This document presents a numerical analysis of heat transfer in helically grooved tubes. It discusses heat transfer enhancement techniques such as internal grooves that can increase surface area and turbulence. The objective is to numerically investigate the effects of helical groove parameters like number, helix angle, depth and width on heat transfer efficiency. Validation with previous studies shows maximum errors of 15% for friction factor and 13% for Nusselt number. Results show that heat transfer and pressure drop increase with higher groove number but decrease with larger helix angle.

1. Numerical analysis of Heat transfer
in helically grooved tubes

2. Introduction
• Heat transfer enhancement techniques generally reduce the
thermal resistance either by increasing the effective heat transfer
surface area or by generating turbulence in the fluid flowing inside
the device.
• There are many heat tranfer enhancement techniques like twisted
tape insert, wire coil insert, pipe insert, ribs and perforated tapes,
grooves etc..
• Compared to other heat transfer enhancement techniques,
internal grooves has an advantage of having a better heat transfer
effect than its pressure drop penalty.
NIT SILCHAR, Dept. of Mechanical Engineering 2

3. Literature review
Reference Key findings
Heat transfer
enhancement techniques
and their thermal
performance factor[6]
Chirag maradiya, jeetendra
vadher, Ramesh Agarwal
Twisted tape :- Taper twisted tape does not achieve the thermal performance factor(TPF) more
than 1.05 but increases the heat transfer rate.
Fins :- Ribbed pipe increases heat transfer compared to smooth pipe. At low Re, the performance of
ribbed pipe is good but its effect is reduced with an increase in Re.
Pipe Insert :- Pipe inserts improved the heat transfer considerably with low flow resistance. TPF of
2.7 was obtained at Re of 4000 and it decreased with increase in Re.
Numerical Analysis of
Turbulent Flow and Heat
Transfer in Internally
Finned Tubes
Liu et al. [7]
• Single-phase heat transfer enhancement in internally finned tubes is investigated numerically.
• Resistance coefficient and Nusselt number both increase with the increment of fin number, helix
angle and width and height of fin, among which the helix angle has the largest impact on the
heat transfer enhancement.
Heat transfer & thermal
stress analysis in transverse
grooved tubes[5]
Veysel Ozcheyhan and Necdet
Altuntop
• Investigate the heat transfer and thermal stress distributions in the circular grooved tube and
effects with the distance between two grooves in tube.
• Heat transfer increased & inner surface temperatures decrease owing to the use of grooved tube.
NIT SILCHAR, Dept. of Mechanical Engineering 3

4. Research Gap
• Previous research is done for internal transverse grooves, internal
fins
• There are only few numerical studies for Helical grooves inside the
reciever pipe.
• There is no prior work done for helical grooves, where parameters
such as helix angle, pitch, groove width, groove height are varied
and optimum geometry for better thermal performance is found.
NIT SILCHAR, Dept. of Mechanical Engineering 4

5. Objective
• The objective of this work is numerical investigation of a helical
grooves inside the heat pipe(for solar parabolic trough collector) .
An increase in thermal efficiency is calculated with helical grooves
and compared with the smooth pipe.
NIT SILCHAR, Dept. of Mechanical Engineering 5

6. Validation
• Heat transfer and thermal stress
analysis in grooved tubes by Veysel
O¨ Zceyhan and Necdet Altuntop is
considered.
• The analysis has been conducted for
three different kinds of internally
grooved tubes mean inlet water
velocity of 0.3 m/s. Constant
temperature of 450 K was applied
from the external surface of the
tube. Energy and governing flow
equations were solved using finite
difference scheme. Commercial steel
has been selected as tube material.
NIT SILCHAR, Dept. of Mechanical Engineering 6
Schematic diagram of cross section of circular grooved
tube.

7. Validation
Veysel O¨ Zceyhan Calculated values
Tsurface 410.47 K 412.13 K
Tout 301.23 K 301.67 K
f 0.0096 0.0105
NIT SILCHAR, Dept. of Mechanical Engineering 7
Measured values are in a acceptable rangle of 5% difference

8. Methodology
• Numerical simulations are performed to study the heat transfer
characteristics considering the range of parameters, including groove
number, helix angle, groove depth & groove width.
• Nusselt number and friction factor are calculated with variation of
grooves, helix angle, groove depth and groove width.
• Thermal performance is calculated for 28 different cases, and optimum
conditions are found out.

9. Geometric model
• The helical grooves are placed along the axis with constant pitch and
helix angle.
• The pipe studied have the inner diameter of 0.09m and outer diameter of
0.11m.
• Helical grooves have the depth of 1 mm and width of 2 mm and helix
angles of 20°, 30°,40°,50° at pitch of 75 mm, 53 mm, 36 mm, 23 mm.
• Helical grooves of 4 turns, 5 turns and 6 turns at helical angles of 20°,
30°, 40°, 50° have been studied.
• Helical grooves with widths of 1.5 mm, 2.5 mm and heights of 0.75 mm,
1.25 mm at helical angles of 20°, 30°, 40°, 50° have been studied.
• Pitch is considered as the length of the computational domain for all the
cases.

10. S.no
Helical
angle
pitch (mm)
No. of
grooves
height
(mm)
width
(mm)
1 50 75 6 1 2
2 50 75 5 1 2
3 50 75 4 1 2
4 50 75 5 1.25 2
5 50 75 5 1 2
6 50 75 5 0.75 2
7 50 75 5 1 1.5
8 50 75 5 1 2
9 50 75 5 1 2.5
10 40 53 6 1 2
11 40 53 5 1 2
12 40 53 4 1 2
13 40 53 5 1.25 2
14 40 53 5 1 2
15 40 53 5 0.75 2
16 40 53 5 1 1.5
17 40 53 5 1 2
18 40 53 5 1 2.5
S.no
Helical
angle
pitch (mm)
No. of
grooves
height
(mm)
width
(mm)
19 30 36.3 6 1 2
20 30 36.3 5 1 2
21 30 36.3 4 1 2
22 30 36.3 5 1 1.5
23 30 36.3 5 1 2
24 30 36.3 5 1 2.5
25 30 36.3 5 1.25 2
26 30 36.3 5 1 2
27 30 36.3 5 0.75 2
28 20 23 6 1 2
29 20 23 5 1 2
30 20 23 4 1 2
31 20 23 5 1.25 2
32 20 23 5 1 2
33 20 23 5 0.75 2
34 20 23 5 1 1.5
35 20 23 5 1 2
36 20 23 5 1 2.5
Geometric model configurations

11. Geometry
0.08 m
0.009 m0.011 m
Helix angle = 50° No.of turns = 5
Schematic diagram of cross section of helical grooved tube.

12. Geometry
Schematic diagram of helical grooved tube.
Helix angle = 50°
No.of turns = 4

13. Geometry
0.002 m
0.001 m
Schematic diagram of cross section of helical groove

14. Helix angle = 20° No.of turns = 5 pitch=0.023 m l = 0.08 m
Helix angle = 30° No.of turns = 5 pitch =0.036 m l = 0.08 m

15. Helix angle = 40° No.of turns = 5 pitch=0.057 m l = 0.08 m
Helix angle = 50° No.of turns = 5 pitch=0.075 m l = 0.08 m

16. Helix angle = 50°
No.of turns = 5
Pitch of helical groove =0.075 m
Helix angle = 50°
No.of turns = 4
Pitch of helical groove =0.075 m
Helix angle = 50°
No.of turns = 6
Pitch of helical groove =0.075 m
Pipe with different turns

17. Helix angle = 50°
No.of turns = 5
Depth of groove = 0.75 mm
Helix angle = 50°
No.of turns = 5
Depth of groove = 1 mm
Helix angle = 50°
No.of turns = 5
Depth of groove = 1.25
mm
1 mm
1.25 mm0.75 mm
2 mm
2 mm
2 mm
Pipe with different depths

18. Helix angle = 50°
No.of turns = 5
Width of groove = 1 mm
Helix angle = 50°
No.of turns = 5
Width of groove = 1.5 mm
1 mm
1.5 mm
1 mm
2 mm
Helix angle = 50°
No.of turns = 5
Width of groove = 2.5 mm
1 mm
2.5 mm
Pipe with different width

19. • A grid independence study is carried out to determine a usable
grid for numerical simulation.
• The mesh number chosen in this paper is the minimum of the
mesh number that does not affect the simulation results.
• To prepare the mesh, the Inflation was used near wall surfaces.
Face, edge & body sizing on typical edges, faces and bodies were
used. Trapezoidal elements are used mainly for meshing.
• For accurate simulation, mesh near wall is properly sized, y+ value
is taken as 1. first layer thickness is taken as 0.03 mm.
Grid Generation

20. Grid generation
Geometry after meshing

21. Grid Skewness
Skewness
Percentageofthegrid
Average Skewness of grid is 0.211 which is below 0.7, so the grid generation is
credible as most values are below 0.6.

22. Grid independence test
• When grid numbers increases from 398154 to 528196, difference
of both Nu & f are in between the acceptable range of 5%
Standard mesh Mesh 2 Mesh 3
Nodes 398154 528196 687943
Elements 1401592 1936020 2312860
Nu 147.878 148.005 148.256
f 0.14024 0.14056 0.14062

23. Simplified model geometry
Fluid DomainSolid Domain
Q
Outflow Inlet

24. Boundary conditions
• We set inlet boundary as velocity inlet, the temperature of which is
300 K while outlet boundary as outflow.
• Fluid domain is taken as single phase water with constant physical
properties.
• Inlet water velocity is taken as 0.5 m/s.
• The constant heat flow boundary condition and the given heat flux
is q = 1,10,000 W/m2.
• Solid domain is taken as steel.

25. Computational physics
• k-ω SST model is selected to obtain the detailed flow condition
near the tube wall.
• The coupling solution of pressure and velocity is SIMPLE
algorithm, and the momentum and energy equations are solved by
the second-order upwind scheme.
• The values of residuals in the convergence conditions are less than
1×10-6.

26. Verification of the Numerical Procedure
• Average f can be calculated using Darcy formula[3] :
𝑓 =
2 ∙ Δ𝑃 ∙ 𝐷
𝜌𝑢2
• Average Nusselt number[3] can be calculated:
𝑁𝑢 =
𝑞 ∙ 𝐷
𝑘 ∙ (𝑇 𝑤 − 𝑇𝑓)
• For forced convection heat transfer in smooth circular tubes, the resistance
coefficient f can be calculated using the Filonenko formula[1]
𝑓 = 1.82 ∗ ln 𝑅𝑒 − 1.64
−2
• Nusselt number can be calculated according to the Gnielinski formula[2]:
𝑁𝑢 = 0.012 ∗ Pr0.4
(R𝑒0.87
− 280)

27. Comparison between the calculated value and the theoretical value in smooth tubes. (A) f (B) Nu.
Verification of the Numerical Procedure
85.7
158.5
218.5
270.6
321.3 370.9
419.5
74.4
141.6
204.4
264.5
322.6
379.2
434.6
0
50
100
150
200
250
300
350
400
450
500
0 20000 40000 60000 80000
Nusseltnumber
Reynolds number
Calculated values
Gnielinski
0.00484
0.00386
0.00326
0.00289
0.00266
0.00249
0.00238
0.00425
0.00363
0.00333
0.00314
0.00300
0.00289
0.00281
0.002
0.003
0.003
0.004
0.004
0.005
0.005
0 20000 40000 60000 80000
Frictionfactor
Reynolds number
Calculated values
Filonenko

28. Verification of the Numerical Procedure
• The calculated values of f and Nu are compared with the values of
Filonenko formula and Gnielinski formula, respectively. Calculated
value of f & Nu are in good agreement with calculated value.
• The maximum error between the calculated value and the
theoretical value of the resistance coefficient is 15%.
• The maximum error between the calculated value and the
theoretical value of nusselt number is 13.13%.

29. Results
• Numerical simulations are performed to do study the flow and heat
transfer charecteristics considering range of parameters including
number of grooves, helix angle, groove height & groove width.
• Nusselt number and friction factor is calculated at 4, 5 & 6 grooves,
each at 20°, 30°, 40° & 50° helix angles and the groove height and
groove width are fixed 1 mm & 2mm.
• Nusselt number and friction factor is calculated at widths of 1.5, 2 &
2.5 mm and at height of 1 mm each at 20°, 30°, 40° & 50° helix angles.
• Nusselt number and friction factor is calculated at heights of 0.75, 1 &
1.25 mm and at width of 2 mm each at 20°, 30°, 40° & 50° helix angles.

30. The effect of the groove number on the Nu and f at different helix angles. (A) Nu. (B) f.
A B
129.0
132.0
141.1
161.1
127.7
131.3
135.7
159.2
125.0
127.9
132.8
147.3
120
125
130
135
140
145
150
155
160
165
15 20 25 30 35 40 45 50 55
Nu
Helix angle
N=6 N=5 N=4
0.092
0.099
0.114
0.150
0.091
0.097
0.110
0.138
0.090
0.095
0.105
0.127
0.08
0.09
0.10
0.11
0.12
0.13
0.14
0.15
0.16
0 10 20 30 40 50 60
Frictionfactor
Helix angle
N=6 N=5 N=4

31. The Temperature cloud diagrams and velocity cloud diagram with different groove numbers. (A) N = 4. (B) N =5. (C) N = 6.
A
B
C

32. Effect of Groove Number
• The groove depth and groove width are fixed 1 mm & 2mm, and the number
of grooves are 4, 5 & 6 respectively.
• It can be seen that the Nu and f both increase with the increase of the
number of grooves and Nu and f both decrease with the increase of helix
angle.
• In grooves, because of sharp sides, high shear stress is generated and heat
transfer convection is high, as the number of grooves increases, the number
of sharp corners increase, resulting in an increase in both f and Nu.
• As the helix angle increases, area exposed for heat transfer decreases and ,
the Nusselt number increases with decrease in helix angle.
• The bigger the helix angle,there will be greater obstruction to the incoming
flow . Therefore, the incoming flow has a stronger impact on the windward
side of the groove, and f and Nu both increase.

33. A B
The effect of the groove depth on the Nu and f at different helix angles. (A) Nu. (B) f.
0.091860.090510.08951
0.098370.097190.09556
0.11498
0.11027
0.10697
0.14772
0.13843
0.13472
0.08
0.09
0.10
0.11
0.12
0.13
0.14
0.15
0.16
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Frictionfactor
Groove depth (mm)
50 40 30 20
129.2
127.7
122.6
133.3
131.3
125.7
141.5
135.7
131.4
163.0
159.2
150.5
120
125
130
135
140
145
150
155
160
165
170
0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 1.3
Nu
Groove depth (mm)
50 40 30 20

34. Cloud pictures of velocity and temperature with different groove depths. (A) d = 0.75 mm. (B) d = 1 mm. (C) d = 1.25 mm.
B
A
C

35. Effect of Groove depth
• The number of grooves are 5, the fixed groove width is 2 mm,
and groove depth is 0.75, 1, 1.25 mm respectively.
• It can be seen that both Nu & f both increase with increase of
groove depth as it increases the heat transfer area on both
groove sides and promotes the interactions between the
groove.
• Nu & f both increase with groove height, because the higher
the groove depth, the greater the disturbance to the fluid near
the wall surface. Therefore, the heat transfer coefficient is
enhanced and the resistance coefficient is increased.

36. A B
The effect of the groove width on the Nu and f at different helix angles. (A) Nu. (B) f.
124.9 127.7
129.9
132.2 133.4
135.3
134.5 135.7
143.5142.7
159.2
163.8
120
130
140
150
160
170
1.25 1.5 1.75 2 2.25 2.5 2.75
Nu
Groove width (mm)
50 40 30 20
0.08639
0.09051
0.092770.09387
0.09719
0.10197
0.10234
0.11027
0.12164
0.11890
0.13843
0.15859
0.08
0.09
0.10
0.11
0.12
0.13
0.14
0.15
0.16
0.17
1.25 1.5 1.75 2 2.25 2.5 2.75
frictionfactor
Groove width (mm)
50 40 30 20

37. The cloud picture of velocity and temperature with different groove width. (A)w = 1.5 mm. (B) w = 2 mm. (C) w = 2.5 mm.
A
B
C

38. Effect of groove width
• The number of grooves are 5, the fixed groove depth is 1 mm, and
groove width is 1.5, 2, 2.5 mm respectively.
• It can be seen that the increase of groove width means that the
area of the groove increases, equivalently the area in contact with
the fluid is larger, and grooves are more impacted by the fluid, so
heat transfer and friction resistance are both enhanced.

39. Thermal Performance factor
1.426
1.4631.457
1.193
1.471
1.505
1.485
1.204
1.475
1.543
1.516
1.202
1.1
1.2
1.3
1.4
1.5
1.6
10 20 30 40 50
ThermalPerformanceFactor
Helix angle
N=4
N=5
N=6
• Thermal Performance is highest for
the helix angle of 40°.
• Thermal performance increases with
the number of grooves, it’s highest for
6 and least for 4.
Thermal Performance factor = Nu
Nus
f
fs
• The effectiveness of a heat transfer
enhancement technique is evaluated
by the Thermal Performance Factor
which is a ratio of the change in the
heat transfer rate to change in friction
factor of a smooth pipe.

40. Thermal Performance factor
1.478 1.471 1.467
1.506 1.505 1.502
1.489 1.485 1.479
1.200 1.204
1.193
1.1
1.2
1.3
1.4
1.5
1.6
0.7 0.8 0.9 1 1.1 1.2 1.3
ThermalPerformanceFactor
Depth of groove (mm)
50° 40° 30° 20°
1.437
1.471
1.5051.460
1.505
1.537
1.451
1.485
1.515
1.179
1.204
1.260
1.1
1.2
1.3
1.4
1.5
1.6
1.25 1.5 1.75 2 2.25 2.5 2.75
ThermalPerformanceFactor Width of groove (mm)
50° 40° 30° 20°
Thermal performance factor with change in width of groove and depth of groove a) depth b) width
A B

41. Thermal Performance factor
• Thermal performance factor is highest for the helix angle
of 40° and is least for 20°.
• Thermal performance factor is almost constant with the
variation in depth of groove.
• Thermal performance factor increases with the width of
groove.
• Pipe with 6 grooves and helix angle of 40° has the highest
thermal performance factor.

42. Conclusion
• The parameters are number of grooves(4-6), groove depth (0.7 –
1.25 mm), groove width (1.5 – 2.5mm), helix angle (20–50°) and
the operating condition is Re = 11250.
• Compared with groove depth, groove width has a greater influence
on the flow and heat transfer of internally grooved tubes.
• Among all the geometrical parameters, the helix angle has the
largest influence on the flow and heat transfer in the internally
grooved tube.
• The ideal geometric configuration from my study is helix angle of
40° (pitch=53mm), width of 2.5mm and depth of 0.75mm and
no.of grooves to be 6.

43. References
1. Filonenko, G. K. (1954). Hydraulic resistance in pipes. Teploenergetika 1, 40–44.
2. Gnielinski, V. (1975). New Equations for Heat and Mass Transfer in the Turbulent Flow in
Pipes and Channels. NASA STI/Recon Technical Report A, 75.
3. Dawid Taler, and Jan Taler. Simple heat transfer correlations for turbulent tube flow
4. Zhanwei Liu et al. Numerical Analysis of Turbulent Flow and Heat Transfer in Internally
Finned Tubes
5. Veysel et al. Heat transfer & thermal stress analysis in grooved tubes
6. Chirag et al. Heat transfer enhancement techniques and their thermal performance factor
7. Liu et al. Numerical Analysis of Turbulent Flow and Heat Transfer in Internally Finned
Tubes

44. THANK YOU