A new method to determine the heat transfer coefficient of refrigerated vehicles

A new method to determi the heat transfer c refrigerated vehicles

nt of

Guimei Zhang* and Guichu Sun Department of Transportation, Northern Jiaotong University, Beijing 100044, PR China

Jiankun Li Sifang Rolling Stock Institute, 12 Jiaxin Road, Qingdao 266031, PR China Received 19 November 1992; revised 7 February 1994

A new method is proposed for rapid determination of the overall heat transfer coefficient K of refrigerated and insulated vehicles. By calculating the temperature distribution in the insulation walt using the finite difference method, the following parameters were obtained: the heat inertness coefficient and the conversion ratio. A new formula for calculating the K-value is based on these parameters. The principle and experiments are discussed and analysed in detail in this paper. The results show that the time required by the new method is less than that required by other rapid methods, while the precision is much higher. Compared with the steady-state method, the error is within a limit of 5%. This new method is particularly suited to quality control testing of vehicles in production runs. (Keywords: refrigerated transport; wall; insulation; g eoeicient; simulation; calculation)

Nouvelle mrthode pour d&erminer le coefficient de transfert de chaleur des vrhicules frigorifiques On propose.une nouvelle mbthode pour dbterminer rapidement le coefficient de transfert de chaleur 9lobal K des vbhicules rdfrig&bs et isothermes. En calculant la distribution de temp&ature dans le mur isolant, en utilisant la mbthode des diff&ences finies, on a obtenu les paramOtres suivants: un coefficient d'inertie h la chaleur et un taux de conversion. Une nouvelle formule pour calculer la valeur K se fonde sur ces param&res. On examine en detail le principe et les expbriences effectubes. Les rbsultats montrent que cette nouvelle mbthode est d'une utilisation plus lonoue que les autres, mais qu'elle est plus prbcise. Par rapport h la mkthode en rboime stable, le pourcentage d'erreur est de 5%. Cette nouvelle mdthode eonvient particuli&ement bien pour les essais sur le contrrle de la qualitb des vbhicules, dans les usines de production.

(Mots clrs: transport frigorifique; paroi; isolation; coefficient K; simulation; calcul)

The production supervision of refrigerated and insulated vehicles is performed in various ways. On body production lines, a sample of about 1% of 'prototypes' is tested in the laboratory; 3 days are needed for this process. About 1% of samples are also tested in the workshop, using a rapid method. Several rapid methods are available for determining the K-value t-t 1; however, the precision of these methods is unsatisfactory, because they neglect the unsteady temperature distribution in the insulating material. By calculating the temperature distribution, we have obtained some parameters that may be used to set up a new formula for obtaining improved test results in less time.

Principles

Putz's method a. Putz, using the instantaneous heat transfer coefficient K, = Q/AO, hypothesizes Ks = a + be-~ + ce-°t~; when z--* oo, K , = a . Using Gauss' least-square method, he obtains A ( B E - CC) - G(DE - CF) + H ( C D - BF) a =

n(BE - CC) - D(DE - CF) + F(CD - BF)

where A = [ K i ] , B=[e-2~], C = [ e - L I ~ ] , D = [ e - ~ ] , E=[e-0-2~], f=[e-OA~], G = [ K i e - ' ] , H=[Kie-°-l~], and n is the number of measured points. [e -~] is the sum of all e-~; the rest of the bracketed terms may be derived analogously. Kriha's method 2. Kriha determines dO/dz of two points in the temperature-time curve and obtains

Unsteady-state methods

Unsteady-state methods are based on the equation Q = K A O + W dO/dz, from which various formulae for calculating the K-value have been derived. W= *Present address: Federal Research Centre for Nutrition, Institute of Process Engineering, Engesserstr. 20, 76131 Karlsruhe, Germany 0140- 7007/94/080516-08

© 1994 Butterworth-Heinemann Ltd and IIR 516 Int. J. Refrig. 1994 Volume 17 Number 8

A(Ks 1 - K~2) _

01 \ d z / 1

O2\dz/2

Heat transfer coefficient of refrigerated vehicles: G. Zhang et al.

Nomenclature Heat transfer area (m2) Specific heat (J k g - t K - t ) Overall heat transfer coefficient(W m - 2 K - 1) Heat transfer coefficient in steady state (Win -2 K -1) Heat transfer coefficient in unsteady state (Win -2 K -1) Heat flow rate (W) Temperature of vehicle body (K) Temperature of node i at time z (K) Temperature of node i at time z + Az (K) External air temperature (K) Internal air temperature (K) Outer surface temperature in para-steady state (K) Outer surface temperature in unsteady state (K) Temperature difference between outer surface and external air (K) Water equivalent of vehicle body (J K-1) Spatial mesh size (m)

A C

K K~ Ki

Q T

T, T[ +~ te ti tw¢

t~¢ Atw¢ W AX

Levy's method 3. Levy infers dS/dx=(Q/WX1-8/Sv). According to the internal temperature--time curve, the ratio of (dS/dz)x to (d8/dz)2 is obtained from the following formula:

Greek letters

ae ~i fl

Outer heat transfer coefficient (W m - 2 K -1) Inner heat transfer coefficient (W m-2 K-x) Conversion ratio of temperature difference between wall surface and ambient air in unsteady state to difference in para-steady state; fl = (t'= - t,)/(t,,= - t=) Thickness of insulation layer (m) Temperature difference between internal and external air (K) Temperature difference between internal and external air in steady-state conditions (K) Thermal conductivity (W m-1 K-1) Heat inertness coefficient of vehicle body =dT(z)/dti(,) Density (kg m-3) Time (s) Time interval (s)

5 0 8p 2 p z Az

where 81, 82 and 83 are the temperature differences at times vt, z2 and z3 respectively. Therefore

K= Q

8pA

(d8/dz) x (d8/d~)2

Potynski' s method s

Since

8p=

R = 8p-8X 8p-82

82(81/82- R) = const 1- R

Therefore

Q

g = -SpA

Meffert's method 4 82, 3 -- 81.2(83 - - 82)/(82 -- 81) 8p =

281 - ( 8 0 + 82)

where 80, 81 and 82 are the temperature differences at times %, zl and z2 respectively. Then

where 81 and 82 are the temperature differences at times zx and ~2 respectively, then 8p=

012-0o02

1 -- (83 -- 8 2 ) f l 8 2 - - 81)

K=--

Q 0.A

A new method for determining the K-value Principles of detection. The heat transfer coefficient K is determined by means of internal heating of the vehicle. In the testing period, the heat flow should be constant (or nearly constant), and the outside temperature should also be more or less constant (when there is little fluctuation, the average value may be used). During the heating period, the heat balance equation is as follows: Q dz = ~eAAtwe dr + ~ W dti for

where

~=AAt,,= = flKA(t i - t=)

81,2 - - T2 --T1

82,3

(1)

1

8 d'c t

1:3 8 dr

T3 --'L'2 Jz2

(2)

Substituting Equation (2) into Equation (1): dz dt i W = Q + f l K A ( t , - ti)

Rev. Int. Froid 1994 Volume 17 Numtro 8

(3)

517

Heat transfer coefficient of refrigerated vehicles. G. Zhang et al. Integrating Equation (3) from z~ to 2"2 and z 2 to r3, respectively: fll,2 K A ( ' c 2 - - 2-1) = l n 0 2 - - Op/fll,Z ~1.2 w

(4)

01 - - 0 p / i l l , 2

a stepped line (Figure 1) and separate the insulation wall into n spatial meshes (Figure 2). When the main insulation layer is made of a single material, the heat conduction equations can be expressed by the implicit finite-difference model as follows~2: ] +2f

In 03 - 0p//¢2,3 02 - 0p/f12,3

f12'3K A('c3 - "c2) -

~2,3 W

Bil +2J

B~2-2!

-/

l+2f

(5)

/

Combining Equations (4) and (5) and letting z 2 - r t = T 3 --T21

J

I+2f - 2[

O,fl,,E-Op/

= \02--~2,3----~p,/

m

(6)

~t

m

M

0

T2 I

T~÷a~

(7)

+ i

0

/,o/

U'Bieli

where Sil

Temperature (K)

m

2fBute

where fiLE, fl2,3, ~1,2, ~2,3 are the mean values of fl and ~ respectively in the periods z t - z z and z 2 - z 3 ; 0~, 02, 03 are the temperature differences between internal and external air at times z~, r 2, and z 3 respectively; and 0p = Q / K A . Determination of parameters. The value of ~ is determined as follows. Using the finite-difference method, we obtain the temperature distribution in the insulated layer. For this purpose, we simplify the temperature-time curve into

~

--j 1 + 2f + 2JBi2

AXo~e -

AX0q Bi2 = - -

2

aAz f-

AX:

a_w__

pc

Time (s) Figure 1 Simplificationof the temperature-time curve into a stepped fine Figure 1 Simplification de la courbe temps-tempdrature par une illustration en ' escalier'

i-1

i÷1

n-1

n

In the same way, we obtain the heat conduction equations for an insulation layer consisting of two or more layers of different materials. Solving Equation (7), we o b t a i n the temperature distribution in the insulated layer at any time. F o r example, at time z + iAz, the node temperatures will be T] +ia~, T~ +~A*,.... T~ +v'`, and the temperature of the layer will be T r + ia~ - T~l+ iar-t- T~ +ia, + ... + T~, +ia~

Then tl

t

- Ax

AX

I

T~+(i+ 1)a~

O(i

T~+iA~

t~" + ( 1 + i)A~ - - t~ - i + iA~

The mean heat inertness coefficient of the vehicle body from z I to z2 and r2 to z3 respectively is

~1,2

-

(8)

i=,

m Figure 2 Definition sketch for finite-difference mesh to model a transient one-dimensional heat-conduction analysis Figure 2 Schdma d'application de la mbthode des diffdrences finies, d une paroi isolante, pour analyse de la conductivitd thermique en r~gime transitoire

518

Int. J. Refrig. 1994 Volume 17 Number 8

2m

~a3- j='+' m

(9)

Heat transfer coefficient of refrigerated vehicles: G. Zhang et al.

where m=-

From r1 to ~~ and r2 to z3, the mean value of /I is

z2-71

(10)

AZ

(16)

The value of /I is found as follows. By calculating, we find that, in the temperature-rising period, the temperature distribution in the insulation wall at any time is not a straight line, but a curve. This means that there is not a ‘para-steady state’ but an unsteady state in this period (Figure 3).

Neglecting the influence of the heat bridge in the layer, the heat balance equation is as follows: %A(L - t,) = BK’A(ti - t,)

(17) where

(11)

In the para-steady obtain

state fi= 1. From Equation (11) we

WWW- te)= K’A(ti

- te)

Determination of the overall heat transfer coejficient K.

Combining Equations (6) (8), (9), (16) and (17), we obtain:

(12)

since

5

1

K’=

“$

(13)

1 +’ 0

a,

li

i=l

<1,2 =

m

ai

From Equations (11)-(13), we obtain /I in the unsteady state:

(18)

5

(14) p1,2 =

Pi

EL

m

At time T+Az, z+2Az ,..., T+nAz, let ti be til, and outer surface temperature be tael, ti2,**., tin, t:,, 9. * *9t&e, respectively: then at time z + jAz

(15) Solving Equations (18), we find 8,, which is the temperature difference in the steady state. In order to reduce the influence of individual measurements on precision, it is appropriate to select more groups of 01, 8, and 8,, according to Equation (18); then we obtain eP as ePl, e,,, . . . , epl respectively. So

(j,-

i i=1

epi

(19)

1

Finally, the overall calculated from

heat

transfer

coefficient

K=$

K is

(20)

P Insulation layer -

pararteady-*tat0

+--

Testing

unrteady-rtate

Figure 3

Temperature distribution field in the insulated layer during the heating process Figure 3

Champ de distribution de la temp&ature isolke au tours du processus de chaufage

dam me couche

Results obtained by the new method

Using the above method and the steady-state method, we performed experiments in a wagon type B7. The insulation materials of the B7 wagon are polyurethane

Rev. Int. Froid 1994 Volume 17 Numbro 8

519

Heat transfer coefficient of refrigerated vehicles." G. Zhang et al. that of Putz, Kriha, Levy, Meffert and Potynski, we used the same test data to calculate the K-value by each method. The results of the different methods for a test period of 11 h are shown in Table 1.

for the floor, polystyrene for the walls and polyethylene for the roof. The average thickness of the material is 0.198 m, the average thermal conductivity is 0.041 84 W m - 1 K - 1 , the average density is 30.113 kg m -3, the average specific heat is 1.913 kJ kg -1 K -1 and the heat transfer area is 206.73 m 2. In accordance with Annex 1, Appendix 2 of the ATP agreement 13 we obtained K ~ = 0 . 4 0 0 W m -2 K -1 in steady-state conditions. (In our steady-state conditions the variation of the inside and outside temperatures was +0.15 K. The average heat dissipation over the steady state of 12 h was used in the calculation of K~.) Based on current proposed amendments to the text of the ATP agreement 14, the error of K~ is within 5%. The temperature increase is shown in Figure 4. The K-value calculated by the new method is shown in Fieure 5, and the error is shown in Figure 6. This shows that within 11 h of testing, the error of the instantaneous K-value is always lower than 5% compared with K o~, if the temperature difference between the inside and outside of the vehicle, 01, is taken from the time of onset of heat conduction to the outside of the vehicle, and if the time intervals between detecting points 0~ and 02, and 02 and 03 exceed 200 min. From Equations (19) and (20) we obtain K =0.3987 W m--2 K - ~. Compared with K~ = 0.400 W m - 2 K - 1 the error is 0.33 %, and hence the precision is satisfactory. To compare the precision of the new method with

Experimental results using an insulation box The box is made of three layers o f different materials; details are listed in Table 2. The heat transfer area is K-value ( W / m e KI 0,43 0,42' 0,41 0,4 0,39 0,38 0,371 680

elO

e20

SaO

S40

SSO

eeo

eTo

Figure 5

The K-value of wagon B7 within the test period by the new

method Figure 5 Valeur K du wagon BT, au cours de la p~riode expbrimentale, dbfinie par la nouvelle mbthode Error of K-value (%) 6,5

296!

5

............................................................................................................................

4,5

i

292

SO0

Time (min.)

Temperature (K)

2"i

SgO

................................................................................................................................

4

2 9 0 ......................................................................................................................................... 288

2a6i

, -~-4

284 i

2,6

~

2

........................................

1,5

2 8 2 ..................................................................................................................................... 280 0

L

*

J

i~

1

2

3

4

5

L

;

i

J

i

6

7

8

9

10

11

12

~

O'

............

sao

690

e00

eto

,i e20

eao

...........i122 ........... e40

e60

eeo

670

Time(min.)

external air temp.

Figure 4 Temperature-rising process in wagon B7 Figure 4

.........................................................................

0.6

Time (h) temperature-rising

,

1

Figure 6 The error of the K-value of wagon B7 Figure 6

Processus d'blbvation de la tempbrature clans le wagon B7

Erreur de la valeur K du wagon B7

Table 1 Calculation results for wagon B7 with different rapid methods Tableau 1 Rbsultats de calcul pour le wagon B7, avec diffbrentes mbthodes rapides Putz's method

Kriha's method

Meffert's method

Potynski's method

New method

28.03-54.33" 44.27 °

2.24-30.24 6.50

11.62-19.74 16.00

11.84-19.89 16.25

0.11,5.20 0.33

Error range (%) Error of mean K (%)

"For Putz's method, the test time of 11 h is not a sufficient condition (four readings, 3 h interval between detecting points after reaching para-steady state of temperature distribution), which leads to significant error. If the time is prolonged to 15 h, the error will be 2.35%, as shown in Table 3

Table 2 Composition of the insulation box Tableau 2

Composition de la bofte isolante Thickness

Material

Outer layer of plywood Asphalt paper and cork Inner layer of wood

520

Int. J. R e f r i g . 1 9 9 4

Volume

(m)

Thermal conductivity (W m -1 K -1)

Specific heat (kJ kg -1 K -1)

(kg m -3)

0.006 0.053 0.023

0,0167 0,0465 0.0167

Z5116 2.0934 2.5121

600 250 250

17 Number

8

Density

Heat transfer coefficient of refrigerated vehicles: G. Zhang 4.71 m 2. In accordance with Annex 1, Appendix 2 of the ATP agreement la we obtained K ® : 0 . 9 6 3 0 W m - 2 K - 1 in steady-state conditions. (In our steady-state conditions the variation of the inside and outside temperatures was + 0.15 K. The average heat dissipation over the steady state of 12 h was used in the K~ calculation.) Based on current proposed amendments to the text of the ATP agreement 1", the error of K oois within 5%. The temperature increase is shown in Figure 7. The K-value obtained by the new method is shown in Figure 8, and the error is shown in Fioure 9. According to Equations (19) and (20), K is 0.9594 W m -2 K -1. This shows that the new method reduces the test time to 8 h; the error is 0.39% compared with Koo. Temperature (K)

330

926 322 i 318 914 310

900 902 298 294

.....i"-i -i-i t ( 0

1

2

']"-i' T--T "T-i-.="--!-'Y "i-T--:- "i-.~-'i '-~--" "i-'T~ "',~ .~.... I t t I I t t i { i I I 3

4

5

6

7

8

9

10

11

12

13

14

~

For comparison, we also calculated the K-value by the other unsteady-state methods. The results are listed in Table 3. Discussion

The new method is more precise than other unsteadystate methods because it contains some modifications to the theoretical basis of the previous methods. Previous rapid test methods have assumed that the temperature distribution in the insulation layer is para-steady-state in the temperature-rising period. This implies that 'the distribution is a straight line (Figure 3). The new method is based on the fact that the distribution at any time in this period is a curve. It therefore conforms to reality, requires less test time and is more precise than other unsteady-state methods. The K-value obtained by the new method is an overall value, based on experimental and reference values. In calculating, the inside and outside temperatures should be input. The thickness, thermal conductivity, density and specific heat of the insulation material are also required. As there are three kinds of insulation material in wagon B7 (as stated earlier), the average values of the above-mentioned physical properties can be used. Mean values are obtained from the following formulae:

16

21 + A2)~2 + A3 )~3 2 = Ax 6--] 62 63(~;

Time (h) Internal air temp.

et al.

external air temp.

~__ A161 + A262 + A363

AI + A 2 + A 3

Figure 7 Tg~mperature-rising process in insulation box Figure 7 Processusd'~l~vationde la temperaturedans la bo~teisolante

Ax + A 2 + A 3

(21) p-

Axp161 + A2P262 + A3P363

(22)

A t 6 1 + A2J2-I- A363 1

K-wdue (W/me K)

0,99

4

................................................................................................................................................................................................

0,99

916

................................................................................................................................................................................................

Error of K-value (%) ....................................................................................................................................................................................................

o ., ,.

0,93

...........................................................................................................................................................................................

0,92

............................................................................................................................................................................................

0,91 I 0,9

...........................................................................................................................................................................................

i

i

i

i

;

I

i

I

400

410

420

430

440

450

460

470

480

Time (rain.)

0,4 0

Figure 8 K-valueof the insulationbox within the test period by the new method Figure 8 Valeur K de la botte isolante, au cours de la p~riode expkrimentale, dkfiniepar la nouvelle mkthode

400

I

I

I

1

I

I

I

410

420

490

440

460

460

470

490

Time (rain.) Figure 9 Error of the K-value of the insulationbox

Figure 9 Erreurde la valeur K dana la botte isolante

Table 3 Calculated results for insulation box using different methods Tableau 3 R$sultats calculuspour la bofte isolante en utilisant diffJrentes m$thodes

Required time (h)

Error (%) Within 8 h test time Within the time required

Putz's method

Kriha's method

Meffert's method

Potynski's method

New method

15

12

13

13

8

49.12-120.12°

0.49-17.4

7.51-16.13

6.57-13.69

0.30-3.71

2.35

3.31

4.9

4.1

0.39

°See footnote to Table 1.

Rev. Int. Froid 1 9 9 4 V o l u m e 17 N u m 6 r o 8

521

Heat transfer coefficient of refrigerated vehicles: G. Zhang et al. c-

A l c l p t 6 1 + A2c2#2t~2 + A3C3P363

(23)

A 1Plfi1 + A2P2fi 2 + A3P363

where 2, 6, p, c and A are as defined in the Nomenclature, and subscripts 1, 2 and 3 refer to the three types of insulation material. The data book indicates the range of values. For example, the thermal conductivity of polystyrene is 0.04074).0465 W m - ~ K - ~. According to the above three formulae, the range of the average thermal conductivity is 0.0374-0.0462 W m -~ K - ~ ; the mean value is 0.0418 W m -~ K -~. The range of average density is 26.19234.034 kg m - 3 ; the mean value is 30.113 kg m -3. The range of average specific heat is 1.821-2.005 kJ kg-1 K - ~ ; the mean value is 1.913 kJ kg-~ K - ~ . Using these mean values, the K-value is 0.3987 W m - 2 K - 1, and its error is 0.33%. It is possible to use mean values of )~, p and c because, in Equation (18), these variables play a very small part in determining the overall K-value, and hence their accuracy has little influence on the result. Repeated calculations (Table 4) have shown that, as long as the input data are within the average range, the error of the K-value obtained by the new method is always much lower than 5 % compared with the result from steady-state methods. As stated earlier, the error of K ~ is within 5%. Hence the error of the K-value obtained by the new method is within 10%. As there are three layers of different insulation materials in the insulation box, the K-value was calculated by using the temperature field determined by means of the heat conduction equations considering three layers of different materials. In our experiments, there are more heat bridges in wagon B7 than in the insulation box, but the error of the K-value obtained by the new method is 0.39% and 0.33% respectively compared with K ~ . This shows that, although actual vehicles may have more or fewer heat bridges, this method is still applicable. The test time for wagon B7 is longer than that for an insulation box, because its insulation characteristics are better. By calculating the temperature distribution in the insulation layer of wagon B7, we find that over 3 h after the start of the test, the outer surface temperature of the vehicle is slightly higher than that of the external air. Hence from this time on some heat is being transferred to the outside. The experiment is stopped after another 8h. In addition to the insulation material in the vehicle, there are metal sheets 1 m m thick outside the wall and 3 m m thick on the floor. The different composition

influences the K-value and is taken into account by using heat conduction e q u a t i o n s considering three layers of different materials. However, as the thermal conductivity of metal is very high, its influence on the K-value may be neglected. In the process of the experiment, we used a Fluke 2200B data logger to measure the air temperatures and a PC for data processing. Extra equipment is not required. With an I B M - P C XT and special software the calculation time is about 1 h. Although this new method requires more computing power, the expense in this respect is much less than for an extended test using the steady-state method.

Conclusions

1. The test time required by this new method is less than that required by other unsteady-state methods and the precision is higher. 2. The practical conditions of this new method are as follows. F r o m the time of onset of heat transfer to the ambient air until the end of the experiment, 8 h are needed. The time interval between detecting points should be /> 200 rain. A K-value can be determined for every three points. When K ~ is 0.400 W m - 2 K - 1 , the total test time is 11 h: the lower the K-value, the longer the test time. 3. The error of this new method is much lower than 5%, as compared with K ~ . In our two tested samples, the error was 0.33% and 0.39% respectively. 4. Using this new method, t h e test conditions m a y be changed appropriately. The variation of temperature in the chamber should be within + 1.5 K. 5. This new method is therefore suitable both for test stations and for workshops for determining the overall K-value.

References 1

2

3 4

Table 4 Calculated results using different thermal conductivities, densities and specific heat for wagon B7 Tableau 4 Rbsuhats calculbs en utilisant dif[~rentes conductivitks

5

thermiques, les densit~s et la chaleur massique pour le wagon B7

Thermal conductivity, 2 ( W m - 1 K -1) 0.0374 0.0462 0.04183 0.04183 0.0462

522

Density, p

K

(kgm -3)

Specific heat, c (Jkg - 1 K -l)

26.192 34.034 34.034 26.192 30.113

1.821 2.005 1.821 2.005 1.913

0.3961 0.3922 0.3888 0.4043 0.4043

Error

6

(%)

Int. J. Refrig. 1994 Volume 17 Number 8

0.98 1.96 2.79 1.08 1.08

7

Putz, L. Methode zur Berechnung des station~iren Endwertes

der W~irmedurchgangszahl von isolierten Bef'6rderungsmitteln IA method for the calculation of the stationary coefficient of heat transmission of insulated vehictesl Kiiltechnik (1964) 16 312-314 Kriha,J. Instation~ire Zust~inde bei Messungen der W/irmedurchganszahl an Kiihlfahrzeugen und Beh/iltern. deren Auswirkung und Berechnung (Unsteady states during the measurement of the overall coefficient of heat transfer on refrigerated vehicles and containers, the effectsand calculations} Ki~ltetechnik (1965) 17 239-243 Levy, F. L. A quick method for testing the overall heat transmissioncoefficientby dispensingliquid nitrogen,Unpublished paper. London I1963) Melfert,H. F. TE Transient thermal testing of insulated vehicles: methods and results Bull IIF-IIR (1966) 5i~53 Potynski,J. L'exactitude de la d~termination du coefficientdes pertes thermiques Ken regime permanent et en regime variable (Accuracy of determination of the heat transfer coefficientK in steady-state and variable conditions) X l l l Int Congr of Refrigeration Washington (197t) 4 383-391 Hornl~rg,H., Koll~m~llet'g~, H., Sehramm. K.-H., Kiphard, W. Auswerteverfahren zur Bestimmung des K-wertes yon Kiihlwagen nach sieben-bis achtstiindiger MeBdauer(Evaluation method for the determination of K of refrigerated rail cars after seven--eight hours) Eisenbahntechnische Rundschau (1966) 11 418-424 Patz, L. Das Temperaturfeld fiir einen isolierten Kasten bei stetiger Temperaturver/inderung ~m inneren desselben (The temperature field in an isolated box with continual inside temperature changes) Ki~Itetechnik (1968/10 314-319

Heat transfer coefficient of refrigerated vehicles: G. Zhang et al. 8 9 10

Lorentzen, G. Accelerated heat leakage testing of insulated containers. An evaluation of transient and steady state methods Bulletin IIF-IIR (1973) 1 23-31 Sakal, I., Iwashita, M. Prediction of the unsteady state cooling load in refrigerated containers XIII lnt Congr of Refrigeration Washington (1971) 4 393-399 Bigot, E., ~ IL M6thodes rapides de d6termination du coefficient global de transmission thermique des engins de transport fi temp6rature dirig6e (Rapid methods for determining the overall heat transfer coefficient(K) for controlled temperature transport vehicles) IIF-IIR Commission D2 Vienna, Austria (1978) 1-16

11

BoMrin,BL, Cam~rese, R., Cortdla, G., Minotto, G,'Paaozzo, G. Tests of insulated vehicles: extrapolation of transient K-value IIF-IIR Commissions B2, C2, D1, D2/3 Dresden, Germany

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Mao Dongshen Heat Transfer Calculations using Numerical Method Northern Jiaotong University (1986) Agreement on the international carriage of perishable foodstuffs and on the special equipment to be used for such carriage ( A TP ) ECE, Geneva (1970) Stera, A. C. Proposed changes by the I1R to ATP agreement 1970 XVII1 Int Congr of Refrigeration Montr6al, Quebec, Canada (1991) 4 2045-2046

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