39 th National Conference on Fluid 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 Engineering National Institute of Technology Rourkela Rourkela 769008 (Odisha), India Sameer Khandekar Department of Mechanical Engineering Indian Institute of Technology Kanpur Kanpur 208016 (UP), India
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NUMERICAL STUDY OF AXIAL BACK CONDUCTION IN MICROTUBES
A quantity that gives relative importance of conduction heat transfer compared to the energy flow carried by the fluid
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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
39th National Conference onFluid Mechanics and Fluid Power
Surat, December 13-15, 2012
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
39th National Conference onFluid Mechanics and Fluid Power
Surat, December 13-15, 2012
15 December 2012 Surat, India 3
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
39th National Conference onFluid Mechanics and Fluid Power
Surat, December 13-15, 2012
15 December 2012 Surat, India 5
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).
39th National Conference onFluid Mechanics and Fluid Power
Surat, December 13-15, 2012
15 December 2012 Surat, India 6
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)
39th National Conference onFluid Mechanics and Fluid Power
Surat, December 13-15, 2012
15 December 2012 Surat, India 7
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
39th National Conference onFluid Mechanics and Fluid Power
Surat, December 13-15, 2012
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:
39th National Conference onFluid Mechanics and Fluid Power
Surat, December 13-15, 2012
15 December 2012 Surat, India 9
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
39th National Conference onFluid Mechanics and Fluid Power
Surat, December 13-15, 2012
15 December 2012 Surat, India 10
Grid Independence Test:
VARIATION OF LOCAL NUSSELT NUMBER ALONG THE CHANNEL AXIS FOR DIFFERENT GRIDS
- Re 250
- Zero wall thickness
39th National Conference onFluid Mechanics and Fluid Power
Surat, December 13-15, 2012
15 December 2012 Surat, India 11
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
39th National Conference onFluid Mechanics and Fluid Power
Surat, December 13-15, 2012
15 December 2012 Surat, India 12
f fi
ffo fi
T T
T T
w fi
wfo fi
T T
T T
DIMENSIONLESS LOCAL WALL AND BULK FLUID TEMPERATURE
39th National Conference onFluid Mechanics and Fluid Power
Surat, December 13-15, 2012
15 December 2012 Surat, India 13
f fi
ffo fi
T T
T T
w fi
wfo fi
T T
T T
DIMENSIONLESS LOCAL WALL AND BULK FLUID TEMPERATURE
39th National Conference onFluid Mechanics and Fluid Power
Surat, December 13-15, 2012
15 December 2012 Surat, India
LOCAL NUSSELT NUMBER
zz
f
h DNu
k
zz
wz fz
qh
T T
39th National Conference onFluid Mechanics and Fluid Power
Surat, December 13-15, 2012
15 December 2012 Surat, India
LOCAL NUSSELT NUMBER
zz
f
h DNu
k
zz
wz fz
qh
T T
39th National Conference onFluid Mechanics and Fluid Power
Surat, December 13-15, 2012
15 December 2012 Surat, India 16
AVERAGE NUSSELT NUMBER
Constant wall temperature Constant wall heat flux
39th National Conference onFluid Mechanics and Fluid Power
Surat, December 13-15, 2012
15 December 2012 Surat, India 17
TEMPERATURE CONTOUR
(Constant wall temperature)
Tw = 360 K
Re = 100
Ksf = 12.8
39th National Conference onFluid Mechanics and Fluid Power
Surat, December 13-15, 2012
15 December 2012 Surat, India
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.
39th National Conference onFluid Mechanics and Fluid Power
Surat, December 13-15, 2012
15 December 2012 Surat, India 19
39th National Conference onFluid Mechanics and Fluid Power
Surat, December 13-15, 2012
15 December 2012 Surat, India 20
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