Modelling Performance Electric Heater.pdf

8/11/2019 Modelling Performance Electric Heater.pdf

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INTERNATIONAL JOURNAL OF ENERGY RESEARCHInt. J. Energy Res. 2004; 28:12691291Published online 18 August 2004 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/er.1029

Modelling and performance analysis of an electric heater

Ashraf M. Bassily1,n,y and Gerald M. Colver2

1Gharian University, P.O. Box 64735, Gharian, Libya2Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, U.S.A.

SUMMARY

Electric heaters are used extensively in many industrial applications. There are several interactingparameters that affect heater performance and contribute to its cost. Such parameters are: coil length, coildiameter, helix diameter, coil pitch, number of turns, coil emissivity, heater wall emissivity, applied voltage,air flow rate, air temperature at the heater outlet, insulation thickness, and the heater dimensions. Three

conical heater configurations were selected for preliminary optimization. A conical heater configurationwith outer ring coils was found to give the highest heater efficiency, the easiest and least expensive tomanufacture, and was selected for detailed modelling. In the simulation model, the heater wall was dividedinto four annular sections and the continuous heater coil was divided into four segments of four ring coils.Energy and heat transfer equations were written for each ring coil, each section of the wall, and the air pasteach ring coil. Equations for coil resistance and power, air properties, heater geometry, and configurationfactors are added to form a system of 220 nonlinear equations. Engineering equation solver (EES) was usedto solve the system of equations. The results were checked by comparing the heater efficiency based on theaverage inlet and outlet air temperatures, and the heater efficiency based on the heater losses. Bothefficiencies matched well in all calculations. The effects of varying the identified heater parameters on theheater performance were studied and discussed. The results indicate that increasing the coil length andairflow rate, while reducing coil emissivity, wall emissivity, and wire diameter could improve heaterperformance. Copyright # 2004 John Wiley & Sons, Ltd.

KEY WORDS: coiled wires; a conical heater; energy efficiency; an efficient heater; an insulated heater

1. INTRODUCTION

Electric heaters have a wide variety of industrial applications such as drying, air conditioning,

and water heating. Electric heaters involve many interacting parameters such as coil length, wire

diameter, helix diameter, coil pitch, the number of turns, coil emissivity, wall emissivity, applied

voltage, insulation thickness, air flow rate, and the heater dimensions. Increasing coil diameter

increases its heat transfer area, but also reduces coil resistivity; thus, increasing coil power for

the same coil length. Increasing coil length increases its heat transfer area and coil resistivity;

thus, reducing coil power for the same coil diameter. Varying the coil dimensions also influences

its temperature, which affects the temperature and properties of the surrounding air. That affectsthe heat transfer coefficient of the coil, which influences its temperature even further. Reducing

Received 22 May 2003Accepted 4 September 2003Copyright# 2004 John Wiley & Sons, Ltd.

yE-mail: [email protected]

nCorrespondence to: A. M. Bassily, 31 Ahmed El Barrad Street, 11241 Cairo, Egypt.


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coil emissivity reduces the radiation loss to the surrounding and increases heater efficiency.

Detrich et al. (1990) showed that increasing coil pitch increases the heat transfer coefficient of

the coil. Literature review has shown that no model for an electric heater has yet considered the

interaction of all the above-mentioned parameters. Modelling of the electric heater is an

essential step for optimization and performance analysis. An optimum design of the electricheater minimizes extreme coil temperatures and the associated thermal stresses, leading to

longer operating cycles, longer life for the heating element, and saving in energy usage. This

paper gives a detailed model comprised of 220 nonlinear equations for a conical electric heater.

The model determines the energy losses from the heater, the temperature distribution along the

coil (simulated by separate ring coils), along the heater wall, and of air past each ring coil. In

addition, the model determines the effect of changing the above-mentioned heater parameters

on heater performance.

2. PRELIMINARY OPTIMIZATION OF THREE CONFIGURATIONS

OF THE HEATER

Figure 1 shows the three conical heater configurations that were selected for optimization. The

inner rows of ring coils are in contact with increasingly hotter air. The main idea of the heater

configurations is to reduce the temperature of the inner coils (the second, third, and fourth rows)

by increasing the convection heat transfer coefficient of ring coils as air passes through the

heater; thus, reducing the temperature of the inner coils and achieving a relatively uniform

temperature distribution. Energy balance and heat transfer equations were written for each of

the three heater configurations, which included balances on the coil, heater wall, and the air flow

passing each coil. In that model, a single value of temperature represented the temperature

distribution for the coil and a single value represented the temperature distribution for the

heater wall. Interactive Thermodynamics (IT) software, Intelli Pro, Inc. (1996) was used to solve

the resulting 30 nonlinear equations.The optimization was based on maximizing the heater efficiency in terms of the dimensions of

the coils, emissivity of the coil, and of the wall subject to a constant mass flow rate for air and an

Outer Coil Inner Coil

1st

row

2nd

row

3rd

row

4th

row

Air

(a) (b) (c)

Figure 1. Three different configurations for the electric heater. (a) a heater with outer coils; (b) a heaterwith inner coils; (c) a heater with inner and outer coils.

Copyright # 2004 John Wiley & Sons, Ltd. Int. J. Energy Res. 2004; 28:12691291

A. M. BASSILY AND G. M. COLVER1270


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outlet air temperature of 400 K. The univariate search was carried out. The procedure involved

holding all but one of the parameters constant while optimizing the heater efficiency relative to

the remaining parameter. This maximizing process was then repeated for each parameter. By

this method, the heater configuration of Figure 1(a) was found to give the highest heater

efficiency and also the least sensitivity of efficiency to the parameters (coil dimensions, etc.)variation. In addition, the same heater configuration was also found to be the easiest and least

expensive to manufacture.

3. DETAILED MODELLING FOR ONE CONFIGURATION OF THE HEATER

Detailed modelling for the best heater configuration (Figure 1(a)) will be illustrated. The heater

wall was divided into four sections of equal area, as shown in Figure 2. The heater coil was

divided into four ring coils that simulate the continuous coiled helix of an actual heater. The

four sections of the heater wall are labelled wall 1, wall 2, wall 3, and wall 4, respectively. The

four ring coils are labelled coil 1, coil 2, coil 3, and coil 4, respectively. In the analysis, energy

equations were written for each section of the heater wall, each ring coil, and for the air flowpast each ring coil. The equations of heat transfer were written to include convection and

radiation at each section of the heater wall and each ring coil. Equations for air properties,

configuration factors, and heater geometry made up the additional equations necessary to

complete the model.

Section 4

of the heater wallHw4

Hw3

Hw2

Hw1

Section 3

of the heater wall

Section 2

of the heater wall

Section 1

of the heater wall

Coil 3

Coil 1

Coil 2

Coil 4

0.1524m

0.05m

0.05m

0.05m

Hh

Air flow

Doh

Hs

Figure 2. Illustrated diagram of the electric heater.


MODELLING AND PERFORMANCE ANALYSIS 1271


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3.1. Calculation assumptions

1. Steady state conditions.

2. The four ring coils are located at 0.1524, 0.2032, 0.254, and 0.3048 m from the heater

inlet, respectively.3. The heater outlet is connected to a heater duct that is 0.1016 m in diameter so that the

outlet diameter of the heater is constant at 0.1016 m.

4. The length of each coil is proportional to the diameter of the heater cone at the point of

location of that ring coil.

5. The materials of the heater wall and of the ring coils are homogenous.

6. A single value of temperature represents the temperature distribution on each ring

coil.

7. A single value of temperature represents the temperature distribution on each section of

the heater wall.

8. The inlet air temperature to the heater is constant and equal to the surrounding

temperature of 305 K.

9. The hemispherical emissivity of the heater wall is not a function of the direction ofradiation or its wavelength.

10. The hemispherical emissivity of the surroundings is taken as a constant of 0.9 and that it

is not a function of the radiation direction or its wavelength.

11. The hemispherical emissivity of the ring coils is not a function of the direction of

radiation or its wavelength.

12. Radiation heat that reaches any ring coil from a neighbouring ring coil is very small

compared with the radiation heat emitted from the neighbouring ring coil so that

radiation exchange between ring coils is neglected.

13. The four ring coils simulate a continuous coiled helix with a constant applied voltage at

its coil terminals.

14. The flow through the heater is strongly non-uniform with higher velocity and cool

temperature in the empty centre and lower velocity and hot temperature in the coilregions; both due to wall friction and the resistance of the coils. Therefore, the flow is

assumed to be in two zones. Cool zone through the empty centre and hot zone near the

ring coils. The two zones mix as the flow passes the fourth ring coil, as shown in

Figure 3. The thickness of the hot zone is assumed to be 3.3cm measured

perpendicularly from the heater walls, as shown in Figure 3. Such a value is determined

assuming that the centre line of the hot zone passes through the centre of the insulators

that support and centre the ring coils. The flow area of the hot zone is determined by

subtracting the cross-section areas of the ring coils and insulators from the cross-section

area of the hot zone. For the purpose of determining the temperature difference of

convection heat transfer, it is assumed that the temperature of air in the region occupied

by each ring coil in the hot zone is constant and equal to the average temperature of the

inlet and outlet for that ring coil, as shown in Figure 3.15. For the purpose of determining a correction factor for the Nusselt number due to

ring coil arrangement, each ring coil is modelled as two adjacent rows of tubes.

The diameter of each tube equals the coil diameter. The transverse distance between

tubes equals the pitch of the ring coil and the longitudinal distance equals the helix

diameter.




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16. The heat loss occurs by convection from the external wall to the surroundings at a

constant convection heat transfer coefficient of 6.5 W m2 K1.

3.2. Defining the stretching factors

From the geometry of Figure 2, the length of ring coil 1 is given by the following equation:

Lc1 pDhxnc1 1

whereDhxis the helix diameter andnc1 is the number of turns of ring coil 1. Similarly, the helix

diameter to the pitch ratio for ring coil 1pc1can be determined from the coil geometry (please

see Figure 3) and is given by the following equation:

pc1 Dhxnc1

2pHh Dho=2 tana 0:1524 tan a Hs

Lc1

2p2Hh Dho=2 tana 0:1524 tan a Hs

fc1Lc

pLch2

whereHhis the total height of the heater, Dhois its outlet diameter,Hsis height of the insulators

that support the ring coil,Lchis a chosen length,fc1 is the stretching factor for ring coil 1, and a

is the cone half angle. The stretching factor is introduced to determine the effect of varying the

transverse distance and is defined as a ring coil length ratio multiplied by a dimensionless

number. The ring coil length ratio is the ratio of the ring coil length to the length of the

peripheral of the ring coil path. The dimensionless number is chosen to give the stretchingfactors values between 0.25 and 1.0 as feasible values that can be manufactured and installed.

The corresponding values for pciare 0.8 and 2.55, respectively. The dimensionless number is

chosen by picking a value for the length Lch. The stretching factor affects the length of the ring

coil and its convection heat transfer coefficient by changing the helix diameter to pitch ratio.

Equations for other ring coils dimensions can be written in a similar manner.

Coil 1

Coil 2

Coil 3

Coil 4

Ti

Tav1

Tav2Tav3

Tav4

To

0.0508 m

0.1778 m

0.127 m

0.0508 m

0.127 m

0.0254 m

Tav1

Tav2Tav3

Tav4

ToToTi Cool Zone

0.033 m

0.033 m

Hh

Hs

Dho

Figure 3. The temperature distribution of air in the heater.


MODELLING AND PERFORMANCE ANALYSIS 1273


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3.3. Energy balance for the heater ring coils

Applying the energy equation for ring coil 1, gives

QQec1 QQrc1w1 QQrc1w2 QQrc1w3 QQrc1w4 QQrc1w5 QQrc1ehc1Ac1Tc1 Tav1 3

The energy equation can be applied for ring coils 24 in a similar manner.

3.4. Energy balance for air past the ring coils

Applying the energy equation for a control volume of air in the hot zone as it passes from the

heater inlet across ring coil 1, gives,

hw1Aw1Tw1Tinl hw2Aw20:127Hw1

Hw2Tw2Tinl hw2Aw2

Hw1Hw2 0:127

Hw2Tw2Tav1

hw3Aw30:1778Hw1 Hw2

Hw3Tw3 Tav1 hc1Ac1Tc1 Tav1 2 mmahzcpa Tav1Tinl 4

Similarly, the energy equation can be applied for a control volume of air in the hot zone as itpasses across ring coils 24.

3.5. Energy balance for the heater wall

Applying the energy equation for section 1 of the heater wall gives

QQrc1w1 QQrc2w1 QQrc3w1 QQrc4w1 QQrw2w1 QQrw3w1 QQrw4w1 QQcw2w1

hw1Aw1Tw1 Tinl hw1oAw1oTw1 Tinl QQrw1e 5

Similarly, the energy equation can be applied for sections 24 of the heater wall.

3.6. Evaluating the heat transfer coefficient from the heater ring coils

The angle between the flow direction and the ring coil surface is not 908as in the case of the flow

past a cylinder. Dutrich et al. (1990) showed that the average Nusselt number for flow past

coiled wires is less than that for cross flow past a single cylinder. The data of Dutrich et al.

(1990) indicate that for a helix diameter-to-pitch ratio of less than 1.0, and a Reynolds number

of more than 20, the ratio of the Nusselt number for flow past a coiled wire to that for flow past

a single cylinder (Nur) approaches 0.95 and increases as the Reynolds number increases. Dutrich

et al. (1990) also found that the wire diameter does not influence the ratio of the Nusselt number

(Nur). Extrapolating the data given by Dutrich et al. (1990), we get the following expression

for the correction factor for the Nusselt number as a function of the helix diameter to the pitch

ratio (p):

Nur 1 1:15 103 Re8:0555106 Re2p 6

Equation (6) is valid for a Reynolds number of 140 or less. For a Reynolds number of greater

than 140, Nuris assumed to be 1.0. The heat transfer coefficient of coil 1, hc1 can be found using

the Churchill-Bernsteins equation for flow over a single cylinder (Hodge, 1990) and the




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correction factor of Equation (6) so that,

NuD Nur 0:3 0:62Re

1=2D Pr

1=3

1 0:4=Pr2=31=4 1

ReD

282 000

5=8" #4=58

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