Effect of Insulated Oblique Plates on Heat Transfer and Recirculating Flow in a Channel

doi:10.4236/jamp.2014.26048

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Journal of Applied Mathematics and Physics, 2014, 2, 405-410

Published Online May 2014 in SciRes. http://www.scirp.org/journal/jamp

http://dx.doi.org/10.4236/jamp.2014.26048

How to cite this paper: Zhan, Y.X. and Park, T.S. (2014) Effect of Insulated Oblique Plates on Heat Transfer and Recirculat-

ing Flow in a Channel. Journal of Applied Mathematics and Physics, 2, 405-410. http://dx.doi.org/10.4236/jamp.2014.26048

Effect of Insulated Oblique Plates on Heat

Transfer and Recirculating Flow in a

Channel

Yinxiao Zhan, Tae Seon Park

School of Mechanical Engineering, Kyungpook National University, Daegu, South Korea

Email: [email protected]

Received March 2014

Abstract

Flow and heat transfer characteristics of a channel with oblique plates which are mounted pe-

riodically on the channel wall have been numerically investigated in a laminar range. The main

objective of the present study is to find the effect of the tilt angle of oblique plate on pressure drop

and heat transfer characteristics in unsteady states. To get the different conditions of the heat

transfer and flow evolution, two key parameters of the Reynolds number and the tilt angle of ob-

lique plate are considered. At

Re200, 600=

, the tilt angles are changed for the range of 50˚ - 13 0˚.

The computational results show that the heat transfer and pressure drop are strongly dependent

on the tile angle and Reynolds number. When the flows are unsteady, the tilt angle has an impor-

tant role in the heat transfer enhancement. Oscillatory structures induce the better mixing of the

therm al field and promote the wall heat transfer. For a constant plate length, the wall heat trans-

fer is maximized near the 90˚ - 100˚. This is strongly coupled with the variations of flow mixing

induced by the oblique plate.

Keywords

Heat Transfer Enhancement, Reynolds Num ber , Flow Oscill atio n

1. Introduction

In general, when the flow in a channel is destabilized by periodic disturbance promoters, the heat transfer is sig-

nificantly changed [1]. This technique has been frequently adopted for heat transfer devices because the promo-

ter enhances the wall heat transfer.

Several studies of oscillatory flow and heat transfer in a channel were carried out. Valencia [2] [3] investi-

gated flow structure and heat transfer in a channel with periodically mounted transverse vortex generators in the

Reynolds number range of steady to oscillatory flow. They found self-sustained oscillations enhanced mixing

between the core fluid and the fluid near the wall. Saha and Acharya [4] analyzed the unsteady three-dimen-

sional flow and heat transfer in a pin-fi n heat exchanger. They showed the heat transfer is enhanced significantly

when the flow becomes unsteady. Guzman and Valle [5] investigated a transition scenario of two Hopf bifurca-

Y. X. Zhan, T. S. Park

406

tions when the flow evolves from a laminar to a time-dependent periodic and then to a quasi-periodic flow. And

the increase of the Nusselt number is higher for a quasi-periodic than for a periodic flow regime.

On the other hand, the flow structure and heat transfer in a channel attached the rib is investigated by several

researchers. Sriharsha et al. [6] discussed the influence of rib height on the local heat transfer distribution and

pressure drop in a channel with 90˚ continuous and 60˚ V-broken ribs. They indicated that the heat transfer

augmentations caused by 60˚ V-broken ribs are higher than those of 90˚ continuous attached ribs. But as the rib

height increases, the enhancement by the broken ribs is decreased. Tanda [7] [8] studied flow and heat transfer

in a rectangular channel with 45˚ angle rib on one/two walls. They showed that secondary responsible for heat

transfer performance are presented.

The effects of Reynolds number and tilt angle of the oblique plate attached to the upper wall of the channel

were studied numerically by using the finite volume method. The tilt angle is changed for the range of 50˚ - 130˚

and plate length is selected as 0.4 H. Here, H is the channel hei g ht. The present study is to elucidate the effects

of tilt angle of the oblique plate on heat transfer and pressure drop for various Reynolds number.

2. Numerical Methods and Flow Condition

2.1. Governing Equation

The flow is two-dimensional with constant properties. The x-axis is taken in the flow direction and the y-axis is

perpendicular to the flow direction. The flow is assumed to be laminar and incompressible. Buoyancy force is

neglected. The governing equations for continuity, momentum and temperature are given by

( )0

∂=

∂

(1)

()[ ()]

ij i

jijj i

UU F

t xxxxx

ρ µδ

∂

∂∂

∂ ∂∂

+=+ ++

∂∂∂∂∂ ∂

. (2)

() ()

j jj

txxpr x

∂∂∂ ∂

. (3)

represents the streamwise mean pressure gradient, which needs to be calculated dynamically in order to

maintain a constant mass flow rate and

is the kronecker delta.

2.2. Numerical Methods and Boundary Condition

The spatial discretization is performed with the fourth-order compact scheme The viscous term and the other

terms are evaluated by the fourth-order central difference. A nonstaged grid arrangement is adopted and the

momentum interpolation technique is employed to avoid pressure-velocity decoupling. The PISO algorithm is

employed for pre ssure-velocity coupling [9]. The momentum and energy equations are solved with second-or-

der upwind scheme. Periodic boundary condition with constant mass flow rates is specified at the inlet and out-

let of the channel. No-slip and constant wall temperature conditions are specified on the upper and lower walls

of the channel. Oblique plate is insulated. In order to assess the accuracy of these computations, the grid inde-

pendence is carried out in the analysis by adopting different grid distributions of 150 × 60, 170 × 80, 200 × 100

and 230 × 120. The grid systems of 220 × 120 show a satisfactory solution.

2.3. Configuration

Figure 1 shows the flow geometry and the coordinate system. It is consisted of two walls channel of height H

with insulated a thin oblique plate (t = 0.02 H) on the upper wall. Upper and lower walls are maintained at a

constant temperature. The lengths of the oblique plates is

0.4 H

, channel height is H. The periodicity length L

2.5 H

. For all cases, the inclination angle of the plates varies from 50˚ to 130˚ with an increment of 10˚.

To validate of the present numerical method, the numerical results of Cheng and Huang [10] are compared

with the present result (not shown in here). The present numerical prediction shows a very good agreement with

the numerical results of Cheng and Huang. So, this provides a strong confidence in further investigation of

channel flow with the oblique plate.

Y. X. Zhan, T. S. Park

407

Figure 1. Flow configuration.

3. Results and Discussion

Figure 2 shows time mean streamlines and temperature contours for α = 50˚, 70˚, 90˚, 130˚, respectively, at

Re 200

. Recirculation regions are identified between the baffles for all tilt angle. Center of the recirculation is

moved to the downstream due to the effect of the oblique plate tilt angle. Instantaneous streamlines and temper-

ature contours during one time period of flow are presented in Figure 3 at

Re 600=

, α = 50˚, 90˚. It can be

seen that vortices induced by oblique plate along the walls remove to the downstream. The main stream moves

toward the upper and lower walls in an alternating manner. At the same time, the counter-rotating vortices are

also generated along the lower wall by the oblique plate. Compared with the α = 50˚ and α = 90˚, larger size of

vortices are formed and the number of the vortices is increased for the case of α = 90˚. As the result, more active

mixing and scalar transport are induced.

The wall heat transfer depends on the geometrical condition. Figure 4 shows the Nusselt number for different

tilt angles, as

increase. The local Nusselt number is defined as follows:

(/) /()

NuTy HTT=∂∂ −

. The

mean Nusselt number along the channel wall is expressed by integrating the local Nu on the channel wall:

avg

NuL Nudx=

∫

As can be seen that,

is increased as increasing

. In steady state, the variation of

is not sensitive to the tilt angle. But as

increases, the local

is strongly depends on the tilt angle.

For small

, the recirculating flow reduces the local

because it makes the thermal boundary layer thicker

(see Figure 2). For larger Re, size and number of the vortex plays major role for heat transfer enhancement (see

Figure 3). We can see that

is maximized at

≈°

This paper is to present the effect of the tilt angle on flow structure and heat transfer. Figure 5 shows distri-

bution of time-averaged local

, time-averaged local skin friction coefficient

and time-averaged pres-

sure coefficient

along upper wall at

Re 600=

. The value of

reflects the appearance of flow separa-

tion and reattachment. The peak is related to the accelerated flow caused by positive vorticities near the upper

wall. It shifts from downstream to upstream as increasing the tilt angle. This represents that the vortical region

varies with the tilt angle. In the vicinity of 90˚, the oblique plate generates a flow pattern characterized by high

velocity and velocity gradients, which generate higher shear stresses, consequently, a higher friction coefficient.

Therefore, the peaks of

are strongly related to the local maximum of

. To show pressure distribution

on the upper wall, pressure coefficient, defined as

() / (12)

p refm

C ppU

= −

where

is the static pressure on the wall and

ref

is a reference pressure. The pressure on the upper wall

drastically increases as tilt angle increases to 90˚. It demonstrates that flow should be strongly dependent upon

tilt angle.

Figure 6 presents the distribution of time-averaged pressure coefficient

along the upper wall for α = 50˚,

90˚. For both cases, they have a similar distribution trend, near the upstream plate pressure is decreased as

increases, however, when flow move towards next plate, pressure is increased with increasing

. It is clear

that the pressure drop of the α = 90˚ along the upper wall is larger than that of the α = 50˚ at the same

. It is

interesting that the flow at

/ 0.1xL H=

for α = 90˚, experiences strong acceleration and favorable pressure

gradient. This trend remains until

/ 0.5xL H=

and then the pressure becomes adverse in the rest of the wall.

This pressure distribution gives more steep velocity gradient. It results in the enhanced the heat transfer.

In order to demonstrate the effect of the oblique plate on flow field, Figure 7 shows root mean square of ver-

tical velocity fluctuation (

rms

) along the connection between the two tips of the neighboring oblique plate at

Flow

periodic boundaries

computational

domain

Y. X. Zhan, T. S. Park

408

Figure 2. Streamlines and temperature fo r α = 50˚, 70˚, 90˚, 130˚, Re = 200.

Figure 3. Instantaneous streamlines and temperature contours during one period for α = 50˚, 90˚, Re = 600.

Figure 4. Average Nusselt number for different Re and tilt angle.

avg

6080100 120

Re=1 00

Re=2 00

Re=3 00

Re=4 00

Re=5 00

Re=6 00

Re=7 00

Re=8 00

Y. X. Zhan, T. S. Park

409

Figure 5. The mean

, skin friction coefficient and pressure coefficient on the on the upper wall (Re = 600).

Figure 6. Pressure coefficient along the upper wall for different Re.

Figure 7. Vertical velocity fluctuation at the tip of oblique plate.

0.5 1 1.5 2 2.5

-1E-05

1E-05

L/H

0.5 1 1.5 2 2.5

-0.0005

0.0005

0 0.51 1.52 2.5

130

N u

0 0.51 1.52 2.5

0.5 1 1.5 2 2.5

-1E-05

1E-05

130

L/H

0.5 1 1.5 2 2.5

-0.0005

0.0005

130

α=100ο

α=110ο

α=120ο

α=130ο

α=50

α=60

α=70

α=80

α=90

L/H

0 0.5 1 1.5 2 2.5

-0.001

0.001

α=90

L/H

0.5 1 1.5 2 2.5

-0.001

0.001

Re=200

Re=400

Re=600

Re=800

α=50

L/H

rms

00.5 1 1.5 2 2.5

0.0006

α=50

α=60

α=70

α=80

α=90

α=100

α=110

α=120

α=130

Re=200

L/H

rms

0 0.5 1 1.5 2 2.5

0.015

Re=600

Y. X. Zhan, T. S. Park

410

Re 200,=

600

. It is clearly seen that the vertical velocity fluctuation suddenly increases when α = 90˚, 100˚ for

both

Re200, 600=

. It means that obstruction of the flow due to the oblique plate is more severe. It induces

flow sweep motion to the lower wall or imping to the upper wall. The variations of

rms

according to the tilt

angles well are very similar the change of

avg

in Figure 4.

4. Conclusion

Fluid flow and heat transfer characteristics of channel flow with oblique plate have been numerically investi-

gated by the finite volume method. The computational results show that the heat transfer and pressure drop are

strongly dependent on the different tilt angle and Reynolds number. In the steady state, the effect of the tilt angle

on the heat transfer and pressure drop is not obvious. But when the flow becomes in the unsteady state, tilt angle

affects significantly on the heat transfer enhancement and pressure drop. Because when tilt angle is

≈

, the

strong vertical velocity fluctuations and steep velocity gradients along the channel wall are induced. This struc-

ture induces a better mixing of the thermal field and promotes the wall heat transfer.

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