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Subject: Thermal Engineering IJRITE

ANALYSIS OF CONJUGATE HEAT TRANSFER IN MICRO FIBERS

B. Srikanth1, Medapati Sreenivasa Reddy2.

1 Research Scholar, Department of Mechanical Engineering, Aditya Engineering College, Surampalem, Andhra Pradesh, India.

2 Professor, Department of Mechanical Engineering, Aditya Engineering College, Surampalem, Andhra Pradesh, India.

Abstract

The present work on ANALYSIS OF CONJUGATE HEAT TRANSFER IN MICROFIBERS an extensive study is conducted

for convective flow in a microfiber subjected to partial heating situation. The effect AXIAL BACK HEAT is explained in

a microfiber, which is developed when a developing laminar flow and heat exchange are simultaneously seen on a heat

transfer surface. The present thesis takes in to consideration that the outer surface is maintained at a unvarying wall

temperature and other boundary conditions are: (i) The total span of the microfiber will be subjected to unvarying

temperature. (ii) Ten percentage of span of inlet and outlet of the microfiber are insulated and remaining span will be

subjected to unvarying temperature. (iii) Ten percentage of span of inlet of the microfiber is insulated remaining span

will be subjected to unvarying temperature. (iv) Ten percentage of span of outlet of the microfiber is insulated

remaining span will be subjected to unvarying temperature. An investigation on Computational fluid dynamic analysis

is conducted for the above mentioned situations at wide range of conductivity ratios, Reynolds numbers, and

thickness to diameter ratios. The result variations and inferences are discussed in detail.

*Corresponding Author:

B. Srikanth, Research Scholar,

Department of Mechanical Engineering,

Aditya Engineering College, Surampalem, Andhra Pradesh, India.

Email: [email protected].

Year of publication: 2017

Paper Type: Review paper

Review Type: peer reviewed

Volume: IV, Issue: I

*Citation: B. Srikanth, Research Scholar “Analysis of

Conjugate Heat Transfer In Micro Fibers” International

Journal of Research and Innovation (IJRI) 4.1 (2017) 572-580.

Introduction

About Axial Back Conduction:

Let us consider the two situation one is constant heat

flux and another is constant wall temperature. For the

first situation microfiber is subjected to constant heat

flux on its outer surface. Whenever the heat applied on

the outer surface, flows along the solid wall of the

microfiber by means of conduction. it reaches the

fluid–solid interface, the heat flows in to the water and

get carried along with the fluid flow. The heat is added

continuously to the fluid in the direction of the flow.

The bulk fluid temperature is increasing linearly

because of surface area is increasing linearly in the

direction of flow. So, the wall temperature of microfiber

is also increase linearly in the direction of fluid flow.

We can find the wall temperature of microfiber is given

by:



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We can find the wall temperature of microfiber by

using the above equation.

(

)

Graph between local wall, bulk fluid temperature and

length of the microfiber (a) constant wall heat flux (b)

constant wall temperature.

Figure.1.1 (a) we can observe that graph between local

wall, bulk fluid temperature and length of the

microfiber at constant wall heat flux. In the second

situation the microfiber is subjected to constant wall

temperature on its outer surface, the local wall, bulk

fluid temperature is nonlinear. We can observe the

graph between local wall, bulk fluid temperature and

length of the microfiber at constant wall temperature

on its outer surface of microfiber form figure 1.1 (b).

The bulk fluid temperature approaches equal to

surface temperature at the outlet of the microfiber. By

the consider these two situation, let us take any two

points on axial direction (both solid and liquid) there is

a maximum temperature between outlet and inlet of

the This axial high temperature distinction leads to

potential for thermal conduction axially along the

strong, furthermore along the fluid towards bay of the

fibre i.e. in a bearing inverse to the heading of fluid

stream. Such a circumstance is known as "axial back

conduction" and prompts conjugate temperature

exchange. Starting currently it is normal that beneath

such ailment there won't be any heat conduction, yet

needs to affirm this from the present work.

LITERATURE REVIEW

The concept of axial back conduction is not another

idea, somewhat an entrenched idea at this point.

Furthermore this idea is not constrained to micro

channels as it were. A point by point audit on early

advancements on axial wall conduction in customary

size heat exchangers is exhibited by Peterson (1999).

Numerous studies do exist in open writing that

arrangement with axial wall conduction in customary

size channels.

For a 3D rectangular moulded micro channel

numerical reproduction was completed by Moharana

and et al, (2012). In this investigation a substrate of

altered size (0.5 mm x 0.4 mm x 50 mm) was chosen

and the channel tallness and width were shifted

autonomously such that the micro channel angle

proportion shifts from 1.0 to 4.0. And Moharana et al,

(2012) found the impact of micro channel angle

proportion on axial back conduction. The Continuous

heat flux limit condition was connected at the base of

the substrate while all its different surfaces have been

kept protected. After the reproduction it was found

that the normal Nu was least relating to channel

perspective proportion of 3.0, regardless of the

conductivity proportion of the working fluid and the

solid substrate

Rahimi and et al. (2012) concentrated on the axial heat

conduction impact on the local Nu. at the passage and

completion district of roundabout small scale funnel.

He suggested the outcome for steady heat flux limit

condition

Moharana et al. (2012) contemplated the impact of

axial conduction in a microfiber for extensive variety of

Re, proportion of wall thickness to internal width and

thermal conductivity proportion. A two dimensional

numerical recreation has been completed for both,

consistent wall heat flux and steady wall temperature,

at the external surface of the fibre, while stream of

fluid through the microfiber is laminar, all the while

creating in nature. After the re-enactment it has been

demonstrated that ksf assumes an overwhelming part

in the conjugate heat exchange process. At the point

when the steady heat flux limit condition is connected

on the external surface of the microfiber, there exists

an ideal estimation of ksf for which the normal Nusselt

number (Nuavg.)

SIMULATION

This is the two dimensional analysis is carried by

Ansys Fluent to understand the effect of axial back

heat of microfiber will be exposed to the unvarying

temperature for four different situations. These

situations are discussed below.



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Situation 1: The total span of the microfiber will be

subjected to unvarying temperature. see

Fig.

Situation 2: Ten percentage of span of inlet and outlet

of the microfiber are insulated and

remaining span will be subjected to

unvarying temperature; see Fig.

(a) Total span of the microfiber is heating.

(b) Ten percentage of span of inlet and outlet of the microfiber are insulated

Assumptions:

The fluid flow inside in the microfiber is done on

the following assumptions.

1. Steady-state condition.

2. Laminar flow.

3. Incompressible flow.

4. Single phase.

5. Constant thermos physical properties.

3.2 Dimensions of the Microfiber:

Inner radius of microfiber δf

= 0.2 mm

Length of the microfiber L =60 mm

The ratio of thickness to internal radius of microfiber δsf =1 to 10

The ratio of thermal conductivity of solid to fluid Ksf =2.26 to 646.21

3.3 2d Modelling:

We have done modelling and solved the above

problem using Ansys-Fluent. We have drawn the two

dimensional diagram for microfiber using ansys 16

version. The below figure is 2d model of microfiber of

δsf =10.

2d modelling of microfiber

3.3 Grid independence test:

After the modelling the grid independence test is very

important for simulation. In this area we have

considered three different grid sizes of 3600*30,

4200*35 and, 4800*40. The below graph 3.3.(a) shows

between Nu number for zero wall thickness of

microfiber is heated at outer surface constantly. This

figure incorporates both creating and completely

created zone for three diverse cross section sizes of

3600x30, 4200x35 and 4800x40 (for half of the

transverse area), for Re = 100. The local Nu number at

the completely created stream administration (close to

the fibre outlet) changed by 0.8% from the cross

section size of 3600x30 to 4200x35, and changed by

under 0.4% on further refinement to work size of

4800x40. Changing from first to the third work, no



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obvious change is watched. In this way, the last

framework (4800x40) was chosen.

(a) Meshing of microfiber (size of 3600x30)

(b) Meshing of microfiber (size of 4200x35)

(c) Meshing of microfiber (size of 4800x40)

Boundary Conditions:

Boundary conditions of microfiber for different

situation are:

At, Z=0 to Z =L and r =0, symmetric axis

(3.5)

At, Z=0 and r=0 to r =δf, u =ū

(3.6)

At, Z=L and r=0 to r =δf gauge pressure

(3.7)

At, z=0 & r =δf to r=δs +δf,∂T/∂z = 0

(3.8)

At, z=L & r=δf to r=δs +δf,∂T/∂z = 0

(3.9)

z=0 to L, r=δs +δf,

(3.10)

Ansys fluent trademark is helpful in comprehending be

needed differential equations. For weight data

distribution, standard plan was made use of. The

calculation of speed weight coupling in the multi

Framework arrangement system was given using

SIMPLE calculation. Second arrange upwind when was

the reason behind the comprehension of momentum

and energy equations.The value of 10 -6 is utilised as a

datum for coherence and energy questions while for

vitality equations data is in the order of 10 -9. Water

enters the microfiber with a slug speed profile.

RESULTS AND DISCUSSION

As earlier discussed in simulation, the microfiber inner

radius is constant. The wall thickness of the microfiber

will be varied from 1 to 10, to know the impact of wall

thickness on the behaviour of the heat transfer. Let us

consider a laminar flow of fluid through a microfiber

subjected to either steady wall high temperature or

steady heat flux, we can find the highest transfer

coefficient, when the solid fluid interface experienced

by steady heat flux. Under perfect situations (where

wall thickness is equal to zero), we can find the value

of the Nusselt number will be 4.36,if solid fluid

interface experienced by steady heat flux. And nusselts

number will be 3.66 for steady wall temperature. For

all intents and purposes each waterway will devour

some limited barricade thickness and in light of

conjugate high temperature exchange conditions not

ensured to take the same limit situation at the solid-

fluid boundary which connected on the external

surface of the fibre. The target of this work is to locate

the genuine limit condition experienced at the rock-

hard-fluid crossing point of a microfiber endangered to



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fractional heating by consistent barricade temperature

at external surface.

Constraints at concentration were axial variety of wall high temperature, greater part liquefied temperature, and home-grown(Nu) . In the 1st place, "Case-1" the total length of the microfiber is heated . Fig. 1.1. Shows the variation of wall temperature and fluid temperature under perfect situation. Figure 4.1 demonstrates dimensionless wall and best part fluid temperature as a component of δsf and Re. The wiped contour speaks to straight variety of main part fluid temperature between the bay and the outlet of the micro duct; its restricting qualities in dimensionless structure are 0 and 1. Under perfect conditions, the bulk fluid high temperature changes directly among the bay and the exit if the fibre is imperilled to steady heat flux limit condition. At lower stream Reynolds number 100 and less estimation for δsf (=1), axial variety of major fluid temperature can be seen to be far from straight variety and near the illustrative variety which is the situation when the fibre is subjected to

consistent wall temperature situation. The outcomes in above graph are autonomous of ksf with the exception of at low estimation of ksf = 2.26. Besides, the wall temperature is verging on steady all through the length of the fibre aside from close to the channel; because of creating stream. An examination of prompts the supposition that the concrete watery boundary for this case encountering consistent wall malaise;which is precisely equivalent to the genuine limit state connected at external surface of the fibre. This implies for this case there is not at all axial stream at heat to mutilate limit complaint at rock-hard-liquid crossing point.

Graph between wall, fluid temperature and length of

microfiber for situation-1

Next, the estimation of δsf expanded from 1 to 10, while

every single other parameter continuing as before as in

graph (a). Presently, it seen in 4.1(b) that the outcomes

not any high autonomous of ksf. Furthermore, the

mainstream fluid temperatures are similarly nearer to

specked contour, showing that the genuine limit

condition next to the solid-fluid crossing point is

floating missing from the isothermalization. Which

likewise be affirmed at the estimations of fence

temperatures; which were not any more consistent for

low estimations of ksf. This demonstrates lower

conductive wall material and upper wall thickness

floats as of real limit condition first.

Temperature variation of microfiber with variation of

δsf =1 and 10 for situation 1

In Case-2, the length of inlet and outlet of 6mm of the microfiber is protected. Actually the fluid temperature

and wall temperature of the microfiber must be equal to the initial temperature of the fluid.. The two vertical specked lines speak to the heating measurement of the microfiber. As a result of inadequate conductivity of the hedge material, there will be conduction of heat in the wall close to the gulf in a course inverse to the bearing of stream of fluid. This will be seen where bulk liquid temperature begins transcending zero in the middle of z = 0 to 6 mm (i.e. z* = 0 to 0.0215). For most minimal ksf the estimation of bulk fluid temperature and in addition wall high temperature are verging on equivalent to zero and consistent in the extent z = 0 to 6 mm (i.e. z* = 0 to 0.0215). With expanding ksf, the estimation of both the wall and the bulk temperature begins ascending in the protected region close to the bay. Because of axial back conduction in the wall of the microfiber. Greater the estimation about f, less the obduracy to stream of heat by conduction; consequently more the ascent in both

the wall and the bulk fluid temperature.

Graphs above relates to δsf = 1 while graph 4.2 (b) relates to δsf = 10. Higher region of fractious-area of solid prompts low updraft imperviousness to axial conduction under same conditions. This can be seen by direct examination amongst the incline of wall temperature in the locale z < 6 mm (or z* < 0.0215) is higher contrasted with its partner in Fig.



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Graph between wall, fluid temperature and length of microfiber for situation-2.

Next, for higher stream Re, the bulk fluid temperature

floats from illustrative towards straight variety in the

middle of the two dabbed vertical lines, which

compares to the heated zone. This demonstrates

higher stream Re prompts the condition at the solid-

fluid interface more towards dependable wall heat

mutability than secure wall temperature

Microfiber protected on external surface in locale z > 54 mm . In this area the majority fluid temperature rests practically steady the instance of δsf = 1. This because on account of as there is not any heat expansion in this locale. Besides, the partition temperature is marginally greater than the majority of fluid temperature, along these lines there is not at all any heat exchange from the wall to fluid with the exception of at the least ksf. For (ksf = 2.26) , the contrast amongst the fluid and wall temperature is most extreme contrasted with other ksf values toward the begin of end protection. In this way for ksf = 2.26,

the wall temperature begins to diminish at last protected locale toward stream of liquid. For greater stream the Re, the distinction amongst bulk liquefied and the fortification temperature is high at z = 54 mm and z* = 0.194 contrasted with less stream Regarding (contrast at graph. 4.2(e) and Fig. 4.2(a)). Consequently this situation temperature begins diminishing toward stream of liquid because of exchange of heat across the wall to the fluid.

Temperature variation of microfiber with variation of

δsf =1 and 10 for situation 2

Graph between heat flux and length of microfiber for situation-2

It is unmistakably apparent that genuine heat flux experienced at the fluid-solid boundary is roughly axially uniform/consistent regardless of the conductivity proportion (ksf), thickness proportion (δsf). At high thickness proportion (δsf), the genuine heat flux practiced at the fluid-solid interface is considerably more than for lower (δsf). This subjective example of axial variety in heat flux is because of the way that low thermal conductivity proportion and

lower thickness proportion (δsf) prompts higher axial thermal resistance in the wall and the other way around. Appropriately, at higher δsf low axial thermal resistance of the wall prompts noteworthy back conduction; this impact turns out to be actually more unmistakable with expansion in conductivity proportion (ksf). As should be obvious in above graphs that we can observe that for specific separation through channel toward axial area the estimation of proportion of heat flux is around consistent for all ksf



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with worth about equivalent to 2 and 10 for the instance of δsf = 1

and 10 separately. And additionally this outcome is

likewise similar at high Re as appeared in Fig. 4.5(c)

and Fig. 4.5(d). Heat flux at solid-fluid interface is

mostly rely on upon wall thickness when external

fringe steady wall temperature is connected which can

be observed by these plots.

Graph between heat flux and length of microfiber for

situation-2

From fig. 4.5-4.6 it is clear that for all condition as

illustrated earlier as four cases and shown

inFig.3.2,theheatflux( )is strong function of δsf. But

it is a week function of Re and ksf due to axial back

condition

Immediate ramifications the axial variety of bulk fluid

temperature and dimensionless wall, and

dimensionless wall heat chooses estimation native Nu,

which have been displayed next in graphs.

Graph between Nusselts number and length of


The above graph speaks to axial variety of local Nu for

the microfiber exposed to Case-1 heating, which were

comparing outlines of first and fifth As talked about

before, in the event that the limit state knowledgeable

at the rock-solid-watery interface is near steady

fortification heat flux, then the local Nu at completely

created region merge near Nuq = 4.36. And if the limit

condition experienced at the solid-fluid interface is

near steady hedge temperature, then the native(Nu)* in

the completely created sector will meet near 3.66. The

two constraining estimations of Nusselt number were

spoken .

For less stream Re and low wall thickness, the

completely created (Nufd) are somewhat greater than

NuT and estimation for Nufd) increments diminishing

estimation for ksf, which is seen in above figure .

Besides the wall thickness expanded to δsf = 10,

keeping every single other parameter unaltered, the

local Nusselt esteem increments at every axial area

and for estimation of ksf. Be that as it may, this

increment is touchy to ksf, and the low the ksf, the high

the expansion in local Nu. This can be shown in above

figure.

For case 2appeared in 3.2(b) the graph of narrow Nu is

appeared in above Fig. 4.10. It is clear from here the

conduct of local Nu plot toward axial area is diverse at

protected position on both sides at bay and outlet.

Butt at the channel the estimation of local Nu is steady

up to span of protection and it then diminishes up to

the quality for completely created stream and again it

diminishes all of a sudden at the exit and again

increments in the protected region.

It is watched that for high ksf and δsf the limit state at

the solid-fluid interface progressively attitude the

pattern more like a consistent heat flux limit

condition, albeit isothermal limit ailment is connected

at the external piece of microfiber. The axial varieties

of local Nu are introduced in above graph i.e.for a

inclusive variety of thermal conductivity proportion

(ksf), Flow (Re) and the thickness proportion (δsf)



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Graph between Nusselts number and length of


CONCLUSION

The following conclusions are understood from the

present investigations:

For completely heated microfiber (in situation

1), it is found that the estimation of Nuavg is

expanding with diminishing estimation of ksf

and the rate of expansion of Nuavg is higher for

littler estimations of (ksf < 50). Besides, while

different parameters staying same, for lower

δsf, Nuavg is higher contrasted with higher δsf.

The distinction between the Nuavg values

(relating to δsf = 1, 10) at lower ksf is higher

contrasted with at higher ksf values. At long

last, the estimation of Nuavg increments with

expanding stream Re while different

parameters are consistent.

Pattern watched at instance for fractional

heating system where (i.e. 10% of aggregate

duration) is protected from the outlet end is

subjectively like that saw if there should be an

occurrence of full heating yet with a few

deviations as sketched out underneath. The

estimation of Nuavg begins diminishing with

diminishing estimation of ksf up to around ksf

equivalent to 40. On further diminishing

estimation of Ksf, estimation of Nuavg begins

expanding quickly. Consequently, there occurs

an ideal ksf at which Nuavg is lowfor this case.

Furthermore, contrast at Nuavg values for ksf is

high contrasted with the instance of full

heating.

For purpose of heating situation 2 (i.e. 10 % of

aggregate span is protected close to channel

and the outlet each) the normal Nuavg for high

wall thickness (i.e. δsf = 10) increments

through diminishing estimation to ksf at low

increments strongly at estimation of ksf also

additionally diminished past fifty . Precisely

similar pattern likewise taken after for low wall

span (that is δsf =1), yet at slightly bring down

estimation for ksf, and estimation about Nuavg

begins diminishing. By this there is not at all

axial conduction at compacted wall because of

greater axial thermal confrontation. Axial

thermal resistance is low by the side of high

wall thickness. Precisely comparable pattern

also watched for which the exit end is

protected at theSituation-3 space heating.

Generally, great axial conduction pointers to

limit state practised at fluid -solid interface is

high near steady heat fluidity state contrasted

with really connected consistent wall

temperature condition on its external surface.

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solve conjugate heat transfer problems: The

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pp. 87-94

AUTHORS

B. Srikanth,

Research Scholar,


Aditya Engineering College, Surampalem,

Andhra Pradesh, India.

Medapati Sreenivasa Reddy,

Professor,


Aditya Engineering College, Surampalem,

Andhra Pradesh, India.

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