numerical study of axial back conduction in microtubes

39th National Conference onFluid Mechanics and Fluid Power

Surat, December 13-15, 2012

15 December 2012 Surat, India 1

NUMERICAL STUDY OF AXIAL BACK CONDUCTION IN MICROTUBES

Manoj Kumar Moharana

Department of Mechanical EngineeringNational Institute of Technology Rourkela

Rourkela 769008 (Odisha), India

Sameer Khandekar

Department of Mechanical EngineeringIndian Institute of Technology Kanpur

Kanpur 208016 (UP), India



15 December 2012 Surat, India2

Introduction:

Conventional tube

Microtubes

ri

t

ir 1t

s

f

A1

A

Microchannel on solid substrate

i ir r1 or 1

t t




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

Conventional channel: Bahnke and Howard (1964)

Microscale counter-flow heat exchangers: Peterson (1998, 1999)

Literature Review:

Conduction parameter =axial heat transfer within the solid

energy flow carried by the fluid in the channel




Axial conduction number (M)*:

cond s s s

conv f p f f

q k A TM

q c u L A T

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 is 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

Maranzana et al. (2004)




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 flows in microchannel heat transfer applications are

simultaneously developing in nature.

Circular microtubes are used in many applications

Motivation for the present work:

Moharana et al., Optimum Nusselt Number for Simultaneously Developing Internal Flow Under Conjugate Conditions in a Square Microchannel, Journal of Heat Transfer, 134(2012) 071703(01-10).




Optimum average Nusselt number:

sf s f/ 1 - 16

Flow rate (Re):Thickness ratio:

sf s fk k / k

Conductivity ratio:

0.345 - 635100 - 1000*Journal of Heat Transfer, 134(2012) 071703(01-10)




PROBLEM STATEMENT

Microtube and its computational doomain

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



15 December 2012 Surat, India

u 0

21u u p u

2

p

ku T T

C

Liquid domain:

2T 0

Solid domain:

f f s

T0 at z 0,Land r ( )

z

f sq 0 or T cons tan t at r

f f

Tk h(T T ) at r

r

u u at z 0

fu 0 at r

p 0 at z L

T u0, 0 at r 0

r r

Governing Equations: Boundary conditions:




PROBLEM STATEMENT

Microtube and its computational doomain

3-D 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

Peripherally averaged local wall temperature

Area averaged Bulk fluid temperature




Grid Independence Test:

VARIATION OF LOCAL NUSSELT NUMBER ALONG THE CHANNEL AXIS FOR DIFFERENT GRIDS

- Re 250

- Zero wall thickness




VARIABLE PARAMETERS:

ssf

f

1.0 – 16.0

Flow rate (Re):

Channel aspect ratio:

ssf

f

kk

k

Conductivity ratio:

0.33 - 702

100 - 1000

z

s z zsf z z z

w ff f0

A h D qzz* , A , Nu , h , Nu Nu dz

L A k T T

Terminology:

s f zo o

s f f

( ) qQq , q q ,

2 ( )L q




f fi

ffo fi

T T

T T

w fi

wfo fi

T T

T T

DIMENSIONLESS LOCAL WALL AND BULK FLUID TEMPERATURE




LOCAL NUSSELT NUMBER

zz

f

h DNu

k

zz

wz fz

qh

T T




AVERAGE NUSSELT NUMBER

Constant wall temperature Constant wall heat flux




TEMPERATURE CONTOUR

(Constant wall temperature)

Tw = 360 K

Re = 100

Ksf = 12.8




Some Concluding Remarks:

1. Ks/kf determines the extent of the axial conduction in the tube wall.

2. Relative tube thickness also play a role in axial back-conduction.

3. Increasing flow Re reduces the axial back-conduction.

4. A constant temperature boundary condition applied on the outer surface of the tube can manifest itself as a constant heat flux boundary condition on the actual fluid-solid interface

5. For constant heat flux boundary condition, the results explicitly indicate the existence of an optimum value of the thermal conductivity ratio for maximizing the Nusselt number, for a given flow rate and wall thickness ratio.

6. 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.




PROBLEM STATEMENT

MICROTUBE 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

numerical study of axial back conduction in microtubes

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