Plane Thermoelastic Waves in Infinite Half-Space Caused


FACTA UNIVERSITATIS  

Series: Mechanical Engineering Vol. 15, N
o
 3, 2017, pp. 495 - 506  

https://doi.org/10.22190/FUME171001027D 

 

Original scientific paper
 

EXPERIMENTAL INVESTIGATION OF THE CONVECTIVE 

HEAT TRANSFER IN A SPIRALLY COILED CORRUGATED 

TUBE WITH RADIANT HEATING 

UDC 662.6 

Milan Đorđević
1
, Velimir Stefanović

2
, Mića Vukić

2
, Marko Mančić

2
 

1
University of Priština, Faculty of Technical Sciences, Kosovska Mitrovica, Serbia 

 

2
University of Niš, Faculty of Mechanical Engineering, Niš, Serbia

  

Abstract. The Archimedean spiral coil made of a transversely corrugated tube was 

exposed to radiant heating in order to represent a heat absorber of the parabolic dish 

solar concentrator. The main advantage of the considered innovative design solution is 

a coupling effect of the two passive methods for heat transfer enhancement - coiling of 

the flow channel and changes in surface roughness. The curvature ratio of the spiral 

coil varies from 0.029 to 0.234, while water and a mixture of propylene glycol and 

water are used as heat transfer fluids. The unique focus of this study is on specific 

boundary conditions since the heat flux upon the tube external surfaces varies not only 

in the circumferential direction, but in the axial direction as well. Instrumentation of 

the laboratory model of the heat absorber mounted in the radiation field includes 

measurement of inlet fluid flow rate, pressure drop, inlet and outlet fluid temperature 

and 35 type K thermocouples welded to the coil surface. A thermal analysis of the 

experimentally obtained data implies taking into consideration the externally applied 

radiation field, convective and radiative heat losses, conduction through the tube wall 

and convection to the internal fluid. The experimental results have shown significant 

enhancement of the heat transfer rate compared to spirally coiled smooth tubes, up to 

240% in the turbulent flow regime. 

Key Words: Archimedean Spiral Coil, Corrugated Tube, Heat Transfer 

                                                           
Received October 01, 2017 / Accepted November 20, 2017 

Corresponding author: Milan ĐorĊević 

Faculty of Technical Sciences, Kneza Miloša 7, 38220 Kosovska Mitrovica, Serbia  

E-mail: milan.djordjevic@pr.ac.rs 



496 M. ĐORĐEVIĆ, V. STEFANOVIĆ, M. VUKIĆ, M. MANĈIĆ 

 

1. INTRODUCTION  

The utilization of modern paraboloidal concentrators for conversion of solar radiation 

into heat energy requires the development and implementation of compact and efficient 

heat absorbers. That is why this research is directed toward an innovative design solution 

that involves the development of the heat absorber made of spirally coiled tubes with 

transverse circular corrugations. The main advantage of the considered design solution is 

a coupling effect of the two passive methods for heat transfer enhancement - coiling of the 

flow channel and changes in surface roughness. The presence of the superimposed secondary 

convection in the curved channel flow suppresses axial propagation of the initial turbulent 

fluctuations so that the curvature stabilizes the flow while the transition from the laminar to 

the turbulent flow is delayed. On the contrary, the transversal corrugations act as turbulence 

promoters since the flow turbulence level is increased by a separation and reattachment 

mechanism. The corrugations act as roughness elements and disturb the existing laminar 

sublayer. Furthermore, Morton [1] found that heated pipes also develop vortices resulting 

from a combination of the radial-directional and the downward motions of the fluid 

particles induced by the displacement of the boundary layer and developed along the pipe. 

The substantial features of each of these effects (curvature, corrugated wall and heating) 

are increased heat and mass transfer coefficients due to the cross-sectional mixing of fluid 

elements as well as enhanced frictional losses. Assessment of the overall impact of the 

stated effects is impossible either with analytical models or even with numerical ones 

without the existence of relevant empirical data for their calibration.  

Spiral tubes or spiral coils were introduced in 19
th

 century and have been widely used 

in various thermal engineering applications, such as heat exchangers, electronic cooling, 

chemical reactors, etc. They have better heat transfer performance and compactness in 

comparison with commonly used straight tube exchangers, which results in their occupying 

less space. The transport phenomena occurring in spiral tubes are more complicated than 

those in straight tubes. Secondary flows observed in the flow patterns, induced by the 

centrifugal force, significantly affect the flow field and heat transfer. 

Most of the studies of thermal-hydraulic processes in the coils have been dedicated to   

helical coils. Much less work has been reported on the hydrodynamics of flow and heat 

transfer in spiral coils. The property of a continuously varying curvature along the length 

makes spiral coil flows never fully developed unlike helical ones. Secondly, the distinction 

of the flow regime needs specification of two critical Reynolds numbers instead of just one 

[2]. Naphon and associates [3, 4] experimentally and numerically studied heat transfer and 
flow developments in the spirally coiled smooth tubes. They stated that the Nusselt number 

and pressure drop obtained from the spirally coiled tube are for 1.49 and 1.50 times higher 

than those from the straight tube, respectively, under constant wall temperature boundary 

condition. Their conclusions could not be considered general since the average Nusselt 

number and pressure drop are not appropriate for evaluation of heat transfer and flow 

characteristics of the tubes with a constantly varying curvature. Several numerical studies [5-

7] have been published, which examined the flow and heat transfer phenomena in spiral 

tubes. These papers investigate the laminar flow of Newtonian fluids in coils, while those 

that investigate turbulent flow conditions are rare. Moreover, all take into account two 
common thermal boundary conditions – constant wall temperature and constant heat flux.  

Even though the interest in spiral coiled systems is on the rise, there are still very few 

published articles on spiral coil tubes. They are less popular compared to helical ones, 



 Experimental Investigation on the Convective Heat Transfer in a Spirally Coiled Corrugated Tube …   497 

 

which have attracted major attention in the study of coiled tubes for heat transfer. There is 

very little information about the Nusselt number as well as correlations, and in the 

absence of appropriate correlations, the traditional approach is to use the correlations 

developed for circular or helical tubes with an average curvature.  

Examining the research studies on thermal-hydraulic processes in straight tubes with high 

values of relative roughness it can be concluded that the appropriate correlations for 

determining the coefficients of friction and heat transfer in the laminar flow regime almost 

do not exist. Furthermore, the results of different authors differ significantly in general 

conclusions. It can be concluded that there is a lack of data for a range of geometrical 

parameters and the Reynolds number for transversely corrugated straight pipes having large 

relative roughness. Moreover, no reference concerning hydrodynamics and heat transfer in 

spiral tube coils with transverse corrugations was found. Another specific aspect of this 

investigation is that the heat exchanger in the model under consideration is subjected to a 

radiant asymmetrical heat flux, while most of the existing correlations for convective heat 

transfer are valid for flow in channels with direct, uniform heating. 

2. EXPERIMENT 

The objective of this paper was to experimentally study the distribution of the 

convective heat transfer in a spirally coiled corrugated tube exposed to radiant heating 

that is characteristic of parabolic dish solar concentrators. Investigation of the influence of 

hydraulic, physical and thermal conditions, as well as the geometry of the spirally coiled 

corrugated heat absorber, on the local intensity of heat transfer and pressure drop was 

conducted using modern experimental methods. 

The Archimedean spiral, with a pitch slightly larger than the maximal outside diameter 

of the corrugated coiling tube, was selected out of different types of spirals in order to 

achieve the most favorable ratio of active surface area and the total volume of the heat 

absorber in the parabolic dish receiver. The geometrical characteristics and experimental 

configurations of the transversely corrugated straight pipe and the transversely corrugated 

Archimedean spiral coil are shown in Figs. 1 and 2, respectively, while Table 1 shows 

geometrical parameters of the tested configuration. 

      

Fig. 1 Profile of transverse corrugated       Fig. 2 Geometry and configuration  

          pipe made of stainless steel AISI 304 [8]              of transversely corrugated  

 Archimedean spiral coil 



498 M. ĐORĐEVIĆ, V. STEFANOVIĆ, M. VUKIĆ, M. MANĈIĆ 

 

In order to simulate the real working conditions of the heat absorber an experimental 

installation is constructed. The installation consists of a spirally coiled corrugated tube of 

heat absorber with an accompanying flow loop and a radiant heating system. The 

schematic diagram of the hydraulic system is shown in Fig. 3. The entire experimental 

apparatus enables variations of the following operating parameters: 1) intensity of the 

incident radiant heat flux; 2) flow rate and flow direction of the working fluid, and 3) 

angle of inclination of the spiral heat exchanger in relation to the horizontal plane. 

Table 1 Geometrical parameters of the tested configuration 

Transversely corrugated straight tube Transversely corrugated Archimedean spiral coil 

d 9.3 mm minimum internal diameter Rmin 25 mm minimum radius of the coil 

d0 11.7 mm maximum internal diameter Rmax 202 mm maximum radius of the coil 

dmax 12.2 mm maximum external diameter N 13 - number of coil turns 

s 0.25 mm wall thickness L 9.324 m length of the coil  

e 1.2 mm corrugation depth Le 0.5 m length of entrance section 

pc 4.2 mm corrugation pitch ps 13.6 mm spiral coil pitch 

 

Fig. 3 Schematic diagram of the test loop 

In addition to water, a mixture of propylene glycol and water (90% and 10% by volume, 

respectively) was also used to expand the experimental range. The volume flow rate is 

measured with the flask and the ultrasonic flow meter (Kamstrup, type 66W02F1318), while 

the flow is regulated by the TA-STAD balancing valve. Pressure drops were measured with 

a hydrostatic pressure gauge (up to a maximum pressure drop of 20 kPa) and a differential 

pressure gauge (for pressure drop values greater than 20 kPa). Measuring the temperature of 

the working fluid at the inlet and outlet of the coil was performed with two Pt100 

temperature sensors positioned in the mixing chambers. 

In order to measure variations of the tube wall temperature along the axis of the tube, 

as well as its circumferential direction, a total number of 35 type K thermocouples 

(Chromel-Alumel, wire diameter ϕ0.22 mm) were located on the outside surface of the 



 Experimental Investigation on the Convective Heat Transfer in a Spirally Coiled Corrugated Tube …   499 

 

tube in a special arrangement so that there was one thermocouple station in the middle of 

each turn of the spiral coil.  

At some thermocouple stations, either two or four thermocouples were welded to the 

tube surface using a capacitor discharge welding machine, which is specially designed 

and operated for research purposes. Peripheral locations at these stations were specified 

as: location  A (θ=0°) corresponds to the outer side of the tube cross section (the furthest 

from the curvature center), location B (θ=90°) corresponds to the side of the tube cross 

section which is directly subjected to radiant flux, location C (θ=180°) corresponds to the 

inner side of the tube cross section (the closest to the curvature center) and location D (θ 

= 270°) receives heat only by air convection and conduction through the tube wall. Since 

the tube is corrugated, the thermocouples were located both at the basic, minimum, diameter 

of the tube, as well as on the tops of the corrugations, at the maximum diameter of the tube. 

The schematic diagrams of thermocouple arrangements around the circumference of the tube 

cross section are shown in Figs. 4 and 5. The additional 9 thermocouples were located in the 

middle of the remaining turns of the spiral coil on the minimum tube diameter. After the 

thermocouples were connected, the coil surface was coated with temperature resistant flat 

black paint "Pyromark 2500", whose minimum guaranteed absorptance is 0.9 [9].  

  

Fig. 4 Circumferential locations of thermocouples at the minimum diameter of the tube 

The outputs of thermocouples were connected to two input modules NI 9213, with 16 

channels both, and one input module NI 9211 with 4 channels, which allow simultaneous 

recording of signals from 36 thermocouples. The input modules were connected to the 

computer via a ethernet chassis NI cDAQ-9188, while the software package LabVIEW 

2013 was used for recording temperature values and generation of reports. 

The incident heat flux upon the tube external surfaces varies both in the circumferential 

and axial direction. It was obtained by the radiant heating system, which is specifically 

designed for the purposes of this experimental research. Detailed analyses of the radiant heat 

flux produced by the quartz heating system and radiant absorption characteristics of the 

corrugated curved tubes could be found in our previous papers [10,  11]. 
 



500 M. ĐORĐEVIĆ, V. STEFANOVIĆ, M. VUKIĆ, M. MANĈIĆ 

 

 

Fig. 5 Circumferential locations of thermocouples at the maximum diameter of the tube 

Kline and McClintock [12] method was used to estimate uncertainties involved in the 

calculation of the heat transfer coefficient and Nu number. They vary up to 3.72% and 

3.85% for calculated values of the heat transfer coefficient and Nu number, respectively. 

3. THERMAL ANALYSIS 

The flow in the heated curved tube with corrugations is very complex, characterized 

by the existence of the secondary flows with recirculation cells in the plane normal to the 

direction of axial velocity and formation of vortices in the corrugations. The combination 

of these factors, along with nonuniformity of the boundary conditions, both in the axial 

direction and around the circumference of the tube, as well as the uncertainty in determining 

the local fluid conditions, make solving the problem of heat transfer by analytical methods 

impossible, thus necessitating an experimental procedure. 

The method of calculation of each of the quantities necessary for estimating the heat 

transfer coefficient at the inner surface of the tube is presented. The local values of heat 

transfer coefficient hi and Nu number for any given axial (z) and circumferential (θ) 

location (denoted as │z,θ) at the inner surface of the tube were calculated according to: 

 i ,
i ,

i , b

|
|

| |

z

z

z z

q
h

T T










 (1) 

 i , i
,

f

| |
Nu |

|








z z

z

z

h d


 (2) 

where Ti is the inner surface local temperature of the tube, di is tube internal diameter and 

λf is the thermal conductivity of the transport fluid. Bulk temperature of the fluid at some 

axial location is defined as: 

 

c

b

c

1
d 

A

T TU A
VA

 (3) 

where U is the local velocity vector, T is the local fluid temperature and V is the average 

velocity at the considered cross-section, whose area is Ac: 



 Experimental Investigation on the Convective Heat Transfer in a Spirally Coiled Corrugated Tube …   501 

 

 

c

c

c

1
d 

A

V U A
A

 (4) 

Thermophysical properties of water [13, 14] and a mixture of propylene glycol and 

water (90% and 10% by volume, respectively) [14, 15] are treated as temperature-dependent 

and were obtained as polynomial functions of temperature.  

3.1. Calculation of total heat input 

The net heat flux at the outer surface at any specific axial location along the spiral and 

at any angular position (qoǀz,θ) can be considered equal to the net heat flux at the 

corresponding radial location of the inner surface of the tube (qi ǀz,θ). This assumption is 

justified by a relatively small thickness of the wall, as well as relatively large values of the 

heat transfer coefficient that characterize all the flow regimes in the considered geometry. 

Heat losses and gains from the outer surface of the coil are due to convection qconv ǀz,θ and 

radiation qrad ǀz,θ to the outside environment. These heat losses will also be a function of 

the axial and circumferential position around the tube cross section, as the tube surface 

temperature is not uniform. 

The net heat flux at the outer surface is given by: 

 
o , abs , conv , rad ,

| | | |
z z z z

q q q q
   
    (5) 

where qabs ǀz,θ is absorbed radiative heat flux. Analytical expressions for the calculation of 

qconv ǀz,θ
 
and qrad ǀz,θ are: 

 conv , o o , cav| ( | )z zq h T T    (6) 

 
4 4

rad , o , amb
| ( | )
 
 

z z
q T T  (7) 

where ho is the local value heat transfer coefficient at the outer surface of the tube, Tcav and 

Tamb represent the temperature of the air in the cavity of the receiver and ambient, respectively, 

while ζ and ε denote the Stefan-Boltzmann constant and emissivity, respectively. 

Heat transfer coefficient at the outer surface of the tube wall ho 
was determined according to 

the relation given by Churchill and Chu [16]: 

 
1/ 6 9 /16 8 / 27 2

o ai
air

e

r

kv

 [0.60 0.387·Ra /  (1 (0.559 / Pr ) ) ]
d

h


    (8) 

where the Grashof and Rayleigh number are defined as: 

 
3 2 2

ekv air air air
Gr ·  /   d g T    (9) 

 
air

Ra=Gr·Pr  (10) 

In previous equations dekv is the equivalent external tube diameter, g is the Earth gravity 

acceleration, ΔT is the temperature difference between the boundary layer and the bulk 

fluid, while λair, ρair, βair, μair and Prair are thermal conductivity, density, volumetric temperature 

expansion coefficient, dynamic viscosity and Prandtl number of air, respectively.  



502 M. ĐORĐEVIĆ, V. STEFANOVIĆ, M. VUKIĆ, M. MANĈIĆ 

 

Assuming stationary heat transfer, an energy balance can provide a relationship 

between the net value of the heat flux at the outer surface of the tube and the thermal 

power of the absorber formulated by the parameters of the working fluid: 

 

2

o , o ave ave out in

0 0

| d d ( )




   

L

z
q d z V c T T  (11) 

where ρave, cave, Tout and Tin are average density, average specific heat capacity, outlet and 

inlet temperature of transport fluids, respectively. 

Based on the previously defined energy balance, the bulk fluid temperature at some 

axial location at a distance l from inlet can be calculated as: 

 

2

o , o ave ave b in

0 0

| d d ( | ), 0




     

l

z l
q d z V c T T l L  (12) 

3.2. Heat conduction in tube wall 

The inner surface local temperature of tube Ti ǀz,θ could be determined based on the 

corresponding values of the outer surface local temperature of tube To ǀz,θ and the local net 

heat flux at outer surface qo ǀz,θ according to the expression: 

 

o
o , i

i

i , o ,

w

|
| | ln

|
| |

2



 

 
   

 
 

 

z
z z

z

z z

d
q d

d
T T


 (13) 

where λw denotes the thermal conductivity of the tube wall.  

4. RESULTS 

Based on the experimental tests of thermal-hydraulic processes in spirally coiled 

corrugated tube of the heat absorber exposed to radiant heating, a systematic study of the 

thermal characteristics of the considered heat exchanger was carried out. The results 

presented are based on 146 complete series of measurements for different experimental 

conditions. The determination of the flow stability criteria and of the critical Re numbers 

has already been shown in our previous work [17]. 

A mixture of propylene glycol and water (90% and 10% by volume, respectively) was 

used as a working fluid in the Reynolds number range Re≈56-1734 and Prandl number 

range Pr≈36.4-255, while water was used in the ranges Re≈1225-16731 и Pr≈3.0-7.0. Pr 

number variation of working fluids is in accordance with the range of temperature that 

characterizes the experimental conditions. The selected Re number ranges guarantee a 

separate existence of all the three flow regimes for all the values of curvature ratio δ 

(δ=de/2R, while R is the radius of curvature), which varies in the range δ=0.023-0.186 and 

is determined by the constructive characteristics of the spiral heat exchanger. 

The local values of Nu number were calculated both at the minimum diameter of the 

tube, as well as on the corrugation crests. In order to determine the values of the peripherally 

averaged Nu number most accurately, the locations of thermocouples at minimum and 

maximum diameter on the same coil turn were positioned at the axial distance equal to the 

half of the corrugation pitch.  



 Experimental Investigation on the Convective Heat Transfer in a Spirally Coiled Corrugated Tube …   503 

 

The correlations between the peripherally averaged Nu number and the Re and Pr 

numbers and the basic geometrical parameter of spiral (δ) were obtained by a multiple 

nonlinear regression analysis, assuming simple exponential models. Proposed correlations 

for laminar, transitional and turbulent flow regimes, as well as the ranges of their 

applicability, are represented by Eqs. (14-16), respectively: 

 
0.61 0.174 0.164

Nu 0.556 Re Pr   (14) 

 100<Re<1200;  40<Pr<190;  0.023<δ<0.146 

 
0.641 0.3 0.11

Nu 0.363Re Pr   (15) 

 1250<Re<3200;  6<Pr<90;  0.023<δ<0.146 

 
0.654 0.43 0.07

Nu 0.289 Re Pr   (16) 

 3500<Re<15000;  4<Pr<7;  0.023<δ<0.146 

Figures 6-8 show the comparisons of experimental data and the best fit lines obtained 

by least squares analysis of the points predicted by corresponding correlations. 

   

       Fig. 6 Graph of the regression model:         Fig. 7 Graph of the regression model: 

 laminar flow trasitional flow 

 

Fig. 8 Graph of the regression model - turbulent flow 



504 M. ĐORĐEVIĆ, V. STEFANOVIĆ, M. VUKIĆ, M. MANĈIĆ 

 

The maximum deviations of the predictions are 8% in the laminar, 7% in the transitional 

and 14% in the turbulent flow regime. 

After obtaining power-law dependences, the possibility of applying some of the 

momentum-heat transfer analogies to spirally coiled corrugated tubes was considered. 

This is a more fundamental approach since analogies are most physically founded and rest 

on a more sound theoretical ground than widely used power-law formulas.   

Di Piazza and Ciafolo [18] indicated that the modified Reynolds analogy is applicable 

in smooth curved pipes with constant curvature. It is valid in the average and only 

approximately is valid locally (analogy is less applicable for a higher curvature). On the 

other hand, Bergles and Morton [19] have shown that for the surfaces characterized with 

large relative roughness no unique relation between friction coefficient and heat transfer 

could be formulated.  

An additional problem in attempting to formulate the momentum-heat transfer analogy 

in this study is the formulation and determination of the local values of the friction 

coefficient in the spiral because of its dependence on the constantly variable curvature of 

the flow channel. Using the normalized values of the friction coefficient in the Petukhov 

and Gnielinski analogies yields values of the peripherally averaged Nu number with 

significantly larger deviations compared to the predictions obtained by power-law models. 

This leads to the conclusion that the momentum-heat transfer analogies cannot be applied 

in general in the tubes with a variable radius of curvature that are characterized by high 

values of relative roughness. 

5. CONCLUSIONS 

The empirical power-low formulas have been suggested to indicate the dependency of 

the peripherally averaged Nu number on Re and Pr numbers and on the curvature in the 

spirally coiled corrugated tubes exposed to radiant heating. A large database reduces the 

influence of random errors, thus making a statistical approach highly reliable. The 

obtained correlations for heat transfer are applicable in wide ranges of flow, physical and 

geometric parameters. The accuracy of the obtained correlations can be compared with 

that of the correlation in the literature about research studies of similar processes, which 

justifies the use of the statistical method. 

The suggested formulas indicate the effects of the considered parameters for the heat 

transfer rate. A relatively high exponent value of the Re number in the laminar flow regime 

indicates the dominant influence of the secondary flows on heat transfer which significantly 

increases the heat transfer rate. The Reynolds number exponent in the turbulent flow regime 

is lower than the value of 0.8, otherwise typical of simple geometries. This is consistent with 

the previous investigation of Ciofalo and Collins [20] who consider the value of the 

exponent for complex flow channel geometries where detachment and reattachment of the 

boundary layer exist. The exponent value of curvature δ decreases with the increase in the 

Re number, which indicates that the secondary flows in the turbulent regime have a 

relatively small effect on the heat transfer. 

The experimentally obtained peripherally averaged Nu number was compared to the 

corresponding one in the smooth spiral coil for identical boundary conditions [21]. The 

Nu number in the corrugated spiral coil is not significantly higher in the laminar flow 



 Experimental Investigation on the Convective Heat Transfer in a Spirally Coiled Corrugated Tube …   505 

 

regime and the increase is slightly more than 50% at the end of the laminar flow range 

(Re≈1300). The enhancement of the heat transfer in the corrugated spiral coil is considerably 

conditioned by the value of the Re number, so that the increase in the Nu number at the end 

of the test range in the turbulent flow regime (Re≈15000) is about 240%. 

Developing flow along with secondary flows make the development of the peripherally 

averaged Nu number rather oscillatory. It makes difficult to represent the differences in 

distribution of the peripherally averaged Nu number along the spiral axial coordinate for the 

cases of inflow to outermost or innermost spiral turn. Those differences are relatively small 

and the proposed power-law formulas cannot account for the complexity of the real 

functional dependences. 

The proposed formulas are applicable for heat transfer in Archimedean spiral coils 

made of transversally corrugated tubes. They cannot be compared to others because, to 

the best of our knowledge, this has not been reported before. These values characterize 

the examined geometry of the corrugations and, according to our assessment, could be 

applied when geometric ratio pc/e ranges from 3 to 5. The future work should be pointed 

to the effects of the basic corrugation parameters on the heat transfer rate. 

REFERENCES  

1. Morton, B. R., 1959, Laminar convection in uniformly heated horizontal pipes at low Rayleigh numbers, 

Quarterly Journal of Mechanics and Applied Mathematics, 12(4), pp. 410-420.  

2. Ali, S., Seshadri, C., 1971, Pressure drop in Archimedean spiral tubes, Industrial and Engineering Chemistry 

Process Design and Development, 10(3), pp. 328-332.  

3. Naphon, P., Wongwises, S., 2002,  An experimental study on the in-tube convective heat transfer coefficients in 

a spiral coil heat exchanger, International Communications in Heat and Mass Transfer, 29(6), pp. 797-809. 

4. Naphon, P., Suwagrai, J., 2007, Effect of curvature ratios on the heat transfer and flow developments in the 

horizontal spirally coiled tubes, International Journal of Heat and Mass Transfer, 50(3), pp. 444-451. 

5. Nakayama, A., Kokubo, N., Ishida, T., Kuwahara, F., 2000, Conjugate numerical model for cooling a fluid 

flowing through a spiral coil immersed in a chilled water container, Numerical Heat Transfer, Part A, 37(2), pp. 

155-165. 

6. Kurnia, J.C., Sasmito, A.P., Mujumdar, A.S., 2011, Numerical investigation of laminar heat transfer 

performance of various cooling channel designs, Applied Thermal Engineering, 31(6), pp. 1293-1304. 

7. Sasmito, A. P., Kurnia, J.C., Wang, W., Jangam, S.V., Mujumdar, A.S., 2012, Numerical analysis of 

laminar heat transfer performance of in-plane spiral ducts with various cross-sections at fixed cross-section 

area, International Journal of Heat and Mass Transfer, 55(21), pp. 5882-5890. 

8. ***, Pliable Corrugated Stainless Steel Resistant to Corrosion CSST Tubes for Plumbing,  Heating 

Systems and Thermal Solar Plants, http://www.eurotis.it (Last Access: 13.07.2017) 

9. Ho, C.K., Mahoney, A.R., Ambrosini, A., Bencomo, M., Hall, A., Lambert, T.N., 2012, Characterization 

of Pyromark 2500 for high-temperature solar receivers, Proc. 6
th
 International Conference on Energy 

Sustainability of ASME, San Diego, USA, pp. 509-518. 

10. ĐorĊević, M., Stefanović, V., Pavlović, S., Manĉić, M., 2015, Numerical analyses of the radiant heat flux 

produced by quartz heating system, Proc. 3
rd

 International Conference Mechanical Engineering in XXI Century, 

Niš, Serbia, pp. 75-80. 

11. ĐorĊević, M., Stefanović, V., Kalaba, D., Manĉić, M, Katinić, M., 2017, Radiant absorption characteristics of 

corrugated curved tubes, Thermal Science, DOI: 10.2298/TSCI160420263D. 

12. Kline, S., McClintok, F., 1953, Describing uncertainties in single-sample experiments, Mechanical Engineering, 

75(1), pp. 3-8. 

13. ***, 2007, IAPWS industrial formulation for the thermodynamic properties of water and steam (IAPWS-IF97), 

The IAPWS-IF97. 

14. ĐorĊević, M., Stefanović, V., Vukić, M., Manĉić, M., 2017, Experimental investigation on the convective 

heat transfer in a spirally coiled corrugated tube, Proc. 18th Symposium on Thermal Science and 

Engineering of Serbia, Soko Banja, Serbia.    

http://www.eurotis.it/
http://www.osti.gov/scitech/search/author/%22Ho,%20Clifford%20K.%22
http://proceedings.asmedigitalcollection.asme.org/solr/searchresults.aspx?author=A.+Roderick+Mahoney&q=A.+Roderick+Mahoney
http://proceedings.asmedigitalcollection.asme.org/solr/searchresults.aspx?author=Andrea+Ambrosini&q=Andrea+Ambrosini
http://proceedings.asmedigitalcollection.asme.org/solr/searchresults.aspx?author=Marlene+Bencomo&q=Marlene+Bencomo
http://proceedings.asmedigitalcollection.asme.org/solr/searchresults.aspx?author=Aaron+Hall&q=Aaron+Hall
http://proceedings.asmedigitalcollection.asme.org/solr/searchresults.aspx?author=Timothy+N.+Lambert&q=Timothy+N.+Lambert
https://doi.org/10.2298/TSCI160420263D


506 M. ĐORĐEVIĆ, V. STEFANOVIĆ, M. VUKIĆ, M. MANĈIĆ 

 

15. ***, 2001, Engineering and operating guide for DOWFROST and DOWFROST HD inhibited propylene 

glycol-based heat transfer fluids, Dow Chemical Company, USA, available at: http://msdssearch.dow.com/ 

PublishedLiteratureDOWCOM/dh_010e/0901b8038010e417.pdf?filepath=heattrans/pdfs/noreg/180-01286. 

pdf&fromPage=GetDoc (Last Access: 15.10.2017) 

16. Churchill, S.W., Chu, H.H.S., 1975, Correlating equations for laminar and turbulent free convection from a 

horizontal cylinder, International Journal of Heat and Mass Transfer, 18, pp. 1323-1329. 

17. ĐorĊević, M., Stefanović, V., Manĉić, M., 2016, Pressure drop and stability of flow in Archimedean spiral tube 

with transverse corrugations, Thermal Science, 20(2), pp. 579-591. 

18. Di Piazza I., M. Ciofalo, 2010, Numerical Prediction of turbulent flow and heat transfer in helically coiled 

pipes, International Journal of Thermal Sciences, 49, pp. 653-663. 

19. Bergles, A. E., Morton, H. L., 1965, Survey and evaluation of techniques to augment convective heat transfer, 

Technical Report NO. 5382-34, Massachusetts Institute of Technology, USA. 

20. Ciofalo, M., Collins, M.W., 1989, k-ε predictions of heat transfer in turbulent recirculating flows using an 

improved wall treatment, Numеrical Heat Transfer, 15, pp. 21-47. 

21. ĐorĊević, M., Stefanović, V., Vukić, M., Manĉić, M., 2016, Numerical investigation on the convective heat 

transfer in a spiral coil with radiant heating, Thermal Science, 20(Suppl. 5), pp. S1215-S1226.