HEAT TRANSFER COEFFICIENTS FOR AIR FLOW IN PLASTIC

CORRUGATED DRAINAGE TUBES1

K. J. Sibley and G. S. V. Raghavan

Department of Agricultural Engineering, Macdonald College ofMcGill University, 21,111 Lakeshore Road, Ste.Anne de Bellevue, Quebec H9X ICO

Received 20 February 1984, accepted 10 September 1984

Sibley, K. J. and G. S. V. Raghavan. 1984.tubes. Can. Agric. Eng. 26: 177-180.

Heat transfer coefficients for air flow in plastic corrugated drainage

Forced convection heattransfer coefficients inside 10.2-cm and 15.2-cm diameter non-perforated, corrugated plasticdrainage tubingwereexperimentally determined for various flow and temperature conditionsthat wouldbe encounteredduring the useof suchtubingas an airductburiedin soil. Results indicate that thedrainagetubeheat transfercoefficientsaresimilar inmagnitude to those found insmooth pipes of thesame nominal diameter. Anempirical relationship relatingNusselt numberto Reynolds numberwas derived which can be used for prediction purposes.

The utilization of plastic, non-perforated, corrugated drainage tubing for air-duct systems is becoming popular due toits low cost and transportability. A recentapplication for the tubing has been in underground duct systems (Oppedal 1979;Cramer and Kammel 1980; Eckhoff andOkos 1980; Richard et al. 1981) in whichthe earth is used as a source for heating orcooling building ventilation air, depending on the time of year.

In order to facilitate proper design ofsuch systems, and for simulation purposes, it is necessary to know the magnitude of the forced convection heat transfercoefficients inside the tubing, as they arethe majorlimitingfactorof heat exchangebetween the air in the ducts and the surrounding soil (Eckhoff and Okos 1980).

In their studyof thermalstoragesfor agricultural purposes, Eckhoff and Okos(1980) determined convective heat transfer coefficients for drainage tubes to be12.5W/m2K and 18.05 W/m2-K for Reynolds numbers of 1.8 x 104 and 3.7 x104, respectively. Information on temperature conditions, tube diameter, andwhether the tubes were perforated or non-perforated were not given. These coefficients were reported to be in good agreement with those predicted by empiricalequations for smooth pipes when the totalsurface area of the ribbed tile was used.

Carson et al. (1980), however, statedthatcorrugated plastic drainage tubing canbe classified as very rough when theroughness height to diameter ratio is takenas corrugation height divided by nominaldiameter.

The present study was undertaken as apreliminary investigation with the following specific objectives:

'Tradenamesare used in this paper for identificationpurposes onlyanddo not implyendorsementor preference over similar products not mentioned.

(1) To experimentally determine forcedconvection heat transfer coefficients in

side 10.2- and 15.2-cm diameter drainagetubing for typical flow and temperatureconditions which would be encountered

during the use of such tubing as an air-ductburied in the soil;

(2) To compare existing smooth tubeand rough tube empirical heat transferequations with the experimental results todetermine whether the drainage tubes exhibit heat transfer characteristics similar tothose of smooth tubes or rough tubes.

THEORY

Using basic heat transfer knowledge forfully developed air flow in tubes andpipes, the total heat transfer occurring forsteady state conditions is given by:

G«ot = Ashwg (Arlmtd) =mCp(Tbi2 - rb„) (1)

where the symbols are defined in the nomenclature section.

Re-arranging terms:

>*avg = mcP (rb,2 - rb„) / as (Arlmtd) (2)

with

Arlmtd =

(Th,2 - Tbtl) I In [(Tw - rbil) / (Tw - rb,2)] (3)

Assumptions associatedwith Eqs. 1and3 are: (1) material specific heats are constant over the length of the tube; (2) theheat transfer coefficients are constantalong the length of the tube; (3) tube walltemperatures are constant.

For tube flow,

rn = pbVavg Acs (4)

and

irdV4 (5)

Substitution of Eqs. 4 and 5 into Eq. 2gives:

>*avg = pb vavg TT*cp (rb,2 - rb„)/4 As(ArImtd) (6)

CANADIAN AGRICULTURALENGINEERING, VOL. 26, NO. 2, WINTER 1984

For the corrugated tubing used in thisstudy, the physical parameters of d and Aswere taken as the average inside diameterand the total surface area including theribs.

For diameter then:

4,avg = (4,min + 4,max) 12 (7)

From geometrical considerations,AU tfrib

As = X it diimiaLx + it X ditmaxL2

Nrib

+ 2 (42,max " rfi2,™) TT/4 (8)N= 1

with

(42,max - ^min) IT /4 = L3 IT 4,avg (9)

and there being two lengths of L3 for eachrib. Equation 8 can be rewritten as:

As = Ndb TT(ditmin L, + ditmax L2 + 2 4,avg L3) (10)

Equation 6 allows the forced convectionheat transfer coefficient for a given flowand temperature situation to be experimentally determined.

The existing empirical heat transfer relations for air flow in tubes, to be compared with the experimental data, aregiven in Holman (1976) and are presentedhere in Table I.

The average heat transfer coefficient forcomparison purposes, then, was calculated by:

/lavg = NU £b,avg/4,avg (14)

MATERIALS AND METHODS

Test FacilityThree types of non-perforated, corru

gated plastic drainage tubing were used,consisting of (i) 10.2-cm diameter SDMtube; (ii) 15.2-cm diameter SDM tube; (hi)15.2-cm diameter Daymond tube.

The SDMtubes hadconcentricringcorrugations, while the Daymond tube had asinglecontinuously spiraling corrugation.Tube surface characteristics are shown in

177

TABLE I. EXISTING EMPIRICAL RELATIONS USED FOR COMPARISON WITH EXPERIMENTAL DATAt

Relation Flow conditions Type Equation Validity range Equation number

Colburn-Reynolds Fully developed,turbulent

Rough Nu= / RebjngPr JJ,

8

Re >2300

0.6 <Pr< 108(11)

Sieder-Tate Fully developed,turbulent

Smooth Nu =0.027/?eg;«vg/>rb:avg ( —V" Re >2300 (12)

Dittus-Boelter Fully developed,turbulent

Smooth Nu = 0.023 Re b°£tPr b% Re >2300 (13)

tNote: Subscriptsimply fluid propertiesto be evaluatedat the temperatures defined as follows:b,avg: Tb>avg = (7V, + rb,2) 12.f,avg: rf>avg = (7W+ rb>avg)/2.

w: 7W = inside wall surface temperature.

Fig. 1 and relevant tube dimensions arelisted in Table II.

The test section of the tube consisted of

a one meter flow development length anda two meter data monitoring length. Carson et al. (1980) determined that a 1-mlength of drainage tube was sufficient fordevelopment of turbulent flow.

Temperatures at the five locations indicated in Fig. 2 were measured by Cop-per-Constantan thermocouples connectedto a Doric Trendicator Model 410A digitalreadout recorder, accurate to 0.1°C. Thermocouples were calibrated using an icebath.

Constant wall temperatures required foreach test run were maintained by surrounding the drainage tube with fast-flowing water in a hydraulic flume as indicated in Fig. 2. Wall temperatures typical of those that would be encountered 1

m beneath ground level in the northernhemisphere were simulated by changingthe water temperature between test runs.A fan was connected to the tube througha transition section. Air flow rate was ad

justed by restricting the open area of thefan inlet. Air velocities were measured bya Thermo Systems Inc. Model 1650 hotwire anemometer accurate to 0.1 m/sec.

Average flow velocity was calculated asthe arithmetic mean of the velocities

measured at 11 points on a tube cross-section located at the beginning of the monitoring section. This method is similar tothe Annular Probe method used by Carsonet al. (1980).

Procedure

A tube under investigation was placedin the hydraulic flume and anchored securely. The fan was switched on and allof the flow velocities were set and measured. The anemometer probe access holewas sealed with waterproof drainage tapeand the flume was filled with water.

Air temperatures were manually recorded for each of the predetermined flowvelocities while the tube wall was main-

t / t'

i^-y-^̂

»-ML,-7slope

178

di,max

i, mm

Figure 1. Drainagetube corrugation characteristic lengths.

TABLE II. DRAINAGE TUBE GEOMETRIC

CHARACTERISTICS

tained at a constant temperature by theflowing water. Wall temperatures werechecked with three thermocouples alongthe data monitoring section of the tube.

The maximum end-to-end wall temperature variation recorded throughout thetests was 0.2°C.

The temperature of the water was thenchanged and air temperature measurements were taken again at each flow velocity. This procedure was repeated untila sufficient number of wall temperature-

Dimension

Daymond 6(mm)

SDM 6

(mm)SDM 4

(mm)

U 16.0 8.0 8.0

L2 8.0 5.0 4.0

LJ 10.6 10.1 6.0

U 10.0 10.0 6.0

Aslope 3.5 1.5 0.5

"i.max 152.0 152.0 102.0

4*» 172.0 172.0 114.0

tCalculated value.

DRAIN/\GE TUBE

AIR

INLET

HYDRAULIC

FLUME

WATER

OUTLET lm

THERMOCOUPLES

2m

FLOW DATA

DEVELOPMENT MONITORING

SECTION SECTION

Figure 2. Schematic diagram of test facility.

AIR OUTLET

t

VWATER

INLET

CANADIAN AGRICULTURAL ENGINEERING, VOL. 26, NO. 2, WINTER 1984

flow velocity-inlet air temperature combinations were tested. Flow velocity andwall temperature ranges were 2.2-9.6 m/sec and 2.0-15.0°C, respectively, whileinlet air bulk temperatures used were between 7.9 and 23.1°C.

The experimental data were analyzedusinga FORTRAN programwrittenfor anAmdahl-V7 digital computer. One set ofcalculations was performed by desk calculator to ensure that the program wasworking properly. Statistical analyseswere performed using Statistical AnalysisSystems (SAS 1982) linear regressionprocedures.

RESULTS AND DISCUSSIONExperimental heat transfer coefficients

were obtained for Reynolds numbersrangingbetween 1.7 x Wand 8.6 x 104.Analysisof the results indicated a high dependenceof the experimentalheat transfercoefficient, /iexp, on flow conditions and alow dependence on tube diameter andtemperature conditions. Further investigation of the experimental data indicatedthat hexp increased with an increase in thedifference between tube wall temperatureand air bulk temperature. Some typical results for the SDM4 tubing are presented in

Table III.

Regression analysis was performed onthe experimental heat transfer coefficientdata using the following classical model:

Nu = CRemPr> (15)

The regression procedures used are outlined in Holman (1976).

Since only one fluid (air) was used inthese experiments, the Prandtl number wasconstant at 0.71 over the range of temperature conditions tested and its effect on the

model could not be determined precisely.Classical heat transfer work suggests avalue of 1/3 for the constant n, thereforethe regression analyses were performedwith n = 0.3.

The models resulting from the regression analyses are presented in Table IV.The data were also pooled to yield theoverall heat transfer model of Eq. 19 inTable IV. A plot of Eq. 19 along with theexperimental data is shown in Fig. 3.Equations 16 and 19 were found to be acceptable models since Holman (1976)states that a final correlation using Eq. 15usually represents the experimental data towithin 25%. When combined with the cor

relation coefficient, the high significancelevels show that Eqs. 17 and 18 are also

TABLE IH. TYPICAL DATA AND RESULTS FOR THE SDM 4 TUBING

vv avg TbA Tb,2 rw hexp /*ST ^CR ^DB(m/sec) (°C) (°C) (°C) Re (W/m2-K) (W/m2-K) (W/m2-K) (W/m2-K)

2.5 19.6 17.4 13.4 17103 9.8 13.9 28.0 12.0

4.8 18.7 17.3 13.4 33318 13.3 23.7 54.4 20.4

9.6 19.1 17.8 13.6 66572 23.4 41.3 108.9 35.5

4.8 19.2 17.7 13.6 33182 13.5 23.7 54.3 20.3

2.5 19.0 14.1 6.4 17409 11.0 14.1 28.2 12.1

4.8 19.0 15.5 6.6 33546 14.4 23.9 54.5 20.4

9.6 18.1 15.8 7.1 67486 20.4 41.8 109.5 35.7

2.5 18.6 12.7 3.9 17552 11.5 14.2 28.3 12.1

2.5 19.0 12.8 4.0 17512 12.0 14.2 28.2 12.1

4.8 17.5 14.0 4.1 34008 13.2 24.1 54.8 20.6

9.6 17.7 14.1 4.1 68135 26.9 42.0 109.8 35.9

9.6 18.9 15.6 4.4 67302 22.5 41.8 109.3 35.7

8.7 7.9 7.1 4.2 66548 19.9 39.9 102.4 34.3

8.7 7.9 7.1 4.3 66548 20.5 39.9 102.4 34.3

2.8 12.6 9.8 4.4 20724 10.8 15.9 32.6 13.6

2.8 12.9 10.0 4.5 20676 11.0 15.9 32.5 13.6

2.8 13.8 10.4 5.4 20554 13.4 15.9 32.5 13.6

2.8 13.5 10.5 6.0 20572 13.2 15.9 32.5 13.6

2.8 13.7 11.0 7.2 20506 13.9 15.8 32.4 13.6

2.8 13.5 11.6 8.5 20469 12.3 15.8 32.4 13.6

2.8 16.3 13.8 9.6 20006 11.9 15.6 32.1 13.4

2.8 15.1 12.8 9.7 20208 14.2 15.7 32.3 13.5

TABLE IV,. RESULTS OF CORRELATIONS USING EQ. 15

Data Correlation Significance Equationset Empirical equation coefficient (r) level number

SDM 4 Nu = 0.463 Re° 485 pjQ.3 0.93 0.01 (16)

Daymond 6i Nu = 0.023 Re0 802/>f0.3 0.68 0.05 (17)

SDM 6 Nu = 1.93 Re° 360 pf4)3 0.60 0.01 (18)

Pooled

data Nu = 0.230 Re° 562p^O.3 0.73 0.01 (19)

CANADIAN AGRICULTURAL ENGINEERING, VOL. 26, NO. 2, WINTER 1984

adequate. Low correlationcoefficients aredue to air velocity measurement inaccuracies near the wall surface due to eddymovements in the large corrugationswhich randomly affected the calculationof the average flow velocity. Since theseinaccuracies were unquantifiable and subject to random variation, an estimate oferror on the calculation of hext could notbe performed. Future work should use amore accurate flow velocity measurementtechnique.

To meet the second objective of thisstudy, the experimental results were compared to the existing empirical heat transfer equations. Comparisons were based onthe magnitude of the average absolute deviation (AAD) between the pooled experimental data and points calculated by eachof the existing empirical equations for thesame temperature and flow conditions.The average absolute deviation was calculated by:

V^emp "exp/

AAD =(20)

where n = the number of experimentaldata points. The Dittus-Boelter relationwas the best predictor of the experimentalresults with an AAD of 5.98 W/m2K. The

Sieder-Tate relation was second best with

an AAD of 7.63 W/m2-K while the

Colburn-Reynolds analogy had an AADof 52.10 W/m2K. Deviation between the

experimental data and the predicted pointsincreased as Reynolds number increased.

From these comparisons it is seen thatforced convection heat transfer coeffi

cients for non-perforated plastic drainagetubes are similar in magnitude to those forsmooth plastic tubing of equal nominal diameter but unequal surface area.

Further evidence of this conclusion is

gained by the fact that when friction factors for smooth plastic pipe were used inthe Colburn-Reynolds analogy instead ofthose reported by Carson et al. (1980) fordrainage tubing, the empirical heat transfer coefficient predictions agree with theexperimental data almost as well as theDittus-Boelter relation does.

It is also interesting to note that modelof Eq. 17 in Table IV is exactly the sameas the Dittus-Boelter relation.

Because of the regular corrugationspresent in the direction of flow, the selection of the proper diameter to be used forthe calculation of the air mass flow rates,and hence, hexp, was in question. Usingmaximum inside diameter, calculationsmight yield higher mass flow rates thanthose physically possible, while calculations using minimum inside diameter

179

I0V^"^^^^""i^^r^H^TH^r • i i i i i i

EXPERIMENTAL

DITTUS-BOELTER

•o

* I02

2 -

i i i i i i J 1—L.

10 10'

Red

10

Figure 3. Nusselt number versus Reynolds number for experimental results and the Dittus-Boelter relation.

might yield lower mass flow rates thanthose which physically exist. Therefore,an average inside diameter was selected asgiven by Eq. 7.

To justify this assumption, a comparison of paired observations between the experimental results and the Dittus-Boelterrelation based on maximum, minimumand average inside diameter was made.Calculations based on average inside diameter gave the closest agreement between the experimental results and theDittus-Boelter relation.

CONCLUSIONS

(1) The drainage tubes tested in thisstudy have inside convective heat transfercoefficients similar in magnitude to thosefound in smooth plastic pipes of the samenominal diameter but smaller surface area.

(2) The Dittus-Boelter empirical equation for fully developed turbulent flow insmooth tubes represents the experimentalresults of this study with an average absolute deviation of 5.98 W/m2-K over therange of flow and temperature conditionstested in this study.

(3) The average inside diameter and total surface area including the corrugationarea should be used for calculation pur

poses.

(4) The empirical relationship of

Nu = 0.230 Re0-56 Pr°3

Re > 2300; Pr = 0.71

(21)

can be used to predict forced convectionheat transfer coefficients occurring in10.2-cm and 15.2-cm diameter non-

perforated, corrugated, plastic drainagetubing for the conditions of:

2.2 m/sec *£ Vavg ^ 9.6 m/sec

2.0°C ^ Tw ^ 15.0°C

7.9°C^rb,1^23.1°C

NOMENCLATURE

A = area (m2)Cp = specific heat at constant pressure(J/kg-K)d = diameter (m)/ = friction factorh = convective heat transfer coefficient

(Wm2-K)K = degrees Kelvink = thermal conductivity (W/m-K)Lx = corrugation width (m)L2 = corrugation spacing (m)L3 = actual length of corrugation height(m)

L4 =(m)

^slope(m)

m =

W =

Nu =

Pr =

Q =Re =

T =

V =

W =

A =

P =

^ =

apparent length of corrugation height

= length of corrugation slope width

mass flow rate (kg/sec)number

= Nusselt number

= Prandtl number

heat flux (W)= Reynolds numbertemperature (K)velocity (m/sec)watt (J/sec)

difference

density (kg/m3)dynamic viscosity (kg/m-sec)

Subscriptsavg = average

b,l = bulk, inletb,2 = bulk, outletb,avg = bulk, averageCR = Colburn-Reynold relationcs = cross sectional

DB = Dittus-Boelter relation

exp = experimentalemp = empiricalf = film

i = inside

lmtd = log mean temperature differencemin = minimum

max = maximum

o = outside

r = rib

s = surface

ST = Sieder-Tate relation

tot = total

w = wall (inside surface)

REFERENCES

CARSON, W. M., K. C. WATTS, and F.DESIR. 1980. Design data for air flow inplastic corrugated drainage pipes. Trans.ASAE (Am. Soc. Agric. Eng.) 23(2): 409-418.

CRAMER, C. O. and D. W. KAMMEL.1980. Underground air inlets for farrowinghouse cooling — a case study. ASAE PaperNo. 80-4556, ASAE, St. Joseph, Mich.49085.

ECKHOFF, S. R. and M. R. OKOS. 1980.Thermal storage comparison and design forrock, saturated soil, and sodium sulfate de-cahydrate for agricultural applications.Trans. ASAE (Am. Soc. Agric. Eng.) 23(3):722-728.

HOLMAN, J. P. 1976. Heat transfer.McGraw-Hill Book Co., New York. 528 pp.

OPPEDAL, A. 1979. Earth energy heats, coolshog buildings from one source. Farm Building News, January-February, pp. 124—125.

RICHARD, P., K. J. SIBLEY, and G. S. V.RAGHAVAN. 1981. Soil as a heat source/

sink for energy conservation in a greenhouse. ASAE Paper No. NAR-81-231,ASAE, St. Joseph, Mich. 49085.

SAS. 1982. SAS user's guide: Statistics. SASInstitute Inc., Cary, North Carolina. 584 p.

180 CANADIAN AGRICULTURAL ENGINEERING, VOL. 26, NO. 2, WINTER 1984