Numerical Investigation of Impinging Jets with Nanofluids on a Moving Plate

In this study a numerical investigation of an impinging jet flow, on a heated moving plate, is presented. The purpose of this study is to numerically investigate the effects of various parameters such as nanoparticle volume fraction, pulsating frequency, plate velocity, Reynolds number on the heat transfer characteristics. Navier-Stokes equations and energy equations are solved with a commercial finite volume based code. It is observed that adding nanoparticles increases the peak value of Nusselt number. It is also observed that the value of Nusselt number at the stagnation point is higher at the low velocities of impingement surface. In the unsteady case, heat transfer enhancement is seen at low frequencies.


INTRODUCTION
Impinging jets have been widely used in industrial applications because they provide high localized heat transfer coefficients.Drying paper and textile products, cooling of gas turbine equipments and walls of combustion chambers, cooling of electronic components, material and production processes and freezing of tissues during surgery operations are some of the different application areas of impinging jets.
In the application of jet impingements, jet configurations can be circular or slot type.Although more investigation can be found about heat and mass transfer of circular type jet in the literature, slot jet impingements have attracted more attention with their high cooling effectiveness, great uniformity and more controllability [1].The common types of impinging jets are with or without confinement.Confined jets have small size advantage, on the other hand easy production process and simple designing are the advantages of the unconfined jets.In the literature it can be encountered to different application models.For example turbulent jet flow on the moving plate [2], laminar jet flow on moving plate [3], impinging jet on obliquely flat surface [4], impinging jet on a porous medium [5] and impinging jet application on a semi circular concave [6].
In order to obtain heat transfer enhancement in jet impingement flows various techniques such as inserting fins or foams can be employed [7].These kinds of techniques require modification in the applied system however using nanofluid in the working fluid is a simple way for improving heat transfer rate and don't need any constructional modification in the application systems [8].
Many researchers have investigated the employment of nanofluids in impingement jets.The numerical investigation on hydrodynamic and thermal fields of Al 2 O 3 -water mixture in a radial laminar flow cooling system has carried out by Rot et.al.In their study [9] with the 10% volumetric concentration of nanofluid the heat transfer enhancement has found up to 200% in the case of Reynolds number which has a value of 1200.Roy et al [10] studied the cooling of electronic equipment for axisymmetric situation under the steady and laminar jet flow condition.Manca et al [11] carried out an application of nanofluid jet impingement for different Reynolds numbers in turbulent flow.Li et al [12] investigated the addition of Cu particles as a nanofluid and they also studied the effect of different jet velocities.Di Lorenzo et al [13] realized nanofluid application for confined type laminar jet flow.An experimental study of confined and submerged impinging jet on a flat ,horizontal and circular heated surface has carried out by Nguyen et al [14] and they had used Al 2 O 3 addition as a nanoparticle during their study.
In this study, Al 2 O 3 with different volumetric concentrations is used as a nanofluid.Laminar impingement jet flow applying on a moving plate have variable velocity and Reynolds number values.Investigation are carried out for both steady and unsteady flow states with computational fluid dynamics methods.

Physical Problem
A schematic description of the physical problem of computational domain considered in this study is shown in Fig. 1.The two-dimensional model of the physical problem has two plates separated with a distance H and length L and the width of slot is W. A jet from the rectangular slot on the top plate impinges on the moving bottom plate.In the study bottom plate is modeled as a moving wall.Velocity of the moving plate is given in the terms of velocity of the jet flow (v j ).Working fluid used in the jet flow is a mixture of water and nanosized Al 2 O 3 particles.Investigations are carried out for the Reynolds numbers which are equal to 100, 200 and 400.For the unsteady flow, the jet has a uniform velocity with a sinusoidal time dependent part (U = U0(1+sin(2πft)) The frequencies of the oscillation (f) are taken as 1,2,4 and 8 Hz respectively.The bottom plate is kept at temperature T h and the top plate is assumed to be adiabatic.During computation, it is assumed that the flow is incompressible, two dimensional, Newtonian and in laminar flow regime.
Figure 1.Geometry of the model

Thermo-physical properties of the Al 2 O 3 -water nanofluid
In the study, the mixture of water and Al 2 O 3 nanoparticles with different volumetric fractions is used as a working fluid and the mixture is assumed to be single phase model.Density, specific heat, dynamic viscosity and thermal conductivity values of Al 2 O 3 and water are given in Table 1.With the assumption of single phase fluid approach the effective thermophysical properties of working fluid are calculated with the following equations and obtained values are shown in Table 2.
The effective density of nanofluid can be found by the following equation based on the classical two phase mixture as where nf, bf and p denote nanofluid, base fluid and nanoparticle respectively.
Under the thermal equilibrium conditions the specific heat of the mixture is given where  denotes volumetric fraction of the nanofluid.
Dynamic viscosity of the nanofluid is computed using the correlation obtained from the least squares curve fitting of the experimental data as Wang et al. [15] Thermal conductivity of the nanofluid is obtained using the well known Hamilton and Crosser [16] model as, Considering the thermal equilibrium and assuming nanofluid behaves as a single phase fluid and its thermophysical properties are evaluated by the equations given above, the Energy where u, v, T and P represent two velocity components, temperature and pressure respectively.
The boundary conditions for the considered problem can be expressed as : Eqs. ( 5)-( 8) along with boundary conditions and initial conditions are solved with FLUENT [17].The convective terms in the momentum and energy equations are solved using First Order Upwind scheme and SIMPLE algorithm is used for velocity-pressure coupling.The convergence criteria for continuity, momentum and energy are set to 10 -3 ,10 -4 and 10 -7 , respectively.Time dependent parts are solved with implicit scheme.
For the unsteady calculations, steady state solutions are used as initial conditions.The computational domain consists of rectangular elements and in this study grid size of 300x36 is used to form the domain.Grid independence of the results has been assured.

RESULTS and DISCUSSION
The purpose of this study is to investigate the effects of nanoparticles and pulsating and non pulsating flow on the heat transfer and fluid flow characteristics for different pulsating frequencies and jet flow velocities and particle volume fractions in the laminar range of Reynolds number between 100 to 400.
In the present study, Reynolds number is varied between 100 to 400 and particle volume fraction is taken between 0 to 6 percent.The ratio of the slot-to-plate distance (H/W) is set to 4 and amplitude of the forcing A is 0.5.The oscillation frequencies f are 1 Hz, 2 Hz, 4 Hz and 8 Hz.The velocity of the moving bottom plate is set to 0.25, 0.5, 1 and 2 times of v jet respectively.The length of the plate L is set to L = 50W.

Steady Case
Velocity streamlines of impingement jet flow for different bottom plate velocities are depicted in Figure 2. Velocities of moving plate are taken 0.25, 0.5, 1, 2 times of jet flow velocity.While plate velocities are changing, volumetric fraction of nanoparticle and Reynolds number values are kept constant at 4% and 100, respectively.For motionless situation of lower plate, impingement jet produces a symmetrical counter vortex at the right and left sections of the plate.When the plate begins to move to +x direction, thermal and velocity streamlines begin to skew to right direction.The reason of this situation is additional drag force exerting on the fluid.Movement of the plate produces a shear stress on the fluid and as a result of this streamlines of jet flow crooks to the +x direction.The behavior of total heat transfer rate with regard to change in frequency is shown in Figure 7.In this investigation volumetric fraction and Reynolds number are taken as 4% and 100 respectively while bottom plate velocities are equal to 0,v jet and 2 (v jet ) respectively.Frequency increase enhances heat transfer rate until a specific value.

CONCLUSION
In the present study, jet impingement flow model that contains a mixture of Al 2 O 3 nanoparticle and water with changing volumetric fractions as a working fluid, on a moving plate with different plate velocities is investigated for both steady and unsteady laminar flows.
Following results are obtained: Plate velocity has an effect on the thermal and flow characteristic distributions of jet flow.When the ratio between the plate and jet velocities increases, plate velocity becomes dominant on the behavior of flow.Shear forces, which are the result of plate movement, force the jet flow to move with the same direction of plate and this causes skews at the isotherms and streamlines.In low plate velocities, stagnation points of jet flow are more distinct and visible and at these points Nusselt number values reach their maximum values, but increasing plate velocities reduces this clarity.For both steady and unsteady jet impingement, increase of volumetric fraction of nanoparticles enhances the total heat transfer rate because adding nanoparticles effect the heat transfer characteristics positively.For pulsating jet impingement, frequency increase enhances heat transfer rate until a specific value and total heat transfer rate increases until 2 Hz.
At the inlet jet section , -W/2≤ x≤W/2 , y =H v jet =v= U o and u=0 for steady state v jet = U o (1+0.5sin(2πft)) and u=0 for unsteady state  At the top plate , no-slip boundary condition with the adiabatic walls are used -L/2≤ x≤-W/2 , y=H ; v=0 , u=0 ,  T/  y=0 W/2≤ x≤L/2 , y=H ; v=0 , u=0 ,  T/  y=0  At the side surfaces, gradients of all variables in the x direction are set to zero x=±L/2 , 0≤y≤H  u/  x=0 ,  v/  x=0 ,  T/  x=0  At the bottom plate moving plate, moving wall boundary condition with constant temperature are used -L/2≤ x≤L/2 , y = 0 ; u = 0 , u = 0.25 (v jet ) , u = 0.5 x (v jet ) , u = 1 x (v jet ) , u = 2 x (v jet ) , v=0 Local Nusselt number is defined as x,t represent local heat transfer coefficient and k denote the thermal conductivity of the nanofluid.Spatial averaged Nusselt number is obtained after integrating the local Nusselt number along the bottom wall as averaged Nusselt number is obtained after integrating spatial averaged Nusselt number along the bottom wall for one period of the oscillation τ as

Figure 2 .
Figure 2. Velocity streamlines of jet impingement for different bottom plate velocities

Figure 4 .
Figure 4.The effect of volumetric fraction on the Nusselt number

Figure 5 .Figure 6 .Figure 6
Figure 5.The effect of volumetric fraction on the total heat transfer rate

Figure 7 .
Figure 7. Change of total heat transfer rate with frequency