HEAT TRANSFER AUGMENTATION OF LAMINAR NANOFLUID FLOW …€¦ · HEAT TRANSFER AUGMENTATION OF...

http://www.iaeme.com/IJMET/index.asp 225 [email protected]

International Journal of Mechanical Engineering and Technology (IJMET)

Volume 7, Issue 3, May–June 2016, pp.225–239, Article ID: IJMET_07_03_021

Available online at

http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=7&IType=3

Journal Impact Factor (2016): 9.2286 (Calculated by GISI) www.jifactor.com

ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication

HEAT TRANSFER AUGMENTATION OF

LAMINAR NANOFLUID FLOW IN

HORIZONTAL TUBE INSERTED WITH

TWISTED TAPES

Prof. Dr. Qasim S. Mahdi

Mechanical Engineering Department,

College of Engineering, Al–Mustansirya University, Iraq

Noor AM. Mohammed

Mechanical Engineering Department,

College of Engineering, Al–Mustansirya University, Iraq

ABSTRACT

In this paper, an experimental study on the heat transfer enhancement and

friction factor characteristics for fully developed laminar CuO/distilled-water

(DI-water) nanofluid flow through horizontal tube inserted with different

geometries of twisted tapes under constant heat flux condition ranged from

4483 to 10000 W/ . =0.08% and 0.35% volume concentrations of CuO

nanoparticles are suspending in distilled water to prepare nanofluid. Twisted

types made from copper material with twist ratios Y=2.6 and 5.3 twist ratios,

thickness t=1 and 2mm and with semicircular and triangular cuts shape were

used to study their effect on twisted tape performance. Results showed that

both convective heat transfer in terms of average Nusselt number and

friction factor have significantly increasing with inserting twisted tape with

nanofluids as working fluid comparing with nanofluids or DI-water in smooth

tube case and this enhancement increases as both Reynold number and

volume concentration increases. Triangular cut twisted tape (TCTT) at Y=2.6

and t=2mm with CuO nanofluid at =0.35% showed the best preformance

among the other twisted tapes on heat transfer enhancement where

increased by 73% than smooth tube with DI-water, while friction factor

increased by 62%. New Empirical correlations have been developed for both

average Nusselt number and friction factor in the terms of the parameters

mentioned above.

Key words: Nanofluid, Twisted Tape, Heat Transfer Enhancement, Friction

Losses.

Prof. Dr. Qasim S. Mahdi and Noor AM.Mohammed


Cite this Article: Prof. Dr. Qasim S. Mahdi and Noor AM.Mohammed, Heat

Transfer Augmentation of Laminar Nanofluid flow in Horizontal Tube

Inserted with Twisted Tapes. International Journal of Mechanical

Engineering and Technology, 7(3), 2016, pp. 225–235.

http://www.iaeme.com/currentissue.asp?JType=IJMET&VType=7&IType=3

1. INTRODUCTION

Enhancement the heat transfer process play an important role in increasing the

efficiency of the most important energy industry applications in heat transfer

including, power generation, chemical production, air conditioning, Transportation

and microelectronics, heating of circulating fluid in solar collector, heat transfer in

compact heat exchangers and many other industrial sectors associated with different

processes depends on the heating or cooling fluid inside tubes. During the last decades

many researchers have been experimentally, investigate the effects of nanofluid

technology and the tabulators' passive techniques on heat transfer enhancement and

pressure drop. Lazarus et al. [2009] experimentally investigated the effect of

convective heat transfer of de-ionized water with a low volume fraction =0.003% of copper oxide (CuO) nanoparticles to form nanofluid flows through copper tube under

laminar flow and heat flux conditions. The results has shown 8% enhancement for

convective heat transfer coefficient of the nanofluid even with a low volume

concentration of CuO nanoparticles. The heat transfer enhancement increased

considerably as the Reynolds number increased. They predicted a new correlation for

local Nusselt number variation along the flow direction of the nanofluid. Alimullah

Anwar [2014] studied experimentally the heat transfer augmentation and friction

factor characteristics through circular tube fitted with full-length helical screw insert

device for laminar and turbulent flow under constant heat flux condition. The results

showed that with this type of inserts a high swirl flow generates which increases the

convection heat transfer, thus Nusslet number increases as twisted ratio decreasing as

compared with plain tube. Akeel Abdullah [2011] studied experimentally the heat

transfer enhancement and pressure drop in turbulent flow of air for Reynolds number

range=5000 to 23000 in a horizontal circular tube under constant wall heat flux

condition fitted with combined conical-ring tabulators and a twisted-tape swirl

generator. It noticed from experimental results that temperature values increases along

the tube length and decrease as twist ratio decreases while the average Nusslet

number increases as Re increases and decreasing as twisted ratio decrease in case of

combined twisted tape and conical ring. The results showed a significant enhancement

in heat transfer process with conical ring tabulator than empty plain tube and much

better enhancement in case of combined twisted tape and conical ring. It's noticed that

the fanning friction factor decreases as Re increases and the values of friction factor

become higher when using conical ring in combined with twist tape than using

conical ring alone and especially at smaller twisted tapes ratio due to increase swirl

flow which leads to higher contact between secondary flow and tube wall. He also

predicted new empirical relationships for Nusslet number and friction factor for

combined conical ring and twisted tape. Esmaeilzadeh et al. [2014] studied

experimentally the characteristics of heat transfer and friction factor enhancement of

ɣ- /water nanofluid in laminar flow region flowing through uniform heated circular tube fitted with twisted tapes inserts with various thicknesses. They noticed

from results that the performance of convective heat transfer becomes better with the

addition of ɣ- /water nanofluid compared with water and the values of

convection heat transfer coefficient increases with increasing volume concentration

http://www.iaeme.com/currentissue.asp?JType=IJMET&VType=7&IType=2

Heat Transfer Augmentation of Laminar Nanofluid flow in Horizontal Tube Inserted with

Twisted Tapes


and becomes much higher when used in combined with twisted tape inserts,

especially with the thicker twisted tape. They indicated that the friction factor values

increases as twisted tape thickness increases when these values compared with the

friction factor values for pure water or with nanofluid, thus the use of twisted tape

inserts leads to larger surface contact and reduction the free flow area causes high

speed swirl flow and increasing the pressure drop.

Many researches attempt to improve the efficiency of heating systems and heat

exchanger by selecting different, geometries, working fluids or operational mode and

boundary condition. To overcome these problems, nanofluids and swirl flow devices

insert are the best techniques used to reduce size and costs of heat exchangers and

achieve a high heat transfer rate with minimum pumping power. Therefore, in this

study the effect of changing the twist ratio, thickness and cutting shape of twisted tape

with the flowing of CuO nanofluids at different volume concentrations through

horizontal uniform heated tube will be investigated in order to get to the desired

efficiency for heat transfer enhancement with less friction losses.

2. EXPERIMENTAL APPARATUAS AND PROCEDURE

2.1. Test Rig Description

Straight copper tube with 14.2mm inner diameter, 0.9mm thickness and 1000mm

length was used as the test section. Ten thermocouples were soldered, five on the

outer upper and five on outer lower surface tube along the test section in opposite

position with an equal distance between them in order to increasing the temperatures

readings accuracy. Thermocouples heads were well insulated. A 0.5mm thickness

asbestos heat resistance insulation wrapped around the tube to electrically isolated it

from the heater coils. Electrical heater coils with rating 1000W, resistivity 4.9

ohm/meter, (2*0.16) mm cross section and 3200mm length are wound tightly around

the tube to heated the test section with the desired heat flux by connecting it to a

Variac voltage transformer that supply an electric AC power to regulate the input

voltage across the heater coils to give a constant heat flux boundary condition along

the test tube. The test tube covered with a layer of fire resistance asbestos insulation

(30mm width and 5mm thickness) and another layer of fiberglass insulation with

50mm thickness to prevent heat losses. Two 4mm pressure taps inserted at the inlet

and outlet of the test section. The test tube has an entrance length before section part

and it's long enough to make sure that the flow is hydro dynamically fully developed

when it's enter the heated section. Figure (1) shows a 3D schematic diagram of

experimental test rig. Figure (2) shows a photograph for the test rig.

2.2. Twisted Tapes Geometries

Twisted tapes were made from copper straight tape with length 1m and width 12mm.

all the types and dimensions of twisted tapes used during the experimental work are

demonstrated in table (1).

Twisted tape manufacturing by clamping one end of the tape and twisting the

other end carefully to reach to the desired twist ratio. The two different cutting shapes

along the twisted tape edge has been extruded out by manufactures special pieces for

each cut shape and then these tapes inserted inside the core tube along the test section

by moving passage (flange) equipment at the end of the test tube. Figure (3) shows the

geometrical details of twisted tapes.



2.3. Data Deduction

Heat transfer calculation

The electric power applied at the tube wall to achieve heating effect was determined

by:

where, I is the electric current d and V the electric voltage deliverers through

heater coils. Assumed well-insulated outer surface tube (no heat losses) therefore the

energy heat transfer to be absorb by the fluid:

where, ṁ is the mass flow rate of water through the horizontal tube, Cp the specific heat

of water and are the inlet and outlet water temperatures for the test tube.

In order to calculate the average heat transfer coefficient inside the tube the well-

known Newton’s law of cooling used as follows, Holman and John [2010]:

where, is the average heat transfer coefficient inside tube, the surface area calculated

from:

and the mean fluid temperatures estimated by:

surface temperature Sami .et al. [2014].

then, the average inner Nusselt's number (Nu) calculated as:

The Internal flow for heated tube is laminar fully developed flow and the Reynold

number values are ranging from 290 to 2000 and its estimate by the relation:

)

The thermal resistant

value across tube wall is

too small thus, the inner surface temperature equal to the outer surface temperature

[ .

Friction factor

The friction factor coefficient ( ) which is related to the pressure drop ( ) across

the heated tube length can be calculated by equation:

where:


Twisted Tapes


where, is the average velocity inside the tube, is the Cross section area of

tube. The thermal conductivity ( ), the dynamic viscosity ( ) and the density of

base fluid are based on (mean bulk temperature).

3. RESULTS AND DISCUSSION

Experimental results for local Nusselt number and friction factor for smooth tube

were compared with the well-known Shah's correlation for the constant heat flux

condition in tubes and Hagen-Poiseuille's equation for pressure drop in laminar flow

respectively to sureness the accuracy of the experimental work results as shown in

figures (4) and (5). The results showed logical agreement with the results from the

mentioned equations.

3.1. Effect of Twist Ratios of Twisted Tape

The variation of average Nusslet number and friction factor at different water

Reynold's number for twisted tape ratios (Y=2.6 and 5.3) are clarified in figures (6)

and (7). From the resulting curves, it can be realized that the enhancement of heat

transfer in terms of average Nusselt number increases by decreasing the twist ratio

and by increasing the Reynold number value. The strength of swirling flow generated

from the twist of the tape depends on the twist ratio thus the swirling flow generates

from lower twist ratio is much higher than for higher twist ratio. Lowering the twist

ratio of twisted tape generates a stronger swirling flow which increases the turbulent

intensity of the main flow in order to improving the viscous boundary layer mixing

near the inner tube wall to augment the heat transfer process. Nusselt number for the

present study improved by 50.6% for Y=5.3 and by 55% for Y=2.6 at Re= 1923 than

for smooth tube case. In basic case for smooth tube the friction factor decreases as Re

increases due to the increasing in pressure drop, but it's found to be with inserting

twisted tape there is a considerable augmented in friction losses and whenever the

twist ratio decreased the friction factor increased and become much higher than for

smooth tube at the same values for Re due to the increasing in shear forces near the

tube wall. The friction factor for the present results increased by 38.47% for Y=2.6

and by 27% for Y=5.3 than those for smooth tube case.

3.2. The Effect of Twisted Tape Thickness

Figure (8) clarify the variation of heat transfer enhancement in terms of average

Nusselt number for twisted tapes thicknesses (t=1mm and 2mm) at different Reynold

number. It's clear from resulting figures that the twisted tape thickness has a

significant effect on the heat transfer process and as the tape thickness increases the

Nusselt number increases. Increasing the tape thickness narrowing the swirling path

flow that enhances the tangential velocities for better mixing to the viscous boundary

layer near the tube wall region. In addition, the tape edge effect which acting like a fin

dissipates heat from the inner tube surface to the working fluid thus increasing this

area improving the convective heat transfer. Nusslet number increased by 62% for

t=2mm and by 54% than t=1mm and for smooth tube respectively, while there was

increasing in friction losses by 23% for twisted tape at t=2mm comparing to twisted

tape at t=1mm as shown in figure (9).



3.3. The Cut Shape Effect of Twisted Tape

The effects of triangular cut twisted tape (TCTT) and the semicircular cut twisted tape

(SCTT) on the variation of average Nusselt number and friction factor are clarified in

figures (10) and (11). As shown, at the same operation condition the heat average

Nusselt number is much higher for TCTT by 4% and by 6% than SCTT and typical

twisted tape respectively and by 65% than for smooth tube case. Generally, the typical

twisted tape (TTT) generates only a swirling flow but in case of adding several cuts

along the twisted tape edge it will produces many local vortices at each cutting section

that provides an excellent mixing for the viscous boundary layers in all direction

along the tube leads to higher improvement in heat transfer enhancement. Also, the

heat transfer enhancement rate depends on the cutting shape which controls the

strength of vortex generated which mean the vortices preformed behind the triangular

cut is more stronger than those preformed through the semicircular cut. On the other

hand, the friction factor enhances more with TCTT by13 % than SCTT and by 27%

than TTT because the addition of these local vortices promotes an additional shear

stress due to increasing in flow mixing between the viscous boundary layers of fluid

at the tube wall and twisted tape.

3.4. Combined Effect of Twisted Tape and Nanofluid on Heat Transfer

Figures (12) and (13) clarified the variation of average Nusslet number ( ) and

friction factor of CuO nanofluid for = 0.08% and 0.35% volume concentrations, flowing at various Reynold numbers through the inserted tube with triangular cut

twisted tape (TCTT) and typical twisted tape for 2.6 twist ratio and 1mm thickness.

It's observed that the heat transfer enhancement reached the highest level during this

study through the joint use of TCTT with CuO nanofluid. Where, the increased by

8% than TCTT without CuO nanofluid and by 22%, 21% than TTT with CuO

nanofluid for the same operation condition and volume concentrations. Also, this

enhancement increases with increasing both Reynold number flow and nanoparticles

volume concentration. Random motion of nanoparticles even at low volume

concentration become more active in convective heat transfer and accelerated due to

swirling flow and local vortices generated by the TTT and TCTT that provides perfect

mixing for the viscous layer for the working fluid. The friction factor for TCTT with

CuO nanofluid increased by 2% for = 0.08% and by 3% for = 0.35% than TCTT

without CuO nanofluide and for the TTT with CuO nanofluid increased by 1.5% for

=0.08 and by 2.7% for =0.35% than TTT without CuO nanofluid for the same operation conditions. The friction losses along the tested tube increases due to

increasing in the turbulent intensity of the flow that accelerating nanoparticles motion

through the swirling flow, which enhances shear stress forces near the inner tube wall.

4. DEVELOPING OF EMPIRICAL EQUATION

The Nusselt number and friction factor experimental results have been correlated by

the following equations:

Nusselt number and friction factor correlation for Twist ratio:

= 1.1 (16)

= 868.8 (17)

Valid for 451<Re< 2100, 2.6<Y<5.3, 5.34<Pr<7.1.

Nusselt number and friction factor correlation for TTT thickness:


Twisted Tapes


= 0.515 (18)

= 294.43 (19)

Valid for 451<Re< 2100, 1mm <t< 2mm, 5.34<Pr<7.1.

Nusselt number correlation for TCTT with nanofluids:

= 0.943 (1+we/ (1+ (20)

Valid for 286<Re< 1772, 0 <de/ < 1.272, 5.34<Pr<7.1, 0 <we/ < 1.363, 0< <0.35.

5. CONCLUSIONS

Generally observation, high heat transfer enhancement and pressure drop occurs with

using the twisted tapes which is depends on the twist ratio, thickness and the cutting

shape for twisted tapes. Twisted tape twist ratio and thickness have greater impact on

heat transfer enhancement instead of adding different cutting shape on twisted tape

body, where increased by 54% and 38% with increasing thickness and twist ratio,

while increased by 27% with adding triangular cutting shape comparing with TTT

with the same dimensions. Triangular cuts showed better performance in heat transfer

enhancement than semicircular cuts which confirms that the fluid velocity accelerates

more through sharp cuts. The CuO nanofluid give better performance on heat transfer

enhancement when it's flowing through the inserted tube with twisted tape than the

flowing in smooth tube and this performance become more efficient with increasing

the nanoparticles volume concentration and Reynold number. Where the highest value

for was for TCTT with 0.35% volume concentration of CuO nanofluid.

Table 1 Characteristic dimensions of the twisted tapes inserted tubes

Insert set Revolution

No.

Thickness

mm

(t)

Pitch(H)

(Y*di)

mm

Width

mm

Twisted

ratio

(Y)

Metal Cut

dimension

Typical twisted

tape (TTT) 30 1 37 12 2.6 Copper ………..

Typical twisted

tape (TTT) 30 2 37 12 2.6 Copper ………..

Typical twisted

tape (TTT) 15 1 75 12 5.3 Copper ………..

Triangular cut

twisted tape

(TCTT)

30 2 37 12 2.6 Copper

width cut

(we=4mm)

depth cut

(de=3mm)

Semicircular cut

twisted tape

(SCTT)

30 2 37 12 2.6 Copper Radius cutting

(re=4mm)

Table 2 Properties for the two types of the nanosized particle at temperature 25C0

Al2O3 Cuo Property

710 535 Cp(kJ/kg.K)

3700 6400 ρ(kg/m3)

46 69 K(W/m.K)

180 120 α x10-7(m2/s)

80 40 Di (nm)



Figure 1 3D schematic diagram of experimental test rig

1) Test section, 2) Water chiller system, 3) Insulated cold water tank, 4) flow meter, 5)

Thermocouples, 6) Valves, 7) Variac, 8) Temperature, 9) water pump.

Figure (2) Photograph for experimental test rig

Thermometer

Manometer

Variac


Twisted Tapes


0

5

10

15

20

25

0 10 20 30 40 50 60 70

Present Experimental Work Shah Equation [1978]

q=6725 W/𝑚

Figure 3 Twisted tapes types and geometries

Figure 4 Comparison between experimental work and Shah Equation at =6725 W/ ,

Re=944



Figure 5 Comparison between experimental work and Hagen equation at =6725 W/ ,

Re=944

Figure 6 Variation of Nusselt number with Reynold number for different twist ratio at =

10000 W/

0

0.05

0.1

0.15

0.2

0.25

0 500 1000 1500 2000 2500

Fric

tio

n f

acto

r

Reynold number

Hagen-Poiseuille equation[1996]

Present Experimental Work

0

5

10

15

20

25

30

35

40

45

50

0 500 1000 1500 2000 2500

Ave

rage

Nu

sse

lt n

um

be

r

Reynold number

Tube with TTT at T.W=2.6


smooth Tube


Twisted Tapes


Figure 7 Variation of friction factor with Reynold number for twisted tapes at different twist

ratios at = 10000 W/

Figure 8 Variation of Nusselt number with Reynold number for twisted tapes at different

thicknesses at = 10000 W/

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 500 1000 1500 2000 2500

Fric

tio

n f

acto

re

Reynold number


Tube with TTT at T.w=5.3

smooth Tube

0

10

20

30

40

50

60

0 500 1000 1500 2000 2500

Ave

rage

Nu

sse

lt n

um

be

r

Reynold number

Smooth Tube

Tube with TTT at thickness =1mm




Figure 9 Variation of friction factor with Reynold number for different thicknesses at =

10000 W/

Figure 10 Variation of Nusselt number with Reynold number for different cut shape of

twisted tapes at = 10000 W/

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 500 1000 1500 2000 2500

Fric

tio

n f

acto

r

Reynold number

Smooth Tube



0

10

20

30

40

50

60

70

0 500 1000 1500 2000 2500

Ave

rage

Nu

sse

lt n

um

be

r

Reynold number

Tube with TTT

Tube with SCTT

Tube with TCTT


Twisted Tapes


Figure 11 Variation of friction factor with Reynold number for different cut shape of twisted

tape at = 10000 W/

Figure 12 Variation of Nusselt number with different volume concentrations of CuO

nanaofluid with TTT and TCTT

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 500 1000 1500 2000 2500

Fric

tio

n f

acto

r

Reynold number

Tube with TTT

Tube with SCTT

Tube with TCTT

0

10

20

30

40

50

60

70

0 500 1000 1500 2000 2500

Ave

rage

Nu

sse

lt n

um

be

r

Reynold number

TCTT with DI-water

TTT with DI-water

TCTT with CUO 0.08%

TTT with CUO 0.08%

TCTT with CUO 0.35%

TTT with CUO 0.35%



Figure 13 Variation of friction factor with different volume concentrations of CUO nanofluid

with TTT and TCTT

REFERENCES

[1] Akeel Abdullah Mohammed, Heat Transfer and Pressure Drop Characteristics of

Turbulent Flow in a Tube Fitted with Conical Ring and Twisted Tape Inserts,

Eng. & Tech. Journal, 29 (2), 2011.

[2] Alimullah Anwar Md., Effect on heat transfer of laminar flow in a tube insertion

of twisted tape, Shri Chatrapati Shivajiraje College of Engineering, Kiran Suresh

Patil, (2014).

[3] Esmaeilzadeh E., H. Almohammadi, A. Nokhosteen, A. Motezaker, A.N.

Omrani, Study on heat transfer and friction factor characteristics of Al2O3/water

through circular tube with twisted tape inserts with different thicknesses,

International Journal of Thermal Sciences, 82, pp.72–83, 2014.

[4] Holman J. P. and John Lloyd, Heat Transfer, Southern Methodist University,

McGraw-Hill Series in Mechanical Engineering, (2010).

[5] Keblinski P., Jeffery A.Eastman, David G. Cahill, Nanofluids for thermal

transport, Materials Today, 8 (6):36–44, (2002).

[6] Lazarus Godson Asirvatham, Nandigana Vishal, Senthil Kumar angatharan and

Dhasan Mohan Lal, Experimental study on forced convective heat transfer with

low volume fraction of CuO/Water nanofluid, Journal Energies 2, pp.97–119,

ISSN 1996-1073, (2009).

[7] Liu .S, M.Sakr, A comprehensive review on passive heat transfer enhancements

in pipe exchangers, Journal ElSEVIER, Renewable and Sustainable Energy

Reviews, 19, pp.64–81, (2013).

[8] Radu Cazan and Cyrus K. Aidun, Experimental investigation of the swirling flow

and the helical vortices induced by a twisted tape inside a circular pipe, Atlanta

Georia, PHYSICS OF FLUIDS, 21, (2009).

[9] Rashidi .F, N. Mosavari Nezamabad, Experimental Investigation of Convective

Heat Transfer Coefficient of CNTs Nanofluid under Constant Heat Flux,

Proceedings of the World Congress on Engineering, Vol III, (2011)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0 500 1000 1500 2000 2500

Fric

tio

n f

acto

r

Reynold number

TTT with DI-water

TCTT with DI-water

TTT with CUO 0.08%

TCTT with CUO 0.08%

TTT with CUO 0.35%

TCTT with CUO 0.35%


Twisted Tapes


[10] Sami D. salman, Abdul Amir H.Kadhm, Mohd S.Takriff, and Abu Bakar

Mohamad, Heat transfer enhancement of laminar nanofluids flow in circular tube

fitted with parabolic-cut twisted tape inserts, Hindawi Publishing Corporation,

The Scientific World Journal, ID 543231, (2014).

[11] Shah R.K., A.L. London, Laminar Flow Forced Convection in Ducts, Supplement

1 to Advances in Heat Transfer, Academic Press, New York, (1978).

[12] Kavitha T, Rajendran A, Durairajan A, Shanmugam A, Heat Transfer

Enhancement Using Nano Fluids And Innovative Methods - An Overview.

International Journal of Mechanical Engineering and Technology, 3(2), 2012,

pp. 769–782.

[13] Sunil Jamra, Pravin Kumar Singh and Pankaj Dubey, Experimental Analysis of

Heat Transfer Enhancementin Circular Double Tube Heat Exchanger Using

Inserts. International Journal of Mechanical Engineering and Technology, 3(3),

2012, pp. 306–314.

[14] Qasim S. Mahdi and Ali Abdulridha Hussein, Enhancement of Heat Transfer In

Shell And Tube Heat Exchanger with Tabulator and Nanofluid. International

Journal of Mechanical Engineering and Technology, 7(3), 2016, pp. 125–138.

[15] Xuan Y., Roetzel W., Conceptions for heat transfer correlation of nanofluids,

International Journal of Heat and Mass Transfer, 43, pp 3701–3707, (2000).

NOMENCLATURE

Cross section area, Average wall temperature,

Surface area, Mean bulk fluid temperature, Specific heat, kJ/kg.K Inlet fluid temperature,

de Cutting depth, m Inner surface tube temperature, Inside tube diameter, m Outer surface tube temperature, Outer tube diameter, m Average inlet velocity, m/sec

Friction factor V Electric volte, Voltage H Pitch, m w Width, m

Inside heat transfer coefficient, W/ . we Cutting width, m I Electric current, Amp Y Twist ratio

K Thermal conductivity, W/m.K Z Axial distance, m L Length, m Viscosity, kg/m.sec Mass flow rate, kg/sec Density, kg/

Nu Nusselt number Volume concentration of nanofluid

Average Nuseelt number

Pr Prandtl number

Pressure drop, Pas

Q Electric power, Watt Adsorbed heat energy, Watt

Heat flux, W/

Re Reynold number

re Cutting Radius, m

t Thickness, m

Surface temperature,

Outlet fluid temperature,

HEAT TRANSFER AUGMENTATION OF LAMINAR NANOFLUID FLOW …€¦ · HEAT TRANSFER AUGMENTATION OF...

Documents

Transcript of HEAT TRANSFER AUGMENTATION OF LAMINAR NANOFLUID FLOW …€¦ · HEAT TRANSFER AUGMENTATION OF...