effect of channel shape on axial back conduction in the solid substrate of microchannels

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




Contents:

Introduction

Literature review

Problem statement

Solution methodology

Results and discussion




Introduction:

Conventional tube Microtubes

ri

t

s

f

A1

A

i ir r1 or 1

t t ir 1

t

Microchannel on solid substrate




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




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)




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




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:




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




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




PROBLEM STATEMENT


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




PROBLEM STATEMENT


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




VARIABLE PARAMETERS:

s

sf

f

2, 8, 16

Flow rate (Re):

Thickness ratio:

s

sf

f

kk

k

Conductivity ratio:

26, 635

200, 500




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




*

h

zz

RePr D

s f

Qq

2 L

zq / q

FIG 3. VARIATION OF DIMENSIONLESS LOCAL SURFACE HEAT FLUX ALONG THE CHANNEL LENGTH

q

zq




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




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




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)




VARYING CHANNEL ASPECT RATIO

W

H

Constant area Constant heating perimeter

Constant heightConstant width

f

f




AVERAGE NUSSELT NUMBER




DiscussionTürkakar and Okutucu-özyurt (2012)*

*Dimensional optimization of microchannel heat sinks with multiple heat sources,Int. J. Thermal Sciences (2012) Article In Press

Channelheight




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.




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




ACKNOWLEDGEMENTS

effect of channel shape on axial back conduction in the solid substrate of microchannels

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