CALCULATION OF FREEZING RADIUS AROUND ...jestec.taylors.edu.my/Vol 14 issue 5 October...

Journal of Engineering Science and Technology Vol. 14, No. 5 (2019) 2913 - 2927 © School of Engineering, Taylor’s University

2913

CALCULATION OF FREEZING RADIUS AROUND VERTICAL TWO-PHASE THERMOSYPHON IN SUBARCTIC CLIMATE

EVGENIY V. MARKOV*, SERGEY A. PULNIKOV, YURI S. SYSOEV

Industrial University of Tyumen, 38, Volodarskogo, Tyumen, 625000, Russian Federation

*Corresponding Author: [email protected]

Abstract

Permafrost is a significant construction problem, as the defrosting leads to

decrease in volume and uneven subsidence of foundations. Thawing of soils is

associated with thermal influence of the structures and global warming.

Therefore, the problem of temperature stabilization of permafrost remains

relevant. Typically, for the temperature stabilization energy-free two-phase

thermosyphons are used. In the southern subarctic climate, thermosyphon

operates under the influence of increased solar radiation. Therefore, the freezing

radius can differ significantly from the designed value. The article is devoted to

the improving of calculation method of freezing radius around two-phase

thermosyphon in areas with subarctic climate. The authors derived formulas for

calculating the average film thickness of the liquid refrigerant on the inner surface

in all parts of the thermosyphon: condenser, overground pipe, underground

thermal insulated pipe, and evaporator. Numerical study has shown that the

thermal resistance of the refrigerant film in thermosyphon with 3 m evaporator

length is 2 orders less than the thermal resistance of the condenser. Thus, in case

of short evaporator the practical calculations soil-freezing radius can be done

without taking into account refrigerant film thickness. The formula for

calculating absorbed direct, diffuse and reflected solar radiation by the condenser

and overground pipe is derived. Required data for a formula coincide with

meteorological quantities. A comparison of two models of system two-phase

thermosyphon - soil - atmosphere showed that the authors’ model reduces the

maximal distance between thermosyphons by 20%. The result is extremely

important in designing of thermosyphons quantity in permafrost stabilization

system at subarctic climate.

Keywords: Heat transfer in soil, Permafrost, Refrigerant film, Solar radiation.

2914 E. V. Markov et al.

Journal of Engineering Science and Technology October 2019, Vol. 14(5)

1. Introduction

Construction on the permafrost usually requires to save temperature of soils low

then freezing point. In zone of subarctic climate, it is impossible to save permafrost

using standard solution: Ventilated cellar or piles foundation. The global warming

and thermal influence of structure leads to defrosting and uneven subsidence. In

such situation, two-phase thermosyphons are used to lower the temperature of soils

and save the stability of spatial position of various structures: Buildings and

pipelines [1-5].

The main design problem is the calculation of quantity and density on the

general layout. The distance between thermosyphons depends on the freezing

radius, which depends on the refrigerating power. Thus, the accuracy of the

calculation directly affects the stability of the structure.

There is a large number of researches devoted to the study of vertical

thermosyphons, which are described in review articles of Jafari et al. [6] and Jadhav

and Patil [7]. Lee and Mital [8] investigated the influence of pressure, length of

evaporator and condenser, type of refrigerant (water and Freon) to the efficiency of

two-phase thermosyphons. Terdtoon et al. [9] investigated the corrosion of inner

surface. Park et al. [10] studied the influence of fill charge ratio to speed of heat

exchanging. Zhu et al. [11] examined the work of semi-open thermosyphon. Noie

[12] investigated the work of thermosyphons in the heat recovery systems and

found the optimal filling ratio. Carvajal-Mariscal et al. [13] developed the method

of designing two-phase thermosyphons with optimal parameters for the

temperature up to 250 ºC. Khazaee [14] got the limits of heat transfer due to dry

out in the evaporator. Lotfi et al. [15] estimated the heat losses in thermosyphon.

Gandal and Kale [16] found that optimal inclination for clear water and glycol-

water solution differ by 10º. Gorelik and Seleznev [17] evaluated the optimal length

of short thermosyphon for the stabilization of permafrost. de Haan et al. [18, 19]

developed new methods for thermodynamic calculation of thermosyphons based

on finite element method and division of time-step to enthalpy and entropy change.

Özbaş [20] investigated the influence of working fluid to the performance of

thermosyphon. Ali and Hassan [21], Menni et al. [22] and Pathak et al. [23] studied

the influence of channel shape to heat transmission.

Despite extensive researches of thermosyphon, there is a gap in the study of

their efficiency in permafrost. There are still no estimates of the influence of liquid

refrigerant film on the soil-freezing radius taking into account real climatic

conditions. Similarly, there are no physically valid formulas and studies that allow

to estimate the effect of solar radiation (direct, diffuse, and reflected) on the

freezing radius. This is probably due to the fact that the value of solar radiation in

the arctic climate is low. Gorelik and Seleznev [17] work is the closest work with

calculation of the freezing radius. Therefore, everywhere further, the comparison

of the authors’ model and the model in [17] was made.

In the southern subarctic climate, the sun radiation becomes more intense, heats

the condenser part and reduces the freezing radius. Therefore, the improving of

calculation method requires to research the influence of solar irradiance to the

freezing radius.

Calculation of Freezing Radius Around Vertical Two-Phase Thermosyphon . . . . 2915


2. Problem Statement

In this article, the authors solved the following 4 problems:

Developing a mathematical model of a vertical two-phase thermosyphon for

calculating the thermal regime of the soil;

Developing a method for calculating the absorbed solar radiation by the

condenser and overground pipe taking into account the available irradiance

data;

Estimating the error in the calculation of the soil freezing radius around

thermosyphon without taking into account the thermal resistance of the liquid

refrigerant film on the inner surface;

Estimating the difference in the calculation of soil freezing radius around

thermosyphon taking into account direct, diffuse and reflected solar radiation

absorbed by condenser and overground pipe using the authors’ model and the

model given in the paper of Gorelik and Seleznev [17].

3. Model of Two-Phase Vertical Thermosyphon

The simulation of two-phase thermosyphon was according to the design scheme

in Fig. 1.

Fig. 1. Calculation scheme for the system

two-phase thermosyphon-soil-atmosphere.

The mathematical model of two-phase thermosyphon was developed on the

basis of the following assumptions:

The heat exchange in the thermosyphon is quasi-stationary. This assumption is

explained by the fact that heat transfer by thermal conductivity in the soil is much

slower than convective heat transfer in thermosyphon. As a result, calculation of

soil temperature around thermosyphon can be done using the quasi-stationary

s

h

rR

conRcon

z

evp

aT

T

gT

conl

evpR

conq

ogq

ugq

evpq

ogl

ugl

evplhi

lowz

evpz

0z

upz

r

condenser

overgroundpipe

evaporator

undergroundpipe

sunE



model and independent from z temperature of the gaseous phase of refrigerant

inside.

The flow of a liquid film along the inner surface is described by Nusselt theory.

The supercooling of refrigerant vapor is insignificant, which makes it possible

to equate the heat flux to the rate of evaporation-condensation taking into

account the heat of phase transition.

In this case, the following fundamental equation of heat balance can be used for

the mathematical model of a thermosyphon:

0up

low

z

zt sunq dz E (1)

Equation (1) differs from the equation given in work of Gorelik and Seleznev

[17] by the term, which is correspond to the absorbed solar radiation. This term will

be discussed below.

In accordance with the design scheme in Fig. 1, the construction of the

thermosyphon consists of four main parts:

Condenser transfers heat to the atmosphere during condensation of

refrigerant vapor.

Overground pipe transfers a small amount of heat to the atmosphere and

supports the condenser above the snow cover.

Underground pipe provides the transfer of liquid refrigerant to the bottom

without heat losses.

Evaporator takes heat from a soil when the refrigerant evaporates.

Using the Newton's law of cooling equation (1) we can find the temperature of

the gaseous phase of refrigerant:

0 evp

loe wvp

zz

z zcon con og og air ug evp sun

gcon con og og ug ug evp evp

K l K l T K Tdz K Tdz E

TK l K l K l K l

(2)

The heat transfer coefficients Kcon, Kop, Kup, and Kevp is:

13

1

1

2 2 2i

con i

con N con R i i i

l RK ln

R s R hn R

(3)

where ξ=1 for the condenser and ξ=0 for another parts; the summation is: 1 - film

of the refrigerant, 2 - wall of thermosyphon, 3 - thermal insulation.

1 1

0 0

2 2

2 2

r R con r R con

r R con r R con

K hR a I hR b

K hR a I hR b

(4)

1 02 2 2r R r R r R r R ra hI hR I hR (5)



1 02 2 2r R r R r R r R rb hK hR K hR (6)

Expressions (3) - (6) are obtained on the basis of an analytical solution of the

heat equation in a thin ring plate and boundary conditions of first type on the inner

radius of the ring and third kinds on the other surfaces.

Convective heat transfer coefficients αr, αR, αN is calculated according to the

theory of boundary layer.

In Eq. (3), the average thickness of the film of the refrigerant in different parts

of the thermosyphon δrca, δroa, δrua, and δrea are unknowns. It will be shown below

that, the film thickness makes an insignificant contribution to the thermal

resistance. But now, we immediately ignore this value. This will not lead to a

significant error in the evaluation of the film thickness, because, on the contrary, it

increases its thickness. Next, we wrote the Nusselt equation for the film thickness

using explicit solution of Navier-Stokes equation for the free movement of fluid by

gravity on a vertical surface:

3

23

tr

rf rr

ff

qgR

z L

(7)

Then we integrated (7) and got the average film thickness for every sections:

1

333 3

4 2 4

con g air rf c

rf con rf

on

rca rccon

K T T l

g R L

(8)

2

rf con rconroa

og g air

f

rf og

g R L

K T T l

4

33 4

3

2rc rc

rf c

og g air rf og

o on rc n f

K T T l

g R L

(9)

rua roa , (10)

3

4rea rua . (11)

Equation (11) is explained by the fact that the section is insulated and the heat

flow is very small.

Thus, we found all the unknowns in equations (5) - (8). It should be noted that

the calculation sequence is as follows: equation (3) - (6), then (2), then (8) - (11).

After this, the iteration cycle is repeated until the values (9) - (12) stop changing.

Problem No 1 solved.

Next, a method for calculating the absorbed solar radiation Esun is described.

The first thing that needs to be established is the set of source data necessary for

calculating. Consider the physical side of the process. Solar radiation during the



passage of the atmosphere is partially scattering in clouds and dense layers. Two

components of solar radiation are measuring at the meteorological stations: direct

and diffuse solar radiation. Direct solar radiation is measuring on a horizontal

surface and the surface normal to the ray. Diffuse solar radiation is measuring only

on a horizontal surface. In addition, albedo of the surface is measuring [24]. All

measurements are given under average cloud conditions.

The overground part of the thermosyphon generally in a vertical position in order

to ensure the maximal flow of liquid refrigerant. Therefore, it is necessary to know

the flux of solar radiation on a vertical surface. However, direct measurements of

these quantities are not systematized. Therefore, the author has developed a method

for calculating Esun, which takes into account the absorption of direct, diffuse and

reflected solar radiation by the vertical overground part of the thermosyphon.

The calculation of direct solar radiation flux on the vertical surface of the

condenser is not difficult, because there is a data of direct irradiance and

horizontal irradiance:

2 22s con r con'sun sunSE R l S (12)

On the contrary, the calculation of the flux of diffuse and reflected solar

radiation is much more complicated. Consider the design scheme in Fig. 2: a

condenser with radius Rr is irradiated by diffuse solar radiation from the height Ha.

At this stage, we will not assume the value of Ha.

Fig. 2. Scheme for calculation of absorbed

sun radiation by condenser and overground pipe.

The area of the infinitesimal element of the cylindrical surface of the condenser

dFcon collects on itself radiation from a source in the atmosphere with an area of

dFa. In accordance with Lambert's law, we can write the density of the energy flow

on a condenser:

2

20 0 0 0

conc

lasun

d con r onon

c

GE d rdr R d d

cos cosl

R

(13)

The result of the integration gives the absorbed energy of diffuse solar radiation:

24

d con sun r conE G R l (14)

kn

an

adF

condF

rR

aH

r

Rcon

ad



A feature of expression (15) is the absence of Ha. Therefore, it is not necessary

to make any assumptions about the dispersion distance Ha.

Solar radiation disperses due to reflection on the not smooth snow surface. In this

case, the mathematical description is similar to dispersion in the clouds. The absorbed

energy by condenser butt include only horizontal irradiance. The summation over the

all components gives us expression for the absorbed solar radiation by thermosyphon:

2 2 22 'susun con sun r con r con og on sun n gcoS S R l RE Q R l

2

sun surf sun r con con con og ogG A Q R l R l

(15)

Expression (15) takes into account the absorption of direct, diffuse and reflected

solar radiation by the overground part of the thermosyphon. Problem No 2 solved.

4. Calculation of Freezing Radius

Next, a numerical study of the soil freezing radius around the thermosyphon was

performed using the classical example (Fig. 3). The ensuring the freezing of the

soil at depths from -4 to -7 m for the object in Western Siberia was the design task.

In accordance with the results of standard strength calculations, it is necessary to

lower the temperature to -0.7 ºС within 5 years before construction. The duration

of the freezing is associated with economic calculation. The main purpose of the

heat transfer calculation is to determining the freezing radius rfr - the distance from

the axis of symmetry to the isotherm -0.7ºC after 5 years at a depth of z = -5.5m.

The calculations were performed using the authors’ model and the model, which is

described in work of Gorelik and Seleznev [17].

The problem was solved in axisymmetric formulation. Thermosyphon is on the

axis r = 0. The characteristics of the thermosyphon are given in Table 1. The

thermosyphon has a total length of 9 m, is made of stainless steel, and the filled up

by ammonia. Soil properties are shown in Tables 2 and 3. Climatic conditions

correspond to the Vorkuta city and are shown in Table 4. The parameters of solar

radiation are shown in Table 5.

Fig. 3. Calculation scheme for determining

the radius of freezing around thermosiphon.

z

conl

ogl

ugl

evpllowz

evpz

upz

0z

8 m

12 m

r

sunQ

sunQ

snow cover

0T n 0T n

0T n

soil inwsurfT n Q

sunE

1Soil

2Soil

evpQ

ugQ



The nonlinear heat equation was used for the numerical study [25]:

wsoil soil w soil

Tc L T

T t

(16)

4 401inw surf air surf sun air aiurf rsQ T A QT b T Ta (17)

Markov et al. [26, 27] and Bhaskar and Choudhary [28] described the

method for calculating the thermal conductivity and isobaric heat capacity by

using transit functions.

The soil temperature at the depth of zero annual amplitudes is 0.5 °C. To

achieve the desired temperature, the snow cover thickness coefficient was 1.091,

which slightly increases the snow cover thickness (Table 4). The duration of the

calculation was 5 years. The problem is solved by the finite difference method in

an implicit scheme.

Table 1. Thermosyphon construction parameters.

lcon log lug levp Rr

1.0 1.0 4.0 3.0 0.2

Rcon δcon Revp δevp h

0.01685 0.0035 0.01685 0.0035 0.002

s εcon εog λcon λR

0.01 0.9 0.9 40 40

λevp λhi δhi λrf ρrf

40 0.06 0.025 0.506 639

νrf Lrf

2.73e-7 1.262e+6

Table 2. Thermal properties of soils.

Soil Type cth cfr λth λfr Tbf Tint

1 Sand 1280 960 2,51 2,93 -0,2 0,2

2 Clay loam 1489 1143 1,57 1,86 -0,1 0,8

Table 3. Physical properties of soils.

Soil Type ρsoil ρsk ρw,tot ρw,max ρw,nf

1 Sand 2125 1800 325 325 0

2 Clay loam 2157 1800 357 357 120

Table 4. Climate and show cover.

Month Tair vair δsn ρsn

1 -20,5 6,2 34,6 230

2 -19,6 5,9 40,0 240

3 -16,6 6,2 45,0 250

4 -9,7 5,9 36,0 283

5 -3,1 6,0 5,6 330

6 5,9 5,4 0,0 0

7 12,0 4,7 0,0 0

8 9,6 4,5 0,0 0

9 3,8 5,0 0,0 0

10 -4,5 5,7 7,3 155

11 -13,5 5,8 22,3 190

12 -17,9 6,4 29,7 217



Table 5. Solar radiation parameters.

Month S’sun, J/m2 Ssun, J/m2 Gsun, J/m2 Qsun, J/m2 Asurf, u.f.

1 21 4 11 15 0.80

2 125 24 51 75 0.79

3 341 106 153 259 0.78

4 458 203 241 444 0.69

5 486 243 362 605 0.43

6 475 260 299 559 0.24

7 584 306 276 582 0.24

8 329 154 213 367 0.24

9 181 68 130 198 0.26

10 106 25 73 98 0.62

11 43 8 20 28 0.79

12 8 2 4 6 0.80

5. Results and Discussion

Figure 4 shows the time dependence of the average thickness of the refrigerant film

in the condenser.

Analysis of the dependence in Fig. 4 shows that the maximum thermal

resistance of the condensate film is no more than 1.04e-4 m2∙K/W. This value is

significantly less than the thermal resistance of the condenser, which is about 2.46e-

2 m2∙K/W. The error created by the absence of a film in the calculation is within

the error of the numerical method. Thus, the thermal resistance of the film does not

have a significant effect on the results of calculating of freezing radius. The position

of the isotherm -0.7 ºC in the calculation without taking into account the film are

not shown here, since there are no visible differences compared to the calculation

in which, the film was taken into account. Problem No. 3 solved.

Fig. 4. Time dependence of average

thickness of liquid refrigerant film in condenser.

Figure 5 shows the temperature distribution in the soil around the thermosyphon

after 5 years.

The freezing radius rfr at a depth of z = -5.5 m of the authors’ model of

absorption of solar radiation by thermosyphon is 1.71 m and in the case Esun = 0 the

radius is 2.05 m. Thus, the calculation according to the authors’ model of

thermosyphon leads to reduction in the radius of freezing by 20%. It is obvious that

heat flow from the soil to the evaporator for the authors’ model is significantly less.

This is confirmed by the results in Fig. 6.

0

10

20

30

40

50

60

0 1 2 3 4 5 6

year

,rc m



Figure 6 shows the value of the difference in heat exchanging in evaporator

(∆Qevp) between the model of Gorelik and Seleznev [17] and the author’s model.

As can be seen, the maximum difference is up to 50 W, i.e., the authors’ model

reduces heat flow. The maximum difference is in a spring, which is associated

with an increase of absorbed solar energy. The second peak is in an autumn, when

the thermosyphon start to work. However, the autumn peak is much smaller,

which is due to the delay in decrease of air temperature relative to decrease of

solar irradiance: according to the Tables 4 and 5 the air temperature in February

is much less than in October, although the solar irradiance in February, on the

contrary, is more. Therefore, thermosyphon operates in conditions of high solar

irradiance in a spring. This is the main feature of operation of two-phase

thermosyphons in conditions of subarctic climate.

The values Esun and ∆Qevp differ by about 3 to 4 times. Despite the heating by

solar radiation, the heat flow from the soil to the evaporator is reduced by no more

than 35% of Esun due to an increase in the refrigerant and soil temperature. The

reducing of freezing radius due to the influence of solar radiation to can be achieved

by an increase in the heat transfer coefficient in the condenser in accordance with

equation (2). This can be implemented by increasing in the number of fins or the

length of the condenser. Problem No. 4 solved.

(a) Esun according to formula (15). (b) Esun = 0 according to Gorelik

and Seleznev [17].

Fig. 5. Temperature distribution in soil around the thermosyphon.

Fig. 6. Difference in heat flow in the two

models and the heat flux of solar radiation.

0 2 4

,z m0

1

2

3

4

5

6

7

8

9,r m

frr

1.71m

0.3

0.2

0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

,T C

0.3

0.2

0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

,z m,T C

frr

0

1

2

3

4

5

6

7

8

90 2 4

,r m

2.05m

0

50

100

150

200

0 1 2 3 4 5 6

Ряд1

Ряд2

,evpQ W

,sunE W

year

W



6. Conclusions

The authors derived formulas for calculating the average film thickness of the liquid

refrigerant on the inner surface for all parts of the thermosyphon: condenser,

overground pipe, underground thermal insulated pipe, and evaporator (8) - (11).

The authors used the iterative method for solving the Nusselt equation.

Numerical study has shown that the thermal resistance of the refrigerant film is 2

orders less than the thermal resistance of the condenser if the length of evaporator is

3 m. Thus, the practical calculations of the temperature regime of the soil can be done

without taking into account refrigerant film thickness for short evaporator part.

The formula for calculating absorbed direct, diffuse and reflected solar radiation

by the condenser and overground pipe is derived (15). Required data for a formula

coincide with meteorological quantities: direct normal irradiance, direct horizontal

irradiance, diffuse horizontal irradiance, albedo of ground surface.

A comparison of two models of system two-phase thermosyphon - soil -

atmosphere showed that the authors’ model reduces freezing radius by 20%. The

significant difference between the models is in the method of calculation of

absorbed solar radiation by condenser and overground pipe of thermosyphon. Thus,

in a subarctic climate with high solar radiation the safe operation of buildings and

structures can be ensured only if the distance between the heat stabilizers is

significantly reduced due to strong heating of the condenser by solar radiation. The

result is extremely important in designing of buildings and structures in permafrost.

Nomenclatures

Asurf Albedo of ground surface, u.f.

bair Back radiation factor of atmosphere, u.f.

cfr Isobaric heat capacity of frozen soil, J kg-1 K-1

csoil Isobaric heat capacity of soil, J kg-1 K-1

cth Isobaric heat capacity of thawed soil, J kg-1 K-1

Ed Absorbed diffuse solar radiation by condenser, W

Esun Absorbed diffuse solar radiation by thermosyphon, W

Fa Surface area of solar radiation diffusion in the atmosphere, m-2

Fcon Condenser area, m-2

Gsun Diffuse horizontal irradiance, W m-2

g Acceleration of gravity, m s-2

Ha Vertical distance from the surface of the condenser to the surface

of solar radiation diffusion, m

K Overall heat transfer coefficient, W m-1 K-1

Kcon Overall heat transfer coefficient of condenser, W m-1 K-1

Kevp Overall heat transfer coefficient of evaporator, W m-1 K-1

Kog Overall heat transfer coefficient of overground pipe, W m-1 K-1

Kug Overall heat transfer coefficient of underground pipe, W m-1 K-1

Lrf Heat of refrigerant vaporization, J kg-1

Lw Heat of fusion, J kg-1

lcon Length of condenser, W m-1

levp Length of evaporator, W m-1

log Length of overground pipe, W m-1

lug Length of underground pipe, W m-1



na Inner normal vector of solar radiation diffusion surface

ncon Condenser surface normal vector

n Outward ground-normal vector

Pra Prundtl number of air, d.l.

Qinw Inward heat flux on the surface of the ground, W m-2

Qsun Global horizontal irradiance, W m-2

Qup Inward heat flux in underground pipe, W m-1

Qevp Inward heat flux in evaporator, W m-1

qt Linear heat source in thermosyphon, W m-1

qug Linear heat source in underground pipe, W m-1

R Distance from the surface of the condenser to the surface of solar

radiation diffusion, m

Rcon Condenser radius, m

Revp Evaporator radius, m

Rr Fin radius, m

r Projection of R on the surface of the ground, m

rfr Radius of freezing, m

SN Surface of unfinned area of condenser, m2

Ssun Direct horizontal irradiance, W m-2

S’sun Direct normal irradiance, W m-2

Sv Direct vertical irradiance, W m-2

s Distance between fins, m

T Temperature of soil, K

Tair Temperature of air, K

Tbf Soil freezing point, K

Tg Temperature of refrigerant gaseous phase, K

Tint Soil freezing interval, K

t Time, s

Va Wind speed, m s-1

z0 Ground level, m

zevp Top of evaporator, m

zlow Bottom of thermosyphon, m

zup Top of thermosyphon, m

Greek Symbols

∇∙ Divergence operator

∇ Gradient operator

αN Convective heat transfer coefficient for overground pipe,

W∙m-2∙K-1

αR Convective heat transfer coefficient for side surface of condenser

fin, W∙m-2∙K-1

αr Convective heat transfer coefficient for condenser fin, W∙m-2∙K-1

αsurf Convective heat transfer coefficient on the surface of the ground,

W∙m-2∙K-1

δcon Condenser wall thickness, m

δevp Evaporator wall thickness, m

δr Refrigerant film thickness, m

δrc Refrigerant film thickness in lowest point of condenser, m

δrca Average refrigerant film thickness in condenser, m

δrea Average refrigerant film thickness in evaporator, m



δroa Average refrigerant film thickness in overground pipe, m

δrua Average refrigerant film thickness in underground pipe, m

δsnow Snow thickness, m

εcon Emissivity of condenser surface, u.f.

εog Emissivity of overground pipe surface, u.f.

εsurf Emissivity of ground surface, u.f.

θ Angle in a cylindrical coordinate system, rad

λa Thermal conductivity of air, W m-1K-1

λcon Thermal conductivity of condenser material, W m-1K-1

λevp Thermal conductivity of evaporator material, W m-1K-1

λfr Thermal conductivity of frozen soil, W m-1K-1

λhi Thermal conductivity of heat insulation, W m-1K-1

λR Thermal conductivity of material of finning, W m-1K-1

λrf Thermal conductivity of refrigerant, W m-1K-1

λth Thermal conductivity of thawed soil, W m-1K-1

νa Air viscosity, m2 s-1

νrf Liquid refrigerant viscosity, m2 s-1

ρrf Density of liquid refrigerant, kg m-3

ρsk Density of dry soil, kg m-3

ρsnow Density of the snow, kg m-3

ρsoil Density of soil, kg m-3

ρw,max Maximal content of water in the soil, kg m-3

ρw,nf Content of non-freezing water in the soil, kg m-3

ρw,tot Content of water in the soil, kg m-3

σ0 Stefan Boltzmann's constant, W m-2 K-4

φa Angle between R and na

φcon Angle between R and ncon

References

1. Viktorovich, L.Y.; Nikolaevich, S.A.; Vladimirovich, P.V.; Yurvevich, Z.M.;

and Dmitrievich, K.V. (2014). Selection optimal technical solutions for laying

the oil pipeline to ensure reliable operation of the pipeline system «Zapolyarye -

Pur-Pe» on the basis of forecasting thermotechnical calculation. Transportation

and Storage of Petroleum Products and Hydrocarbons, 1, 3-7. (in Russian).

2. Ershov, E.D. (1995). Physical and chemical bases of permafrost studies (1st

ed.). Moscow: Lomonosov Moscow State University.

3. Kalyuzhnyy, I.L.; and Lavrov, S.A. (2012). Hydrophysical processes in the

catch basin: Experimental studies and modelling. (1st ed.). St. Peterburg:

Nestor-Istoriya.

4. Kutvitskaya, N.B.; and Minkin, M.A. (2014). Design of beds and foundations

of infrastructure for oil-gas condensate fields under complex frozen-soil

conditions. Soil Mechanics and Foundational Engineering, 51(1), 36-41.

5. Markov, E.V.; Pulnikov, S.A.; and Sysoev, Y.S. (2018). Evaluation of the

effectiveness of ring thermal insulation for protecting a pipeline from the

heaving soil. Journal of Engineering Science and Technology (JESTEC),

13(10), 3344-3358.



6. Jafari, D.; Franco, A.; Filippeschi, S.; and Di Marco, P. (2016). Two-phase

closed thermosyphons: A review of studies and solar applications. Renewable

and Sustainable Energy Reviews, 53, 575-593.

7. Jadhav, A.S.; and Patil, S.A. (2016). Two phase thermosyphon - a review of

studies. International Journal of Engineering Sciences and Research

Technology, 5(1), 193-205.

8. Lee, Y.; and Mital, U. (1972). A two-phase closed thermosyphon.

International Journal Heat and Mass Transfer, 15(9), 1695-1707.

9. Terdtoon, P.; Charoensawan, P.; and Chaitep, S. (2001). Corrosion of tubes

used in thermosyphon heat exchanger for waste heat recovery system: A case

of internal surface. Heat Transfer Engineering, 22(4), 18-27.

10. Park, Y.J.; Kang, H.K.; and Kim, C.J. (2002). Heat transfer characteristics of

a two-phase closed thermosyphon to the fill charge ratio. International Journal

of Heat and Mass Transfer, 45(23), 4655-4661.

11. Zhu, H.; Wang, J.X.; Zhang, Q.H.; and Tu, C.J. (2004). Experimental study on

transient behaviour of semi-open two-phase thermosyphon. Journal of

Zhejiang University Science, 5(12), 1565-1569.

12. Noie, S.H. (2005). Heat transfer characteristics of a two-phase closed

thermosyphon. Applied Thermal Engineering, 25(4), 495-506.

13. Carvajal-Mariscal, I.; Sanchez-Silva, F.; and Polupan, G. (2012). Development

of high efficiency two-phase thermosyphons for heat recovery. Heat

Exchangers - Basics Design Applications, 1(1), 97-116.

14. Khazaee, I. (2014). Experimental investigation and comparison of heat transfer

coefficient of a two phase closed thermosyphon. International Journal of

Energy and Environment (IJEE), 5(4), 495-504.

15. Lotfi, M.; Ghasemzadeh, R.; Kargar, A.; and Behfar, R. (2014). Evaluation of

convective and radiation heat loss on thermosyphon pipe. Proceedings of the

International Conference on Agriculture, Food and Environmental

Engineering (ICAFEE). Kuala Lumpur, Malaysia, 7-11.

16. Gandal, Y.S.; and Kale, V.M. (2014). Comparative study of two phase closed

thermosyphon with different fluids and fill volume ratio. Journal of

Mechanical and Civil Engineering, 11(6), 82-92.

17. Gorelik, Y.B.; and Seleznev, A.A. (2016). About efficiency of the condenser

finning of the short vertical thermostabilizer for building on permafrost. Earth

Cryosphere, 10(2), 78-89.

18. de Haan, V.-O.; Gommers, R.; and Rowe J.M. (2017). Thermodynamic

calculations of a two-phase thermosyphon loop for cold neutron sources.

Cryogenics, 85, 30-43.

19. de Haan, V.-O.; and Knudsen, K.D. (2019). Application of a two-phase

thermosyphon loop calculation method to a cold neutron source. Cryogenics,

97, 55-62.

20. Özbaş, E. (2019). Experimental study of thermal performance and pressure

differences of different working fluids in two-phase closed thermosyphons

usıng solar energy. Journal of Polytechnic, 22(1), 121-128.

21. Ali, K.K.; and Hassan, H.A. (2018). A numerical - experimental study of

turbulent heat transfer flow a cross square cylinder in a channel.



International Journal of Mechanical Engineering and Technology (IJMET),

9(8), 447-461.

22. Menni, Y.; Azzi, A.; and Zidani, C. (2017). Use of wasted triangular-shaped

baffles to enhance heat transfer in a constant temperature-surfaced rectangular

channel. Journal of Engineering Science and Technology (JESTEC), 12(12),

3251-3273.

23. Pathak, K.K.; Giri, A.; and Lingfa, P. (2017). Evaluation of heat transfer

coefficient of a shrouded vertical array of heat sinks (fins): A computational

approach. International Journal of Mechanical Engineering and Technology

(IJMET), 8(4), 319-326.

24. Sidibé, M.; Soro, D.; Fassinou, W.F.; and Touré, S. (2017). Reconstitution of

solar radiation on a site of the littoral in Cȏte D'ivoire. International Journal

of Engineering Research and Technology, 10(1), 19-34.

25. Markov, E.V.; Pulnikov, S.A.; and Sysoev, Y.S. (2018). Methodology for

calculating the safe stop time of underground pipeline with high pour point oil.

International Journal of Civil Engineering and Technology (IJCIET), 9(8),

1699-1705.

26. Markov, E.V.; Pulnikov, S.A.; and Sysoev, Y.S. (2018). Study of frost mound

temperature condition. International Journal of Civil Engineering and

Technology, 9(9), 10-15.

27. Markov, E.V.; Pulnikov, S.A.; and Sysoev, Y.S. (2018). Methodology for

calibration of soil heat transfer model In accordance with results of

measurements. International Journal of Civil Engineering and Technology

(IJCIET), 9(9), 1721-1727.

28. Bhaskar, B.S.; and Choudhary, S.K. (2017). Experimental investigation of heat

transfer through porous material heat exchanger. International Journal of

Engineering Research and Technology, 10(1), 51-60.

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