (21) is based on a finite volume formulation, given by Patankar, (1980) on a staggered grid. SIMPLE (Semi-Implicit Method for Pressure Linked Equations) is used to solve the coupled pressure-velocity equation while Hybrid Differencing Scheme (HDS) of Spalding, (1972) is used for the convective terms.
The key step of the finite volume method is the integration of the dimensionless governing equations (17)-(20) over a two-dimensional control volume CV. The integration of the transport equation may be written in a generic form for the variable as : where S is the source term and dV=dX.dY where P, W, E, N, S denote cell location, west face of the control volume, east face of the control volume, north face of the control volume and south face of the control volume CV respectively (see Fig. 2). The Line by line application of TDMA (Tri-Diagonal Matrix Algorithm) method (Spalding, (1972)) is applied on the system of equations until sum of the residuals became less than10 6 . The developed algorithm was implemented in FORTRAN program. 4

Grid independence study
In order to determine a proper grid for the numerical simulation, a square ventilated cavity filled with Cu-water nanofluid (φ=5%) having a circular cooling cylinder with diameter (D=0.2) is analyzed in two extreme Richardson numbers (Ri=0.1 and 100). The mean Nusselt number obtained using different grid numbers for particular cases is presented in Table 2. As can be observed from the table, a non-uniform 103×103 grid is sufficiently fine for the numerical calculation.

Table 2
Effect of the grid size on for the ventilated cavity filled with the Cu-water nanofluid 0.05 with a circular cooling cylinder with diameter / 0.2 for case C (see Fig. 1)

Validations
In order to validate the present code against various numerical results available in the literature some different heat convection problems are chosen. The first case is the benchmark problem of natural convection in a square cavity which considered by De Vahl Davis, (1983) filled with Air ( = 0.71). Table 3 demonstrates an excellent comparison of the average Nusselt number between the present results and the numerical results found in the literature (Barakos et al., (1994); Dixit and Babu, (2006)). The numerical results of Iwatsu et al., (1993) and Oztop et al., (2009) for a top heated moving lid and bottom cooled square cavity filled with air 0.71 . A 100 100 mesh was used and the computations were done for three different Richardson numbers. Table 4 demonstrates an excellent comparison of the average Nusselt number between the present results and the numerical results found in the literature (Iwatsu et al., (1993); Oztop et al., (2009)) with a maximum discrepancy of about 1.6 %.
Finally, we chose two other different convection problems (natural and mixed convection) to compare the flow structure. Fig. 3 illustrates the comparison of the isotherms and streamlines with that of mixed convection flow in vented cavity contains a circular heater reported by Xu et al., (2014) at (Pr= 0.7, Ri =1.0, Br=1.0, Le=0.1) and with a natural convection heat transfer and flow structures in a square enclosure with circular heater reported by Park et al., (2013) (Ra= 10 6 , Pr=0.7) .

RESULTS AND DISCUSSION
In this section, the mixed convection heat transfer inside a ventilated cavity contains a central cold cylinder with hot temperature at the bottom wall is under study. The effect of three different outlet port locations on the right wall of the cavity (Case A, B and C), and volume fraction 0 0.05 on heat transfer rate are discussed. The size of the circular cooler, , is fixed at 0.2 while the Grashof number, , is kept constant at 10 . Four different values of Reynolds number (Re = 10,31.62,100,and 316.22) are chosen to cover forced (Ri =0.1), mixed (Ri=1) and natural convection (Ri=10 and Ri=100) regimes. The variation of Reynolds number / is made by changing the velocity ( ) of the incoming flow. The effects of Richardson number, Ri, ranging from 0.1 to 100 and the three different outlet port locations (Case A, B and C) on streamlines and isotherms are shown in Fig. 4 and 5. The ventilated square cavity filled with Cu-water is analyzed for case A, B and C. For comparisons, the streamlines and the isotherms for pure fluid and nanofluid are shown by dashed line and solid line respectively. It can be seen from Fig. 4 and 5 that, there is some differences in streamlines and isotherms of pure fluid and nanofluid, which we can explain by the higher viscosity of nanofluid compared to that of the pure fluid which increases the diffusion of momentum in the nanofluid. Generally, the cold inlet fluid moves over the central cylinder before leaving the cavity, the arriving flow strikes to the left side of the cold cylinder, where the flow is directed from the inlet port toward top and down of the cooler and moves to the outlet port. space. The pattern of the streamlines where the circulating vortices near the inlet port almost change with the position of the outlet port ( Fig.4 : case A, B and C). By increasing the Richardson number (Ri>=1), the main flow traverses bottom of the cold cylinder which is due to decreasing of the incoming flow velocity. At Ri=1, mixed convection heat transfer is the dominant regime. The fluid flow occupies the whole of the ventilated cavity and bifurcates near the cold cylinder. It is clearly observed that by increasing Ri to 1, the circulating vortices near the inlet port become smaller in comparison with that of Ri =0.1, due to increased inertia force. The size of the corresponding vortices is bigger for the pure fluid than the nanofluid, it can be explained by the role of forced convection which is more significant for the pure fluid. At this two values of Richardson number (Ri=0.1 and 1), the outlet port position (Fig.4: case A, B and C) has not a significant effect on the streamlines distribution near the inlet port due to the mixed and forced convection are dominant. Fig. 6. Variation of (a) | | and (b) with respect to the volume fraction of the nanoparticles at different Richardson numbers, size and type of nanoparticles.
It is predictable that with increasing the Ri to 10, the circulating vortices near the inlet port almost disappear due to natural convection increases. Therefore, most flow passes through the bottom region. Fig. 4 displays at this Richardson number (Ri=10) that the streamlines form at the left side of the circular cold block is affected by the outlet position. It is clearly observed that the small rotating cell located on the bottom left of the cavity changes with the outlet port locations (case A, B and C).
At high Richardson number (Ri=100), the role of natural convection in formation of flow pattern becomes greater and consequently we can see from Fig. 4 a larger portion of the flow gets in contact with the heated bottom wall indicating a good convective heat exchange. At this Ri, the outlet port position has a considerable effect on the streamlines distribution and the form of the flow in the vented cavity. When the location of outlet port changes from top (case A) to the bottom (case C), the flow which passes at the bottom of the circular cooler increases.
The isotherms exhibited in Fig. 5 (Ri=0.1) are tightened on the heated bottom wall which indicate a good convective heat exchange. For all Richardson number, the intensity of the isotherms at the vicinity of the heated bottom wall increases by changing the outlet port from top to bottom position (case A, B, and C). At Ri=0.1, a large space of the vented cavity is at a uniform cold temperature due to the forced convection is dominant, where the heat provided by the hot wall without passing through the top space of the vented cavity. It can be seen from Fig. 5 at Ri=1, that the isotherms are less tightened with the heated bottom wall in comparison with pervious case (Ri=0.1). A further increase of Ri up to 1, as shown in Fig. 5, leads to decrease the cold zone of the vented cavity in favor of the thermal boundary layer which can be explained by effect of the mixed convection. The isotherms also take the shape of the circular cooler (see Fig. 5). For Ri = 100 (Fig. 5), the isotherms have more deflection on the left side of the circular cold obstacle, in this case, the role of natural convection becomes greater and consequently the cold zone of the vented cavity decrease more. Fig. 6(a-b) shows values of | | and in the same conditions of Fig. 4 and 5 at different outlet port locations (Case A, B and C), Richardson number and volume fraction of nanoparticles. The maximum stream function | | shows in Fig. 4 (9) which indicates that the increasing volume fraction of the nanoparticles, leads to increase in the viscosity of the fluid. Fig.  6(b) shows that changing the outlet port location from top to bottom has a significant effect on the heat transfer rate. Results reveals that the mean Nusselt number increases with reduction of Richardson number. At all Richardson number, it is clear that the most preferable heat transfer is obtained, when the outlet port of the vented cavity is placed on the bottom location (see Fig. 6(b): case C). At low Richardson number (Ri=0.1 and 1) the effect of forced and mixed convection regime is dominant, so we can observe from Fig. 6(b) that there is no significant effect between case A and B. At the corresponded Ri, the heat transfer rate changes weakly with the volume fraction of the nanoparticles and reaches its maximum value when the volume fraction is equal 2% for the most cases. By increasing Richardson number beyond 1, we can clearly observe that case A has become the best for a good heat transfer compared to the case B due to the dominance of the natural convection regime and the effect of the circular block, which hinders the flow of the nanofluid for case B than A.

CONCLUSION
Simulation of the mixed convection heat transfer inside a ventilated cavity contains a central cold cylinder was investigated by the finite volume method. The numerical results are realized for various values of Richardson number 0.1 100 and volume fraction of nanoparticles 0 0.05 . Three different outlet port locations on the right wall of the cavity (Case A, B and C) are studied. According to the presented results, the following conclusions are drawn:  The circular cylinder, the outlet port location, Richardson number, and volume fraction has a significant effect on the streamlines and isotherms.  At all Ri number, the maximum stream function | | decreases by increasing volume fraction of nanoparticles due to the increase in the viscosity of the nanofluid.  At all Ri number, changing the outlet port location from top to bottom has a significant effect on the heat transfer rate.  The best configuration of the system for batter heat transfer is obtained when placing the outlet port on the bottom location of the vented cavity (case C).  At low Richardson number (Ri=0.1 and 1), there is no significant effect on the heat transfer rate between case A and B, it changes weakly with the volume fraction of the nanoparticles and reaches its maximum value when the volume fraction is equal 2% for the most cases.  By increasing Richardson number beyond 1, the case A has become the best for a good heat transfer compared to the case B due to the effect of natural convection and the circular cold cylinder.