3rd European Conference on MicrofluidicsMicrofluidics 2012
Heidelberg, December 3-5, 2012
04 December 2012 Heidelberg, Germany 1
EFFECT OF CHANNEL SHAPE ON AXIAL BACK
CONDUCTION IN THE SOLID SUBSTRATE OF
MICROCHANNELS
Manoj Kumar Moharana
Department of Mechanical Engineering
National Institute of Technology Rourkela
Rourkela 769008 (Odisha), India
Sameer Khandekar
Department of Mechanical Engineering
Indian Institute of Technology KanpurKanpur 208016 (UP), India
3rd European Conference on MicrofluidicsMicrofluidics 2012
Heidelberg, December 3-5, 2012
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Contents:
Introduction
Literature review
Problem statement
Solution methodology
Results and discussion
3rd European Conference on MicrofluidicsMicrofluidics 2012
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Introduction:
Conventional tube Microtubes
ri
t
s
f
A1
A
i ir r1 or 1
t t ir 1
t
Microchannel on solid substrate
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Literature
Conduction parameter =axial heat transfer within the solid energy flow
carried by the fluid in the channel
Bahnke and Howard (1964)Peterson (1998, 1999)
Maranzana et al. (2004)
s s p(k A ) /(m c L)
2cond s
s
conv f p f f
q / L NTUM k
q Bic u
Li et al. (2007)Zhang et al. (2010)
s s s
f p f f
k A TM
c u L A T
The effect of axial conduction in the substrate on the heat transfercoefficient can be neglected if M<10-2.
Conduction number
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Axial conduction parameter:
s s
p
k A
m c L
A quantity that gives relative importance of conduction heat transfer compared to the energy flow carried by the fluid
Ratio of axial heat transfer within the solid duct or tube due to axial temperature gradient in it to the energy flow carried by the fluid in the channel in the axial direction
Conventional channel: Bahnke and Howard (1964)
Microscale counter-flow heat exchangers: Peterson (1998, 1999)
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Axial conduction number (M)*:
cond s s
conv f p f
q k AM
q c u L A
s s s
f p f f
k A TM
c u L A T
Li et al. (2009)†:
s o i Solid
f o i Fluid
T T T
T T T
Axial conduction negligible if M < 0.01
Zhang et al. (2009)‡: Study on conjugate heat transfer in thick micro tube
Criteria for judging the effect of axial wall conduction may vary on case to case basis depending on boundary condition and geometrical parameter
*IJHMT 47(2004) 3993-4004, †IJHMT 50(2007) 3447-3460, ‡IJHMT 53(2010) 3977-3989
SOLID
FLUID
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From review of literature:
An explicit parameter for discerning the effect of axial conduction on
the heat transport coefficient in microchannel flows, under a given
set of geometry and boundary conditions, is still not available.
Most of the studies deal with circular micro tubes.
Most flows in microchannel heat transfer applications are
simultaneously developing in nature.
Rectangular/square microchannels on flat substrates are widely in use
Motivation for the present work:
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Discussion:Chein et al. (2012)*
*Axial heat conduction and heat supply effects on methanol-steam reformingperformance in micro-scale reformers, Int. J. Heat Mass Transfer 55 (2012) 3029–3042
- Silica glasss- Steel - Copper
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PROBLEM STATEMENT
FIG 1. MICROCHANNEL WITH CONDUCTIVE WALLS
Assumptions:
Heat transfer and fluid
flow takes place at
steady state
Flow is laminar,
incompressible
Constant thermo-
physical properties
Negligible heat loss by
- Radiation
- Natural convection
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PROBLEM STATEMENT
FIG 1. MICROCHANNEL WITH CONDUCTIVE WALLS
Three dimensional numerical heat transfer study on commercial CFD platform (FLUENT):
Objective:
Study the effect of axial heat conduction along the solid substrate
Parameters of interest:
Peripherally averaged local heat flux, wall temperature
Peripherally averaged local wall temperature
Bulk fluid temperature
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PROBLEM STATEMENT
FIG 1. MICROCHANNEL WITH CONDUCTIVE WALLS
Three dimensional numerical heat transfer study on commercial CFD platform (FLUENT):
Pressure discretization using STANDARD scheme
SIMPLE algorithm for velocity-pressure coupling
SECOND ORDER UPWIND scheme for momentum and energy equation
Slug velocity profile at inlet with inlet temperature of 300K
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VARIABLE PARAMETERS:
s
sf
f
2, 8, 16
Flow rate (Re):
Thickness ratio:
s
sf
f
kk
k
Conductivity ratio:
26, 635
200, 500
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Grid Independence Test:
FIG 2. VARIATION OF LOCAL NUSSELT NUMBER ALONG THE CHANNEL AXIS FOR
DIFFERENT GRIDS
45×60×30060×80×40075×100×500
x
yz
Grid
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*
h
zz
RePr D
s f
2 L
zq / q
FIG 3. VARIATION OF DIMENSIONLESS LOCAL SURFACE HEAT FLUX ALONG THE CHANNEL LENGTH
q
zq
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f fi
ffo fi
T T
T T
w fi
wfo fi
T T
T T
FIG 4. VARIATION OF DIMENSIONLESS LOCAL WALL AND BULK FLUID TEMPERATURE ALONG THE CHANNEL LENGTH
q
zq
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FIG 4. VARIATION OF DIMENSIONLESS LOCAL WALL AND BULK FLUID TEMPERATURE ALONG THE CHANNEL LENGTH
f fi
ffo fi
T T
T T
w fi
wfo fi
T T
T T
q
zq
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LOCAL NUSSELT NUMBER
FIG 5. VARIATION OF LOCAL NUSSELT NUMBER ALONG THE CHANNEL
h
z
f
h DNu
k
z
w f
qh
T T
Case 1:
Case 2:Lee and Garimella*Hydrodynamically fully developed but thermally
developing flow
*IJHMT, 49(2006) 3060-3067, ‡Advances in Heat Transfer (1978)
Case 3:Shah and London‡Simultaneously developing laminar flow in a square channel (Pr = 0.7)
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VARYING CHANNEL ASPECT RATIO
W
H
Constant area Constant heating perimeter
Constant heightConstant width
f
f
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AVERAGE NUSSELT NUMBER
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AVERAGE NUSSELT NUMBER
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DiscussionTürkakar and Okutucu-özyurt (2012)*
*Dimensional optimization of microchannel heat sinks with multiple heat sources,Int. J. Thermal Sciences (2012) Article In Press
Channelheight
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Conclusions:
1. Ks/kf determines the extent of the axial conduction in the substrate.
2. Thicker substrates lead to a reduction in thermal resistance and
therefore an increase in the axial back-conduction.
3. Increasing flow Re reduces the axial back-conduction.
4. Unless true distribution of temperature at the fluid-solid interface, true
bulk fluid temperature and the heat flux is known, the estimates of
Nusselt number can be misleading.
5. All other factors remaining the same, thin substrates made of low
conducting materials, experiencing high flow rates provide a better
solution in terms of minimizing the effect of axial conduction in the
substrate.
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Summary and Conclusions:
• For a given flow rate and δsf, the thermal conductivity ratio ksf is the keyfactor in determining the effects of axial wall conduction on the heat transportbehavior.
• Higher ksf leads to axial back conduction, thus decreasing the average Nusseltnumber as compared to the Nusselt number obtained for the case when thewall thickness is negligible.
• Very low ksf leads to a situation where the channel heat transfer can becompared to a channel having zero wall thickness with only one side heatedwith a constant heat flux and the rest of the three sides being adiabatic; thisleads to lower average Nusselt number.
• The results explicitly indicate the existence of an optimum value of thethermal conductivity ratio for maximizing the Nusselt number, for a given flowrate and wall thickness ratio.
• It has also been shown that similar phenomena will be observed in substrateshaving a tubular geometry.
• Channel aspect ratio also plays role in axial back conduction
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ACKNOWLEDGEMENTS
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