[American Institute of Aeronautics and Astronautics 10th AIAA/ASME Joint Thermophysics and Heat Transfer Conference - Chicago, Illinois ()] 10th AIAA/ASME Joint Thermophysics and Heat

American Institute of Aeronautics and Astronautics

1

Dynamics of Fluid Flow in a Heated Zig-Zag Square

Microchannel

B. Mathew1 and T. J. John

2

College of Engineering and Science, Louisiana Tech University, Ruston, LA, 71272

H. Hegab3

College of Engineering and Science, Louisiana Tech University, Ruston, LA, 71272

This paper deals with the dynamics of flow in a zig-zag square microchannel subjected to

uniform external heat flux (H2 thermal boundary condition). The heat transfer and fluid

flow characteristics is studied using CoventorWare™. *umerical studies are performed

using microchannels with hydraulic diameter ranging from 100 µm to 300 µm for Reynolds

number between 25 and 500. The angle which each arm of the zig-azg microchannel makes

with the axial direction is varied from between 10o and 30

o with increments of 10

o. The effect

of number of turns in a repeating unit for a specific length of the microchannel is also

investigated in this paper. The *usselt number and Poiseuille number in a zig-zag

microchannel is found to be totally different from that in a straight square microchannel of

the same geometric dimensions. These two parameters are found to increase with increase in

Re for zig-zag microchannels with fixed geometry. The individual effect of each of these

parameters is to increase both *usselt number and Poiseuille number for a specific Reynolds

number. The enhancement is highest with increase in number of turns while it is the lowest

with increase in hydraulic diameter. The enhancement in *usselt number and Poiseuille

number is explained using the flow profile in the microchannels.

*omenclature

A = area

Cp = specific heat

DHy = hydraulic diameter

f = friction factor

fRe = Poiseuille number

H = constant heat flux thermal boundary condition

k = thermal conductivity of the fluid

L = length of straight microchannel that is transformed into a zig-zag microchannel

l = length of each arm of a repeating unit

#u = Nusselt number

P = pressure

∆P = pressure drop

q'' = heat flux

Re = Reynolds number

T = temperature

U = average velocity

V = velocity vector

W = width/height of the microchannel

1 Doctoral Student, Micro and Nano Systems Track, College of Engineering and Science, LA Tech, Ruston, LA

71272; Email: [email protected], Ph: +1-318-514-9618 2 Doctoral Student, Micro and Nano Systems Track, College of Engineering and Science, LA Tech, Ruston, LA

71272; Email: [email protected], Ph: +1-813-514-9618 3 Associate Professor, Mechanical Engineering Program, College of Engineering and Science, LA Tech, Ruston, LA

71272; Email: [email protected], Ph: +1-318-257-3791, Fax: +1-318-257-4922

10th AIAA/ASME Joint Thermophysics and Heat Transfer Conference28 June - 1 July 2010, Chicago, Illinois

AIAA 2010-5056

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


2

X, Y, Z = spatial coordinates

α = arm angle (orientation of each arm of the repeating unit with the x-axis)

µ = viscosity

ρ = density

Subscripts

avg = average

cr = cross section

f = fluid

in = inlet

out = outlet

w = wall

I. Introduction

hannels with hydraulic diameter below 1000 µm are referred to as microchannels in literature [1]. These

channels can have circular, square, rectangular, triangular, and trapezoidal profile. Traditionally microchannels

were fabricated in silicon mainly because the fabrication techniques were well developed for the microelectronics

industry. With the advancement of fabrication techniques present day microchannels are fabricated using materials

ranging from polymers (PDMS, PMMA) to metals (copper, aluminum) to ceramics (glass, silicon carbide) [2, 3].

Current fabrication techniques include chemical etching, mechanical micromachining, molding, laser machining and

LIGA [2, 3]. The advantages of using microchannels in any device are 1) enhanced heat transfer coefficient, 2)

increased surface area density, 3) compactness [4]. The main disadvantages of employing microchannels are high

pressure drops and fouling. The pressure drop associated with a specific flow rate is inversely proportional to the

hydraulic diameter of the channel. Thus with reduction in channel size the pressure drop increases significantly.

Fouling is another issue that has had a negative effect on the commercialization of the field of microfluidics.

Formation of deposits on the walls of a microchannel can significantly reduce the size of the channels and in turn

increase thermal resistance and pressure drop. Current techniques for fabricating microfluidic devices prevent

temporarily disassembling them for cleaning purposes. Researchers are currently investigating ways to mitigate the

problem of fouling in microchannels [5, 6].

Microchannels are incorporated in devices used in several fields of engineering. They are used in microdevices

such as heat sinks, heat exchangers, fuel cells, mixers and chemical reactors. Current trend in the field of

microfluidics is towards integrating more than one unit operation in a single device [7]. For example, the unit

operation of heat transfer and mass transfer with chemical reactions has been combined in a single device to develop

micro fuel cells [8]. The way this is achieved is through the use of a microchannel heat exchanger (MCHX). Mass

transfer with chemical reaction is carried out in one set of channels and the heat generated during this is transferred

to the coolant passing through the other set of channels. The heat transfer between the two different channels helps

maintain the temperature of the reactants within limits. The idea of performing chemical reactions in a MCHX has

been commercialized by Chart Industries [9]. The advantage of incorporating two unit operations in one device is

the monetary and environmental benefit associated with reduction in infrastructure and energy.

The main purpose of employing microchannels, at least in heat transfer devices, is for increasing the heat transfer

coefficient. The reason for enhancement of the heat transfer coefficient with reduction in channel size is due to

thinness of the thermal boundary layer. The thickness of the thermal boundary layer is inversely proportional to the

heat transfer coefficient. In macroscale channels enhancement of the heat transfer coefficient is usually achieved by

the repeated disruption and development of the thermal boundary layer. This helps keep the thermal boundary layer

thin and thus increase the heat transfer coefficient. The already high heat transfer coefficient in microchannels can

be further increased by incorporating the concept of repeated disruption and development of thermal boundary layer

originally envisioned for use in macroscale channels. The several ways in which the repeated disruption and

development of the thermal boundary layer is achieved can be classified as active and passive techniques [10]. For

an active technique external energy is required to achieve the disruption of the thermal boundary layer. With regard

to a passive technique, external energy is not required for the disruption of the thermal boundary layer. Techniques

similar to these can be employed even in microchannels. In this paper a passive method is envisioned by arranging

the microchannel in a zig-zag configuration. The effect of this flow configuration on the heat transfer coefficient is

numerically investigated. The process of repeated disruption and development of the boundary layer comes at the

cost of increased pressure drop. The influence of the zig-zag flow configuration on the pressure drop is also studied

in this paper.

C


3

Fig. 1. Schematic representation of a zig-zag

microchannel and straight microchannel, both of the

same overall lenth.

II. Literature Review

Chintada et. al. [11] performed numerical analysis to study the flow dynamics and heat transfer associated with a

serpentine channel with square cross section and right angled turns. The serpentine channel is subjected to constant

heat flux boundary condition. The Re is varied between 50 and 200 with increments of 50. Two different cases

based on Pr (= 0.7 and 7) are studied. The results are presented in terms of change in Nu and fRe with respect to that

in a straight channel of the same hydraulic diameter. For the fluid with Pr = 7, enhancement in Nu is observed for 50

≤ Re ≤ 200. On the other hand when the fluid with Pr = 0.7 is used, improvement in the heat transfer parameter (Nu)

is found only at higher values of Re. Geyer et. al. [12] numerically studied the flow dynamics in a heated serpentine

square microchannel with circular turns. The Re is kept below 200 for this study. They studied the enhancement in

Nusselt number (Nu) and friction factor (f) associated with both constant temperature and constant heat flux thermal

boundary conditions. The effect of Prandtl number for Re below 200 is also presented in the paper by Geyer et. al.

[12]. With increase in Re the parameters Nu and f increased over that in a straight channel with same dimensions. In

addition with increase Prandtl number the enhancement in Nu and f increased. Between the two thermal boundary

conditions the highest enhancement in Nu is observed for the constant temperature boundary condition. From

simulations, they observed that with increase in the radius of curvature the enhancement in Nu and f decreased. This

work of Geyer et. al. [12] found enhancement in Nu even for fluids with Pr close to that of air which is in direct

contrast to the findings of Chintada et. al. [11]. Sui et. al. [13] theoretically studied the heat and fluid flow

characteristics of a microchannel heat sink with wavy microchannels. The wavy channel they studied is just like a

cosine wave with maximum amplitude not just limited to unity. Water is used as the fluid in this study.

Computational studies are performed using a microchannel with hydraulic diameter of 100 µm for Re between 100

and 800. The channels are subjected to external heat flux as these channels are part of a heat sink used for cooling

electronic devices. The results are presented in terms of enhancement, over that in a straight channel of same

dimensions and flow rate, in Nu and f. The enhancement in Nu and f increased with increase in Re, which is same as

that observed by previous researchers [11, 12]. The enhancement in Nu for 100 < Re < 800 is observed to between

1.1 and 2.2. At the same time the enhancement in f ranged from just 1.1 to 1.5. The fact that the enhancement in Nu

is higher than that in f for a particular Re should act as a motivation for using wavy channels in future designs of

heat sinks. With increase in the maximum amplitude the enhancement in Nu and f increased. From this work it can

be seen that at the lowest Re the enhancement is very small, i.e. just 10%; perhaps indicating that existence of a

threshold value of Re below which no enhancement in Nu and f occurs. From this section it can be seen that there is

currently no study on the flow dynamics in a zig-zag square microchannel. Consequently, it is studied in this paper.

III. Theoretical Model

The entities involved in the computational

domain are considered as a continuum in this

study. Figure 1 represents the schematic of a zig-

zag and straight microchannel. From this figure it

can be notice that a zig-zag microchannel is made

up of several repeating units. One such repeating

unit is shown in Fig. 2. The repeating unit consists

of two equal arms, each of which is aptly named

as the left and right arm. Each of the arms

subtends an angle with the x-axis. Thus the arms

are mirror images of each other. In this study only

the repeating unit is analyzed. Prior to developing

the governing equations describing the flow in the

repeating unit the certain assumptions are made to

simplify the modeling process. These assumptions

are provided below.

1. The flow is taken to be steady in the microchannel.

2. A repeating unit located far from the main inlet and outlet of the microchannel is analyzed.

3. No-slip boundary condition is assumed on the microchannel walls.

4. There is no phase change in the fluid while flowing through the microchannel.

5. External heat loss, axial heat conduction, and viscous dissipation associated with the fluid are assumed to be

negligible. The fluid is assumed to be free of any heat transfer source.


4

l

W

α

Fig. 2. Schematic representation of the repeating unit of a zig-zag

microchannel.

6. Thermofluidic properties of the fluid

are taken to be constant over the

length of the microchannel. For microchannels similar to that

shown in Fig. 1, in the enhancement of

Nu and fRe in the first repeating unit

would not only be influenced by

changing flow directions but also by the

entrance effects existing between the

main fluid line and inlet of the

microchannel. Such entrance effects

would not exist in repeating units far

from the inlet of the microchannel and

thus a repeating unit far from the inlet of the microchannel is analyzed in this paper. This is the idea corresponding

to the second assumption. For this study the analysis is performed on the third and fourth repeating units from the

main inlet of the microchannel.

The governing equations of the square zig-zag microchannel studied in this paper consist of the continuity

equation, the three momentum equations and the energy equation of the fluid. The walls of the channel are not

considered in this study as the heat transfer through it is not of interest. In a real life situation the external heat flux

to which the fluid is subjected would be applied on the outer wall of the microchannel. However, as this is a

theoretical study the heat flux is applied directly on the interface between the fluid and the channel wall. The term

wall would be used in this study to refer to the interface between the fluid and the microchannel. The governing

equations are presented in Eqs. (1) – (3) [14].

Continuity Equation

0=⋅∇→

V

(1)

Momentum Equation →→→

∇+−∇=∇⋅ VpVV 2µ

(2)

Energy Equation

TkTVCp

2∇=∇⋅

→

ρ

(3)

Couple of boundary conditions of the square zig-zag microchannel is needed to solve these set of governing

equations. The boundary conditions for this particular problem are provided in Eqs. (4) – (8). Symbols are used on

the right hand side of some of these equations instead of numerical values. These symbols will replace the actual

value of the parameter it represents in each of the simulations. The range of the parameters that is represented by

these symbols is provided in this section. Equation (4) represents the flow rate at the main inlet of the microchannel.

The governing equations contain the three velocities instead of the flow rate. The three velocities at the main inlet of

the microchannel corresponding to the particular flow rate are calculated by CoventorWare™ based on the cross

sectional area. Thus it is possible to use the flow rate instead of the three velocities as an input for simulations.

Equation (5) represents the no-slip flow condition. It is the velocity at the walls of the microchannel. This boundary

condition also implies that the walls are impermeable. The pressure at the outlet of the microchannel is assumed to

be zero. In reality this may never be the case. In this simulation as the interest is in determining the pressure drop

rather than the absolute pressure this approach simplifies the simulation process. This boundary condition is

mathematically shown in Eq. (6).

⋅

= qQin

(4)

0=== wallwallwall wvu (5)


5

0=outp (6)

Equation (7) represents the heat flux that is applied on the wall of the repeating unit. The heat flux is calculated

using the heat that is supplied to a repeating unit and its surface area. The temperature of the fluid at the main inlet is

kept constant at 273.15 K for all simulation runs and is provided in Eq. (8).

''qqwall =

(7)

KTin 15.273= (8)

It is mentioned earlier that if a symbol is used on the right hand side of a boundary condition then it represents a

range of values for the particular parameter represented by that boundary condition. The range of the parameter

represented in boundary condition expressed in Eq. (4), i.e. flow rate, corresponds to Re from 25 to 500. Using the

hydraulic diameter of the microchannel the average axial velocity (velocity normal to the cross sectional area)

corresponding to a particular Re is determined. From it the flow rate is determined and used as the input for

simulations. The equation necessary for it is provided in Eq. (9). The heat flux for simulation purposes is determined

by assuming that 1 W of heat is supplied to the fluid in the repeating unit. Using this information and the dimensions

of the repeating unit it is possible to determine the heat flux for each of the simulation runs.

Hy

cr

D

Aq

ρ

µRe=

⋅

(9)

CoventorWare™ uses finite volume method to solve these set of governing equations. CoventorWare™ utilizes

PISO algorithm to solve the governing equations. The computational domain is meshed using extruded mesh setting

available in CoventorWare™. In this mesh setting, the surface of the domain in the x-y plane through z = -W/2 is

meshed and the resulting surface mesh is extruded in the third direction, i.e. the z-direction. This type of meshing is

possible only when the cross section is constant in the z-direction. Therefore extruded meshing which is possible

with square and rectangular channels is not possible for circular, trapezoidal and triangular channels. The distance

between each node in the x-y plane is set at 6-15 micrometers while that in the z-direction is kept at 3-7

micrometers. The convergence of three velocities for a particular simulation is believed to be achieved if the

difference between two consecutive iterations is less than 10-4

. Regarding the temperature, it is assumed to have

converged if the residue is smaller than 10-7

for a particular simulation. In addition to the convergence criteria of the

velocities and temperature another criterion on the magnitude of the source term in the continuity equation has to be

satisfied. The magnitude of the source term in the continuity equation should be less than 10-4

. The grid is refined till

the percentage difference in flow rate specified as an input for a particular simulation and that calculated from

computed velocities at several locations of interest in the computational domain is between 1-2%. The flow rate

specified as an input and that calculated using the computed velocities should match very closely since mass has to

be conserved in this problem. In addition, the refinement of the grid will be carried out till the difference between

the average fluid temperatures between two consecutive mesh settings is less than 10-2

.

Using the temperature profile of the fluid in the repeating unit it is possible to determine the heat transfer

coefficient [12]. Equation (10) contains the formula needed for determining the heat transfer coefficient averaged

over a y-z plane. Tw,avg is the average temperature of the wall at the exit of the right arm of the repeating unit shown

in Fig. 2. Tf,avg represents the bulk temperature of the fluid at the cross section of interest. The Nusselt number

corresponding to this heat transfer coefficient can be in turn determined using Eq. (11).

)( ,,

''

avgfavgw

avgTT

qh

−=

(10)

f

hyavg

k

Dh#u =

(11)


6

Fig 3. Flow pattern in multiple repeating units (Re

= 100, Dhy = 250 µm, l = 1000 µm, α = 15o)

Fig 4. Flow pattern in a single repeating unit (Re

= 100, Dhy = 250 µm, l = 1000 µm, α = 15o)

Based on the pressure drop between the inlet and outlet of a repeating unit it is possible to determine the friction

factor. The friction can be determined from the pressure drop using Eq. (12).

LU

PDf

Hy

22ρ

∆=

(12)

Nu and fRe thus obtained are thus for zig-zag microchannels are normalized using the Nu and f Re of straight

microchannel of the same hydraulic diameter. In this manner it is possible to make a comparison of the enhancement

of Nu and f Re in a zig-zag microchannel over that in a straight microchannel. The equations necessary for making

this comparison is provided in Eq. (13) and Eq. (14). Eq. (13) represents the ratio of the Nusselt number in a zig-zag

channel to that in a straight microchannel while Eq. (14) represents the ratio of fRe for the same two channels. For a

zig-zag microchannel to be useful in a heat transfer device the nondimensional Nusselt number (Nur) should be

greater than unity.

straight

zagzig

r#u

#u#u

−=

(13)

( )straight

zagzig

rf

ff

Re)(

Re)(Re

−=

(14)

IV. Results and Discussions

The influence of three different geometric parameters is explored in this study. The three geometric parameters

are 1) hydraulic diameter, 2) orientation (arm angle) and 3) number of turns in a repeating unit. The influence of

each of these parameters is studied for Re between 25 and 500 which is the typical operating range of present day

microfluidic devices. Prior to analyzing the results it is important to check the validity of the governing equations

provided in the previous section. The validity of these equations is checked by applying them to a straight

microchannel and comparing the Nusselt number and Poiseuille number obtained by solving these equations with

those available in literature for microsized channels. A straight microchannel can be considered as an extreme case

of a zig-zag microchannel with orientation (α) set equal to zero. The results, Nu and fRe, thus obtained from such

simulations are compared with the values available in literature and the absolute difference is found to be less than

1% of the conventional value. This exercise concludes the fact that there are no modeling errors in this study.

The flow pattern in a zig-zag microchannel is shown in Fig. 3. In Fig. 3 there are two repeating units. Figure 4 is

a detailed view of Fig. 3 with just one repeating unit. The fluid flow is from the left to the right of the repeating unit.


7

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 100 200 300 400 500

Re

*ur

Dhy = 100 µm

Dhy = 200 µm

Dhy = 300 µm

Fig 5. Effect of hydraulic diameter of *ur of a zig-

zag microchannel (l = 1000 µm, α = 15o)

Fig 7. Cross sectional velocity profile in a straight

microchannel at Re = 200 (l = 1000 µm, α = 15o)

Fig 6. Cross sectional velocity profile in a zig-zag

microchannel at Re = 200 (l = 1000 µm, α = 15o)

The flow pattern represented in Fig. 3 and Fig. 4 is that

of a zig-zag microchannel that is far from the manifolds

connecting the microchannel to the external environment.

The flow is never fully developed in these microchannels.

As can be seen from these figures the velocity profile is

skewed towards one of the walls of the microchannel. The

velocity profile in the left arm is skewed towards its right

wall while in the right arm it is skewed towards the left wall

of the channel. This velocity profile exists because the flow

while moving from one arm to the next tends to move away

from the edge of the turn, i.e. the wall common to two

adjacent arms, before turning. For example, as shown for

the cases in Fig. 3 and Fig. 4 the flow while moving into the

right arm from the left arm does not change direction right

at the edge of the turn. Thus majority of the fluid in the

right arm flows in the region adjacent to its left wall.

Similarly, majority of flow in the left arm moves in the

region close to its right wall since the flow while entering

into it from the right arm does not undergo sudden change

in direction at the edge of the turn.

The effect of hydraulic diameter on Nu is shown in Fig.

5. The hydraulic diameter is varied between 100 and 300

µm with increments of 100 µm. For a microchannel with a

particular hydraulic diameter the heat transfer parameter,

Nu, and the fluid flow parameter, fRe, is higher in

comparison with that of a straight channel with the same

hydraulic diameter. In a zig-zag microchannel secondary

flows are generated at the turns due to centrifugal force

acting on the fluid at this section. Secondary flow causes

mixing of the fluid at the particular cross section it occurs.

A comparison between the fluid velocities at the midsection

of a ziag-zag microchannel and a straight microchannel is

shown in Figs. 6 and 7. In a straight microchannel the

velocity does not have tangential component while the fluid

in a zig-zag microchannel experience tangential velocity as

shown in Fig. 6 using arrows. Mixing occurs at these turns

because of the presence of centrifugal pressure acting on

the fluid due to the change in flow direction at the turn.

This mixing helps redistribute the heat from the regions of

the fluid near the walls to its interior. In a straight

microchannel the only way to distribute heat across various

regions of the fluid at a particular cross section is by

thermal conduction and natural convection. This is not an

effective technique for transferring heat since the thermal

conductivity of common fluids is very low (> 1 W/mK).

Once this redistribution of heat occurs in a zig-zag

microchannel, the temperature of the fluid in the regions

near the wall drops thereby lowering its temperature rise

due to heat transfer downstream of the turn. This lowering

of the fluid temperature in turn reduces the wall

temperature below that would occur in a straight

microchannel. Kandlikar [10] while reviewing several

techniques for enhancing Nu in microchannels has also

concluded that the presence of turns lead to reduction in temperature gradient across the cross sectional area of the

fluid. In addition, the presence of turns lead to disruption of the boundary layer and this too helps enhance the heat


8

0

0.5

1

1.5

2

2.5

0 100 200 300 400 500Re

(fRe)r

Dhy = 100 µm

Dhy = 200 µm

Dhy = 300 µm

Fig 8. Effect of hydraulic diameter on (fRe)r of a

zig-zag microchannels (l = 1000 µm, α = 15o)

Fig 10. Velocity profile in a zig-zag microchannel

at Re = 25 (l = 1000 µm, α = 15o)

Fig 9. Velocity profile in a zig-zag microchannel at

Re = 200 (Dhy = 200 µm l = 1000 µm, α = 15o)

transfer coefficient and thereby the Nusselt number. The

effect of zig-zag configuration on the Poiseuille number is

shown in Fig. 8. Regarding Poiseuille number, it is higher

in a zig-zag microchannel in comparison with that in a

straight microchannel. This is because in addition to the

frictional losses in the repeating unit there are pressure

losses due to separation of flow as well as due to the

presence of secondary flows generated due to the presence

of a turn. Due to the zig-zag nature of the microchannel

flow separates from the wall as it moves from one arm to

other present on either sides of the turn. The occurrence of

flow separation downstream of a turn in a zig-zag

microchannel with hydraulic diameter of 200 µm is shown

in Fig. 9. Comparison of the fluid velocities in the regions

adjacent to the walls of the right arm clearly shows the

presence of flow separation. Flow separation and

secondary flow are known to generate additional pressure

drops in internal flows [15, 16, 17]. These additional

pressure drops contribute to the observed increase in

Poiseuille number. From Figs. 5 and 8 it can also be

noticed that Nu and fRe increased with increase in Re. Nu

increases with Re because the degree of mixing at the

turns increase with increase in Re. The increase in fRe

with Re is because the pressure loses associated with

separation and secondary flows also increase with

increase Re. This can be better understood by comparing

the velocity profile for Re = 25 and Re = 200 in a zig-zag

microchannel with hydraulic diameter of 200 µm. Figure

10 shows the cross sectional velocity profile of the

midsection of the zig-zag microchannel, with hydraulic

diameter of 200 µm and orientation (α) of 15o, for Re = 25

while Fig. 6 represents that for Re = 200. These figures

reveal that the tangential velocity at the turn is higher

when Re = 200 in comparison to that when Re = 25; this

confirms the fact of improved mixing with increase in

Re. Also, by comparing Fig. 9 and Fig. 11 it can be seen

that with reduction in Re flow separation is almost

nonexistent. This increased secondary flow and flow

separation are the causes of the observed increase in fRe

with increase in Re. In a straight microchannel operating

under laminar flow conditions these parameters, Nu and

fRe, are independent of Re [16]. From Figs. 5 and 8 it

can be see that at very low Re the heat transfer and fluid

flow parameter become independent of the hydraulic

diameter of the microchannel just like in straight

microchannels.

After analyzing the effect of hydraulic diameter on Nu

and fRe of a zig-zag microchannel it is clear that it is the

turns that enhance Nu. Two ways of increasing the

influence of turns is by increasing the orientation of each arm with respect to the x-axis or by increasing the number

of turns in a single repeating unit. For the first approach the number of turns/arms and the length of each arm in a

single repeating unit are kept constant but the orientation of each arm with respect to the x-axis is changed. For

purposes of analysis the hydraulic diameter of each arm is kept constant at 150 µm. The orientation angle, α, is


9


at Re = 25 (Dhy = 200 µm, l = 1000 µm, α = 15o)

0

1

2

3

4

5

6

0 100 200 300 400 500

Re

*ur

α = 10o

α = 20o

α = 30o

0

0.5

1

1.5

2

2.5

3

3.5

0 100 200 300 400 500Re

(fRe)r

α = 10o

α = 20o

α = 30o

Fig 12. Effect of orientation on *ur of a zig-zag

microchannel (Dhy = 150 µm, l = 1000 µm)


microchannel (Re= 100, Dhy = 150 µm, l = 1000 µm,

α = 10o)

Fig 13. Effect of orientation on (fRe)r of a zig-zag

microchannel (Dhy = 150 µm, l = 1000 µm)


microchannel (Re = 100, Dhy = 150 µm, l = 1000 µm,

α = 20o)

varied between 10o and 30

o with increment of 10

o. The

influence of heat transfer parameter (Nu) and fluid flow

parameter (fRe) is shown in Fig. 12 and Fig. 13,

respectively. As assumed earlier Nu increases with

increase in the orientation angle, α. This is because with

increase in the orientation angle the flow while passing

from the left arm to the right arm of the repeating unit has

to take a sharper turn. With increase in sharpness of the

turn the degree of mixing due to secondary flows at the

turns increases. The enhanced mixing at the turns brings

about greater reduction of temperature in the regions of

the fluid near to the wall. This greater degree of mixing

associated with sharp turns limit the fluid temperature rise

due to external heat transfer downstream of the turn.

Figure 14, Fig. 15 and Fig. 16 represent the velocity

profile of zig-zag microchannels with hydraulic diameter

of 150 µm for the three different orientations at Re = 100.

These figures reveal that with increase in the orientation

the overall flow velocity as well as its tangential component increases thereby leading to enhanced mixing.


10


(Re = 200, Dhy = 150 µm, l = 1000 µm, α = 20o)


(Re = 200, Dhy = 150 µm, l = 1000 µm, α = 30o)


microchannel (Re= 100, Dhy = 150 µm, l = 1000

µm, α = 30o)


(Re = 200, Dhy = 150 µm, l = 1000 µm, α = 10o)

Figure 13 represents the variation of fRe with increase in orientation. This increase in fRe with α is due to the

fact that with increase in orientation the problem of flow separation intensifies thereby leading to greater pressure

drop. Figures 17-19 represent the velocity profile in the regions near the turn for the three different orientations for

Re = 200. From these figures it can be seen that with increase in orientation the problem of flow separation

intensifies. The region affected by flow separation is bigger in the zig-zag microchannel with α = 30o than in a zig-

zag microchannel with α = 20o. Similar situation can be observed by comparing the microchannels with orientation

of 20o and 10

o. The presence of secondary flow also contributes to pressure drop. As mentioned earlier the

secondary flow gets stronger with increase in orientation. Thus the combined effect of flow separation and

secondary flow leads to observed increase in Poiseuille number with increase in orientation at a particular Re. With

increase in Re the parameter Nu and fRe increased as observed in the previous case of the effect of hydraulic

diameter on Nu and fRe with Re. The reason for this is same as that explained earlier. Also, from Figs. 17-19 it can

be seen that irrespective of the orientation of the zig-zag microchannel the flow pattern is similar to that mentioned

with respect to Figs. 3 and 4, i.e. the majority of fluid flows in the region close to the right wall and left wall in the

left arm and right arm, respectively. The reason for this same as that explained earlier.

Earlier it has been mentioned that the second approach for improving the influence of turns would be by

increasing number in the overall length of the microchannel. This can be done by reducing the length of each arm

thereby increasing the number of turns. In the study conducted in this paper a straight channel with an overall length

of 2000 µm is desired to be converted into a zig-zag channel with the number of turns varying from 2 to 4 and to 6.

The hydraulic diameter of the zig-zag microchannel is kept at 150 µm. When the number of turns is 2 the length of

each arm is 1000 µm. On the other hand when the number of turns is increased to 4 the length of each arm reduces


11


(Re = 300, Dhy = 150 µm, l = 1000 µm, α = 30o)


(Re = 300, Dhy = 150 µm, l = 500.0 µm, α = 30o)

0

1

2

3

4

5

6

7

0 100 200 300 400

Re

*ur

2 turns, l = 1000 µm


6 turns, l = 333.33 µm

0

2

4

6

8

10

12

0 100 200 300 400Re

(fRe)r



6 turns, l = 333.33 µm

Fig 20. Effect of number of turns on *ur of a zig-

zag microchannel (Dhy = 150 µm, α = 30o)

Fig 21. Effect of number of turns on (fRe)r of a

zig-zag microchannel (Dhy = 150 µm, α = 30o)

to 500 µm thereby keeping the overall length at 2000 µm. On increasing the number of turns to 6 the length of each

arm further reduces by 167.67 µm to 333.33 µm. As secondary flow takes place only when there is change in flow

direction and the approach to increase the number of turns should help improve the heat transfer characteristics of a

zig-zag microhannel. Figure 20 represents the effect of change in number of turns on Nu of a zig-zag microchannel

for Re between 25 and 400. From this figure it can be seen that with increase in the number of turns the heat transfer

parameter, Nu, increased for a particular Re. The reason for this is the improvement in mixing of the fluid associated

with the increase in the number of turns across the overall length of the microchannel. Figure 21 shows the variation

of fRe with Re with increase in the number of turns. As expected the fluid flow parameter, fRe, increased with

increase in number of turns. This is because with increase in the number of turns the occurrences of secondary flow

and flow separation increases thereby leading to additional pressure drop for a specific Re. Figures 22-24 shows the

flow pattern in a zig-zag microchannel for three different arm lengths. With reduction in the arm length the number

turns increased. With increase in the number of turns the occurrence of secondary flow and flow separation

increases. This increase in the occurrence of secondary flow and flow separation is the cause behind the

enhancement of Nu and fRe for a specific Re. Like in the previous cases the heat transfer parameter, Nu, and fluid

flow parameter, fRe, increased with Re. The reason for this is same as that explained earlier.

From the study conducted in this paper it is clear that it is the occurrence of secondary flow that is causing the

enhancement of Nusslet number. In addition to secondary flows at the turns, the presence of flow separation after

every turns is also acts to increase the Poiseuille number. For every case of internal flows it is always desirable to

have the highest possible heat transfer coefficient while maintaining the pressure drop at a minimum. However,


12


(Re = 300, Dhy = 150 µm, l = 333.33 µm, α = 30o)

from the results presented in this study such an attribute

does not exist for zig-zag microchannels. Nevertheless, a

zig-zag microchannel due to its higher Nusselt number in

comparison with a straight microchannel of the same

hydraulic diameter might find use as a replacement for

straight microchannels with hydraulic diameter smaller

than that of the zig-zag microchannel itself. This approach

may help reduce the pressure drop across the ends of

microchannel below that in a straight microchannel. One

of the characteristic of zig-zag microchannels is the

stagnation of fluid right after a turn due to flow separation.

This can be a drawback especially if chemical reactions

need to be carried out in zig-zag microchannels. The

selection of the geometric parameters of a zig-zag

microchannel will most definitely be dictated by the

allowable pressure drop and the volume of stagnant fluid

for a particular application. While selecting the geometric

parameters of a zig-zag microchannel it would be most

appropriate to combine the effect of all the three geometric parameters for obtaining the desired thermal

performance subjected to a specific pressure drop.

V. Conclusion

In conclusion, the influence of three different geometric parameters of a zig-zag microchannel is analyzed to

understand their effect on the Nussselt number and Poiseuille number in a heated zig-zag microchannel. Both

Nusselt number and Poiseuille number for a particular zig-zag microchannel increased with Re irrespective of the

hydraulic diameter, number of turns and the orientation. Among the three different geometric parameters studied,

the hydraulic diameter of the microchannel is seen to have the least influence on the heat transfer and fluid flow

parameters. The number of turns across the overall length of the microchannel is observed to have the greatest

influence on both its parameters. With increase in hydraulic diameter the Nusselt number and Poiseuille number

increased for a specific Re. Similarly, with increase in the orientation of each arm and number of turns of the zig-zag

microchannel the two parameters under study increased for a particular Re. The reason behind the enhancement of

Nusselt number and Poiseuille number with the three geometric parameters is the occurrence of secondary flow and

flow separation at the turns present in the microchannel. Depending on the allowable pressure drop several

combinations of geometric parameters can deliver the desired heat transfer performance.

References 1Rosa, P., Karayiannis, T. G., and Collins, M. W., “Single Phase Heat Transfer in Microchannels: The Importance of Scaling

Effects,” Applied Thermal Engineering, Vol. 29, No. 17-18, 2009, pp. 3447-3468. 2Ashman, S., and Kandlikar, S. G., “A Review of Manufacturing Processes for Microchannel Heat Exchanger Fabrication,”

Fourth International Conference on Nanochannels, Microchannels and Minichannels, Limerick, Ireland, 2006 3Tsopanos, S., Sutcliffe, C. J., and Owen, I., “The Manufacture of Micro Cross-Flow Heat Exchangers by Selective Laser

Melting,” Proceedings of Fifth International Conference on Enhanced, Compact and Ultra-Compact Heat Exchangers: Science,

Engineering and Technology, Haboken, New Jersey, 2005. 4Kutter, J. P., and Fintschenko, Y., 2005, Separation Methods in Microanalytical Systems, CRC Press, Boca Raton, FL, 2005. 5Perry, J. L., and Kandlikar, S. G., “Investigation of Fouling and its Mitigation in Silicon Microchannels,” Sixth International

Conference on #anochannels, Microchannels, and Minichannels, Darmstadt, Germany, 2008. 6 Benzinger, W., Schygulla, U., Jager, M., and Schubert, K., “Anti Fouling Investigations with Ultrasound in a

Microstructured Heat Exchanger”, Proceedings of 6th International Conference on Heat Exchanger Fouling and Cleaning -

Challenges and Opportunities, Kloster Irsee, Germany, 2005, pp. 197-201. 7Stankiewicz, A., and Mouljn, J. A., Re-Engineering the Chemical Processing Plant: Process Intensification, Marcel Dekker,

Inc., New York, 2004. 8Delsman, E. R., De Croon, M. H. J. M., Pierik, A., Kramer, G. J., Cobden, P. D., Hofmann, Ch., Cominos, V., and Schouten,

J. C., “Design and Operation of a Preferential Oxidation Microdevice for a Portable Fuel Processor”, Chemical Engineering

Science, Vol. 59, No. 22-23, 2004, pp. 4795-4802. 9Chart Industries, http://www.chart-ind.com 10Steinke, M. E., and Kandlikar, S. G., “Single-Phase Heat Transfer Enhancement Technique in Microchannel and

Minichannel Flows,” ASME International Conference on Microchannels and Minichannels, Rochester, NY, 2004


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11Chintada, S., Ko, K-H., and Anand, N. K., “Heat Transfer in 3-D Serpentine Channels with Right-Angle Turns,” #umerical

Heat Transfer, Part A, Vol. 36, No. 8, 1999, pp. 781-806. 12Geyer, P. E., Rosaguti, N. R., Fletcher, D. F., and Haynes, B. S., “Thermohydrulics of Square-Section Microchannels

Following a Serpentine Path,” Microfluidics and Nanofluidics, Vol. 2, No. 3, 2006, pp. 195-204. 13Sui, Y., Tao, C. J., Lee, P. S., Chew, Y. T., and Shu, C., An Efficient Wavy Microchannel Heat Sink for Electronic

Devices, ASME 2009 Summer Heat Transfer Conference, San Francisco, CA, 2009. 14 White, F. M., Viscous Fluid Flow, 3rd ed., McGraw Hill, 2006.

15 Incropera, F. P., and DeWitt, D. P., Fundamentals of Heat and Mass Transfer, 5th ed., John Wiley and Sons, 2002. 16Crowe, C. T., Roberson, J. A., and Elger, D. F., Engineering Fluid Dynamics, 7th ed., John Wiley and Sons, 2001. 17White, F. M., Fluid Mechanics, 3rd ed., McGraw Hill, 1994

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