Journal of Engineering and Technology for Industrial Applications 
 

 

Manaus, v.8 n.34, p. 12-19. Mar/Apr, 2022 

DOI: https://doi.org/10.5935/jetia.v8i34.804 
 

 

RESEARCH ARTICLE                                                                                                                                             OPEN ACCESS 

 

 

ISSN ONLINE: 2447-0228  

Journal homepage: www.itegam-jetia.org 

 

HEAT TRANSFER ENHANCEMENT IN A P-SHAPE FINNED RADIAL HEAT 

SINK SUBJECTED TO NATURAL CONVECTION: THERMAL 

SIGNIFICANCE OF SLOT AND DIMPLES IN FIN 

Ibrahim Fetuga*1, T. Olabode Olakoyejo2, O. Adekunle Adelaja3 and K. Joshua Gbegudu4 

1, 2, 3, 4 Department of Mechanical Engineering, University of Lagos – Akoka. Yaba-Lagos, Nigeria. 

1 http://orcid.org/0000-0002-1943-4234 , 2 http://orcid.org/0000-0001-9942-1339 , 3 http://orcid.org/0000-0001-9175-8332 , 
4 http://orcid.org/0000-0003-2417-2520  

Email: *fetugaebraheem@gmail.com, oolakoyejo@unilag.edu.ng, aadelaja@unilag.edu.ng, jk.gbegudu@gmail.com 

ARTICLE INFO  ABSTRACT 

Article History 

Received: March 05th, 2022 

Accepted: April 24th, 2022 

Published: April 30th, 2022 
 

 
 

This study presents the optimum design of the radial heat sink for light-emitting diode (LED) 

under natural convection. A radial heat sink with a hollow circular base and a P-shape fin 

type incorporated with either slots or both slots and dimples was numerically investigated 

using the ANSYS (Fluent) commercial code, with the aim of achieving better cooling 

performance at a lower heat sink mass.  The average temperature (𝑇𝑎𝑣𝑔) and mass of the HS 

for various model designs, namely; Type A (HS with plain fin), Type B (HS with slot) and 

Type C (HS with both dimples and slot) were compared to select the best configuration. The 

effect of heat flux (700 ≤ 𝑞̇ ≤ 1900)  on average temperature of radial heat sink was 

investigated. It was found that for all three models, the temperature difference between the 

HS and the ambient air of the fluid domain linearly increased with heat flux. At 𝑞̇ =
1900𝑊/𝑚2, when compared to Type A (HS with plain fins), Type C (HS with slot and 

dimples) models offered the best cooling performance, followed by Type B where the mass 

and average temperature of the heat sink is reduced by 13.7% and 5.1%, 8.3% and 1%, 

respectively. 

 

Keywords: 

Radial heat sink, 

P-shape fin, 

Slot, 

Dimples, 

Natural convection. 

 

 

 

Copyright ©2022 by authors and Galileo Institute of Technology and Education of the Amazon (ITEGAM). This work is licensed 

under the Creative Commons Attribution International License (CC BY 4.0). 

 

I. INTRODUCTION 

Cooling through free convection is suitable, especially for 

small electronics components such as LEDs because it is relatively 

simple, less expensive and eco- friendly. LED is known for its 

durability, efficiency, and cost-effectiveness. Thus, LEDs replaced 

much extant lighting devices. Studies have revealed that more than 

50% of the power required by LEDs is transformed into heat. 

Therefore, it is important to sufficiently cool the LED device for 

smooth operation and higher efficiency. Cooling of the electronics 

component may be active or passive, the most widely used device 

for passive cooling is the heat sink. To meet the demands of higher 

thermal performance for LED devices, the challenges of 

cumbersome heat sinks are always encountered. Therefore, 

cutting-edge technology, perhaps in the aspect of heat sink design, 

materials selection, mass reduction, and as such, is required to 

improve the heat sink's performance. 

II. THEORETICAL REFERENCE 

Several studies have been conducted on the cooling 

performance of the HS for LED devices. Costa and Lopes [1] used 

ANSYS (CFX) commercial codes to conduct a computational 

study on a radial HS having protruded fins under free convection. 

They revealed that the average temperature of the HS is 

insignificantly influenced by the thickness of the fin. Furthermore, 

it was pointed out that the heat sinks average temperature initially 

declined, and then increased with the number of fins. Jang et al. [2] 

numerically performed a parametric study on the arrays of pin fins 

at various height configurations. They observed that the HS with 

the tallest outermost fin yielded the optimum cooling performance. 

Sparrow and Vemuri [3] evaluated the heat transfer characteristics 

of a pin-fin heat sink for several orientations of the installation 

under the conditions of radiation and natural convection. They 

found that the vertical pin-fin provided the best cooling 

http://orcid.org/0000-0002-1943-4234
http://orcid.org/0000-0001-9942-1339
http://orcid.org/0000-0001-9175-8332
http://orcid.org/0000-0003-2417-2520


 
 
 

 

Fetuga et al., ITEGAM-JETIA, Manaus, v.8 n.34, p. 12-19, Mar/Apr, 2022. 

 

 

performance. Yildiz and Yuncu [4] demonstrated a study on the 

thermal performance (TP) of an annular fin mounted on a cylinder 

subjected to natural convection. They indicated that the highest 

heat transfer coefficient (HTC) is obtained at an optimum spacing 

between the fins. Tijani and Jaffri [5] observed the influence of 

perforations on pin-fin HS subjected to force convection. They 

concluded that the HTC is improved by 40% in a HS with 

perforated fins. Jaffal [6] performed both experimental and 

numerical studies on the TP of HS having different fin designs. He 

concluded that heat flux strongly influences the heat transfer rate 

and, more so, HS with perforated fins performed better than others. 

Rath et al. [7] numerically examined the thermal characteristics of 

radial HS consisting of longitudinal corrugated fin with three 

different number of cycles (one cycle, two cycles, and three 

cycles). They revealed that the highest value of fin effectiveness 

and Nusselt number was obtained in corrugated fins with three 

cycles, followed by two cycles and one cycle. Tehmina et al. [8] 

adopted a multiphase Eulerian-Lagrangian model to simulate the 

hydrothermal behavior of three different multiwalled carbon 

nanotubes (MWCNT) heat sinks with hydrofoil pin-fin, rhombus 

pin-fin, and triangular pin-fin, respectively. They concluded that 

better performance was achieved in the triangular pin-fin MWCNT 

heat sink as compared to others. Rahul et al. [9] numerically 

explored the heat transfer enhancement in HS with branched and 

interrupted fins. They reported that HS with branched fins yielded  

better performance, and they further suggested that higher 

performance is obtained in HS with branched fins when the 

symmetrically oriented secondary fins of  the branched fins are far 

from the base of the plate. Ding et al. [10] carried out  experimental 

and numerical studies on the thermal dissipation behaviors of 

vertically oriented finned tubes. They indicated that a Nusselt 

number of about 207% was obtained in a heat sink with finned 

tubes as compared to that of a convectional heat sink. Furthermore, 

they opined that the effects of circular fin pitch and the width of the 

fin were insignificant. Hithaish et al. [11] numerically analyzed the 

hydrothermal characteristics of heat sink with triangular pin-fin at 

different orientations (30 𝑜𝐶 to 60 𝑜𝐶), height of the fin (0.25𝑚𝑚-

0.75𝑚𝑚) and arrangements (alternate backward and forward). 

They revealed that HS with triangular pin fins in alternate forward 

and backward configuration had the highest value of the thermal 

performance index. In this study, the P-shape fin designs are 

proposed to enhance the thermal dissipation of the radial heat sink 

without altering the mass of the HS above the comparable 

convectional HS. Cooling performance of three different HSs (the 

Type A-HS with plain fin, the Type B-HS with slot, and Type C-

HS with both slot and dimples) are compared. 

 

III. METHODOLOGY 

III.1 GEOMETRY DESCRIPTION 

A three-dimensional HS is designed using Design Modeler 

of ANSYS (Fluent) software package. Fig. 1(a)-(c) shows three 

different designs of radial heat sink, Type A-plain, Type B-slot and 

Type C-slot and dimples) respectively. each of the heat sink which 

made of aluminum material consists of P-shape fins attached to 

vertically projected annular cylinder and then mounted on hollow 

circular base. The fins are radially arranged at an equal interval on 

a hollow circular base which projected horizontally. The bottom of 

the HS is subjected to heat flux varied from 700𝑊/𝑚2 to 

1900𝑊/𝑚2, ambient temperature of the air is maintained at 300K. 

Fig. 2(a)-(b) illustrates the schematic diagram of the fin and 

computational domain. A portion of the HS containing one fin is 

demonstrated because of the time consumption as a result of large 

number of grids in the simulation. The details of the computational 

domain and the heat sink parameter are presented in Table 1. 

 

 
Figure 1: SS (a) Type A (Radial HS with plain fins or 

convectional) (b) Type B (HS with slotted fins) (c) Type C (HS 

with slotted and dimpled fins). 

Source: Authors, (2022). 

 

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Fetuga et al., ITEGAM-JETIA, Manaus, v.8 n.34, p. 12-19, Mar/Apr, 2022. 

 

 

 
Figure: 2(a) Schemtic representation of the fin with dimples. 

Source: Authors, (2022). 

 

 
Figure: 2(b) Schemtic diagram of the computational 

domain and HS. 

Source: Authors, (2022). 

 

Table 1: Dimensions of the heat sink. 

Item Parameter Value 

Computational 

domain 
Base radius (𝑅) 37.5mm 

 Height (𝐻) 145mm 

Radial Heat sink 

Circular base 

Inner radius (𝑟𝑖) 9mm 

Outer radius (𝑟0) 22.25mm 

Base thickness (𝑡𝑏) 1mm 

P-shape Fin 

Fin thickness (𝑡𝑓) 2mm 

𝐻19 12mm 

𝐻21 5mm 

𝐿17 4mm 

𝑉20 28mm 

𝑉22 1.5mm 

Fillet radius (𝑟𝑓) 2.5mm 

Sphere/Dimple radius 

(𝑟𝐷) 
0.5mm 

Dimples spacing 2mm 

Slot length (𝐿𝑠) 7.5mm 

Slot width (𝑊𝑠) 0.2mm 

Slot height (𝐻𝑠) 16mm 

Number of fins (𝑁𝑓) 24 

Source: Authors, (2022). 

 

III.2 MESH GENERATION 

The grids were generated using ANSYS Mesh. As depicted 

in Fig. 3(a)-(b), the Qua/Tri hexahedral method was assigned to the 

whole geometry, while the refined mesh of element size of 

0.008mm and 0.009 are assigned to the HS and fluid domain 

respectively. 

 

 
Figure: 3(a) hexahedral grids for computation domain. 

Source: Authors, (2022). 

Page 14



 
 
 

 

Fetuga et al., ITEGAM-JETIA, Manaus, v.8 n.34, p. 12-19, Mar/Apr, 2022. 

 

 

 
Figure: 3(b) hexahedral grids for heat sink. 

Source: Authors, (2022). 

 

III.3 PROBLEM FORMULATION 

The computational simulation of natural convection is 

based on the assumptions stated below. 

1. The flow is assumed to be steady, laminal, and three-

dimensional. 

2. All the properties of air do not depend on the temperature, 

except the density. 

3. The density of the air is computed by using an ideal gas law. 

4. Radiation and magnetic effects are neglected. 

The governing equations are presented below; 

 

Continuity equation 

 

∇. (𝜌𝑣) = 0   (1) 

 

Momentum equation 

 

    
𝐷𝐯

𝐷𝑡
= −

∇𝑃

𝜌
+ 𝜐∇2𝐯 − 𝑔𝑦   (2) 

 

Energy equation 

 

𝜌𝐶𝑝
𝐷𝑇

𝐷𝑡
= ∇. (𝑘∇𝑇) +

𝐷𝑃

𝐷𝑡
   (3) 

 

Ideal gas law is used to compute density of the air 

 

𝜌 =
𝑝𝑎𝑡𝑚

(𝑅 𝑀𝑤⁄ )𝑇
   (4) 

 

𝑀𝑤 denotes the molecular weight of the air, which is taken 

as 28.966 kg/kmol. 

The material properties of the heat sink and the boundary 

conditions adopted for this study are presented in Table 2 and Table 

3, respectively. 

 

Table 2: Boundary conditions. 

Domain Location  Hydrodynamic conditions Thermal conditions 

 

Fluid 

Periodic  𝑢𝑖(𝑟𝑖⃗⃗ ) = 𝑢𝑖(𝑟𝑖⃗⃗ + 𝐿⃗ ) 𝑇(𝑟𝑖⃗⃗ ) = 𝑇(𝑟𝑖⃗⃗ + 𝐿⃗ ) 

 
∇p(𝑥𝑖) = 𝜂

𝐿̅

|𝐿|
+ ∇𝑝∗(𝑥𝑖) 

 

     Outer  Pressure inlet/Pressure Outlet condition 𝑇𝑖𝑛𝑙𝑒𝑡 = 𝑇𝑜𝑢𝑡𝑙𝑒𝑡,𝑏𝑎𝑐𝑘𝑓𝑙𝑜𝑤=𝑇∞ 

 

Solid  

Heat sink base 𝑢𝑖 = 0 
−𝑘𝑠

𝜕𝑇𝑠

𝜕𝑛
= 𝑞̇ 

Symmetric face 𝑢𝑖 = 0 𝜕𝑇𝑠

𝜕𝑛
= 0 

 

Fluid-solid 

 

Interface 

 

𝑢𝑖 = 0 

𝑇𝑓,𝑤𝑎𝑙𝑙=𝑇𝑠,𝑤𝑎𝑙𝑙  

−𝑘𝑓

𝜕𝑇𝑓

𝜕𝑛
|𝑤𝑎𝑙𝑙 + 𝑞̇𝑜𝑢𝑡 = −𝑘𝑠

𝜕𝑇𝑠

𝜕𝑛
|𝑤𝑎𝑙𝑙 + 𝑞̇𝑖𝑛 

 

Source: Authors, (2022). 

 

Table 3: Thermo-physical properties of the heat sink and the air. 

Materials 
𝑪𝒑 

(Jkg-1K-1) 

𝝁 

(Pa.s) 

𝒌 

(Wm-1K-1) 

𝝆 

(kgm-3) 

Air 1005 1.834e-05 0.0242 
𝑝𝑎𝑡𝑚

(𝑅 𝑀𝑤⁄ )𝑇
 

Heat sink 871 - 136.8 2719 

Source: Authors, (2022). 

 

III.4 NUMERICAL PROCEDURE 

The ANSYS (Fluent) software package was used to perform 

the numerical simulation, and was used to solve the continuity, 

Navier-Stokes equations (momentum and energy equation) taking 

into account the boundary conditions and assumptions stated 

earlier. The COUPLE Algorithm was assigned for pressure-

velocity coupling, default value of under-relaxation parameter was 

used, the Least Square cell based was assigned for the gradient 

under spatial discretization and the second-order upwind scheme 

was used for density, momentum, and energy, whilst Body Force 

Weighted was set for pressure. All solver residuals were set to 

convergence criteria of 1 × 10−4. 

 

IV. RESULTS AND DISCUSSIONS 

To select the best design, we compared the average 

temperature of all the cases while maintaining the same conditions. 

 

IV.1 GRID SENSITIVITY STUDY 

The grid sensitivity test was carried out by increasing the 

number of grids from 80000 to 600000. The parameters of type A 

profiles (heat sink with plain fin) at heat flux of 700𝑊/𝑚2 are used 

as reference. As illustrated in Fig. 4, 328221 grid was selected as a 

Page 15



 
 
 

 

Fetuga et al., ITEGAM-JETIA, Manaus, v.8 n.34, p. 12-19, Mar/Apr, 2022. 

 

 

reference grid point from the grid independence test, because a 

further increase in the number of grid points beyond 328221, 

yielded less than 2% in the variation of average temperature of the 

heat sink.  

 

 
Figure 4: Average temperature of the HS at various grid points. 

Source: Authors, (2022). 
 

IV.2 MODEL VALIDATION 

The difference between the average temperature (𝑇𝑎𝑣𝑔) of 

the HS and the ambient temperature of the air (𝑇𝑎𝑚𝑏) is presented 

to compare the numerical results of this study with the 

experimental data of Seung-Hwan et al. [12]. the geometry 

parameters used for validation are 𝑁𝑓 = 20, 𝐿𝑓 = 55𝑚𝑚, 𝑡𝑓 =

2𝑚𝑚, ℎ𝑓𝐿 = 21.3𝑚𝑚, ℎ𝑓𝐻 = 21.3𝑚𝑚, 𝑟𝑖 = 10𝑚𝑚, 𝑟𝑜 = 75𝑚𝑚, 

 𝑡𝑏 = 1.5𝑚𝑚 and 200 ≤ 𝑞̇ ≤ 850. Fig. 5 presents the comparison 

of the temperature difference against the heat flux for the numerical 

results of this work and the experimental data provided by Seung-

Hwan et al. [12]. A good agreement is established between the 

present work and the experimental data of Seung-Hwan et al. [12]. 

 

 
Figure 5: Comparison of temperature difference between the 

numerical results and experimental result. 

Source: Authors, (2022). 

 

IV.3 RESIDUALS PLOT 

 

The residuals plot in Fig. 6 below depicts the convergence 

of the continuity, momentum (velocity) and energy curve for Type 

A heat sink model at a constant heat flux of 700𝑊/𝑚2. 

 
Figure 6: Residuals plot. 

Source: Authors, (2022). 

 

IV.3 EFFECT OF HEAT FLUX (𝒒̇) 

Fig. 7 depicts the influence of heat flux applied to the base 

of a HS on the thermal performance of various model designs. As 

shown in Fig. 7, the difference between the 𝑇𝑎𝑣𝑔 of the HS and 

ambient air (𝑇𝑎𝑚𝑏) increases linearly with heat flux. At  700 ≤ 𝑞̇ ≤
1900, Type C (HS with slot and dimples) has lowest temperature 

difference, followed by Type B (HS with only slot) and Type A 

(plain). At 𝑞̇ =700 𝑊/𝑚2, temperature difference of 16.05K, 

15.12K and 9.83K is reported in Type A (plain), Type B (HS with 

slot) and Type C (HS with slot and dimples) as follows. However, 

at 𝑞̇ =1900 𝑊/𝑚2, Type A, Type B and Type C has a temperature 

difference of 44.48K, 41.7K and 27.05K as followed.  

 

 
Figure 8: Comparison of temperature difference against heat flux 

at different model designs. 

Source: Authors, (2022). 

 

IV.4 COMPARISON OF THE TYPE A (PLAIN), TYPE B 

(HS WITH) AND TYPE C (HS WITH SLOT AND 

DIMPLES) MODEL 

Table 4 compares the average temperature and mass of each 

of the HS designs at a constant heat flux of 1900 𝑊/𝑚2. In respect 

314,8

315,0

315,2

315,4

315,6

315,8

316,0

316,2

0 200000 400000 600000

T a
v
(K
)

Grid points

0

5

10

15

20

25

30

35

40

100 300 500 700 900

𝑇
𝑎
𝑣
𝑔
−𝑇

∞

𝑞 ̇(𝑊/𝑚2 )

Present work

Seung et al. (2010)

0

5

10

15

20

25

30

35

40

45

50

500 1000 1500 2000

T a
vg

-T
am

b
 (K

)

Heat flux (𝑊/𝑚2)

Type A

Type B

Type C

Page 16



 
 
 

 

Fetuga et al., ITEGAM-JETIA, Manaus, v.8 n.34, p. 12-19, Mar/Apr, 2022. 

 

 

to Type-A (Plain) HS design, which has the highest average 

temperature of 344.48K and a mass of 0.00168kg, it is observed 

that by incorporating a slot in the fin as we have in Type-B HS 

model, the average heat sink temperature and the mass are reduced 

by 2.78K and 8.33%, whereas total surface area increases by 

29.58%. This simply means that the Type B model has a better 

thermal performance than the Type A model with just a plain fin, 

because the slot in Type B creates an additional passage or spacing 

in the fin which increases the cooling region or heat transfer area 

of the fin. However, upon the incorporation of both slots and 

dimples to the plain fin, as it is shown in Type C model, the 𝑇𝑎𝑣𝑔 

and the mass of the HS are decreased by 17.43K and 13.69%. 

Among all the model designs, Type C (slot and dimples) has been 

seen to have the best cooling performance and lowest mass. The 

reason for this is that the incorporation of both slot and dimples has 

a greater influence on thermal performance by increasing the heat 

transfer area as compared to the Type B model (HS with slot) and 

the Type A model with a plain fin. 

 

 

Table 4: Average Temperature and mass for various heat sink designs at 𝑞̇ =1900 𝑊/𝑚2. 

Model Total Area 

(mm2) 

Frontal Area (mm2) Volume (mm3) Mass (kg) Temp 

(K) 

Type A 852.87 287.56 618.31 0 .00168 344.48 

Type B 1105.2 287.56 566.90 0.00154 341.70 

Type C 1201.1 269.5 534.96 0.00145 327.05 

Source: Authors, (2022). 

 

IV.4 TEMPERARURE CONTOUR 

Fig. 9 through Fig. 11 visualizes the heat flow between the 

heat sink and fluid domain in the z-x plane and the x-y plane. Heat 

flows in two directions, which are horizontal direction and upward 

direction. Heat flows in a horizontal direction when the cooled air 

from the fluid domain horizontally approaches the outer part of the 

heat sink where it becomes warmer (the temperature of the cooled 

air from the fluid domain gradually increases while approaching 

the outer part of the heat sink). It is also observed that the 

temperature of the air in the outer part of the HS is comparatively 

lower than the temperature in the inner part. Furthermore, the 

warmed air from the outer part of the HS enters the spaces between 

the fins and becomes warmer and lighter as compared to its 

previous state in the outer part. Due to the fact that the surrounding 

air in the outer part of the HS is heavier than the warmed air 

between the fins (which has a higher temperature), density 

therefore plays a greater role here by displacing the warmed air 

between the fins upward in a vertical direction from the inner part 

of the HS. However, the temperature of the HS decreases as the 

cooling air flows from the base to the tip of the HS (the HS which 

is maintained at a relatively higher temperature, is cooled by the 

cooling air).  

 

 

 
Figure 9: Temperature contour plot of the Type A radial HS at 𝑞̇ =1900 𝑊/𝑚2 for (a) 3D view of Type A (b) Side view of Type A (c) 

Frontal view of Type A. 

Source: Authors, (2022). 

 

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Fetuga et al., ITEGAM-JETIA, Manaus, v.8 n.34, p. 12-19, Mar/Apr, 2022. 

 

 

 
Figure 10: Temperature contour plot of the Type B radial HS at 𝑞̇ =1900 𝑊/𝑚2 for (a) 3D view of Type B (b) Side view of Type B (c) 

Frontal view of Type B. 

Source: Authors, (2022). 
 

 
Figure 11: Temperature contour plot of the Type C radial HS at 𝑞̇ =1900 𝑊/𝑚2 for (a) 3D view of Type C (b) Side view of Type C (c) 

Frontal view of Type C. 

Source: Authors, (2022). 
 

V. CONCLUSIONS 

Thermal analyses were conducted to maximize the 

performance of a P-shape finned radial HS under natural 

convection by using ANSYS (Fluent) software. Validation was 

carried out by comparing the numerical results with the available 

experimental data, and the agreement was satisfactory. To 

determine the best design for the P-shape finned heat sink, three 

different designs of heat sink, namely Type A (HS with plain fin), 

Type B (HS with slot) and Type C (HS with slot and dimples) were 

compared based on the 𝑇𝑎𝑣𝑔 and mass of the HS. Among all these 

models, Type C is the most economical and provides the best 

cooling performance because of its lowest average temperature and 

heat sink mass. 

Page 18



 
 
 

 

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VI. AUTHOR’S CONTRIBUTION 

Conceptualization: A.Ibrahim Fetuga, T. Olabode Olakoyejo, and 

K. Joshua Gbegudu. 

Methodology: A. Ibrahim Fetuga and T.  Olabode Olakoyejo. 

Investigation: A. Ibrahim Fetuga and O. Adekunle Adelaja. 

Discussion of results: A. Ibrahim Fetuga, T.  Olabode Olakoyejo 

and O. Adekunle Adelaja. 

Writing – Original Draft: A. Ibrahim Fetuga and K. Joshua 

Gbegudu. 

Writing – Review and Editing: A. Ibrahim Fetuga, T.  Olabode 

Olakoyejo and O. Adekunle Adelaja. 

Resources: T. Olabode Olakoyejo. 

Supervision: T. Olabode Olakoyejo and O. Adekunle Adelaja. 

Approval of the final text: T. Olabode Olakoyejo and O. 

Adekunle Adelaja. 

 

VII. ACKNOWLEDGMENTS 

We appreciate the support of university of Lagos for this 

research. 

 

VIII. REFERENCES 

[1] V. A. F. Costa and A. M. G. Lopes, “Improved radial heat sink for led lamp 
cooling,” Appl. Therm. Eng., vol. 70, no. 1, pp. 131–138, 2014, doi: 

10.1016/j.applthermaleng.2014.04.068. 

 
[2] D. Jang, S. J. Yook, and K. S. Lee, “Optimum design of a radial heat sink with 

a fin-height profile for high-power LED lighting applications,” Appl. Energy, vol. 

116, pp. 260–268, 2014, doi: 10.1016/j.apenergy.2013.11.063. 
 

[3] E. M. Sparrow and S. B. Vemuri, “Orientation effects on natural 

convection/radiation heat transfer from pin-fin arrays,” Int. J. Heat Mass Transf., 
vol. 29, no. 3, pp. 359–368, 1986, doi: 10.1016/0017-9310(86)90206-1. 

 

[4] Ş. Yildiz and H. Yüncü, “An experimental investigation on performance of 
annular fins on a horizontal cylinder in free convection heat transfer,” Heat Mass 

Transf. und Stoffuebertragung, vol. 40, no. 3–4, pp. 239–251, 2004, doi: 

10.1007/s00231-002-0404-x. 
 

[5] A. S. Tijani and N. B. Jaffri, “Thermal analysis of perforated pin-fins heat sink 

under forced convection condition,” in Procedia Manufacturing, 2018, vol. 24, pp. 
290–298, doi: 10.1016/j.promfg.2018.06.025. 

 

[6] J. Hayder Mohammad, “The Effect of Fin Design on Thermal Performance of 
Heat Sink | Journal of Engineering,” J. Eng., vol. 23, no. 5, pp. 123–146, 2017, 

Accessed: Mar. 04, 2022. [Online]. Available: 

https://www.joe.uobaghdad.edu.iq/index.php/main/article/view/45. 
 

[7] S. Rath, Siddhartha, and S. K. Dash, “Thermal performance of a radial heat sink 

with longitudinal wavy fins for electronic cooling applications under natural 
convection,” J. Therm. Anal. Calorim., pp. 1–19, Jan. 2022, doi: 10.1007/s10973-

021-11162-x/figures/18. 

 
[8] T. Ambreen, A. Saleem, M. Tanveer, A. K, S. A. Shehzad, and C. W. Park, 

“Irreversibility and hydrothermal analysis of the MWCNTs/GNPs-based nanofluids 

for electronics cooling applications of the pin-fin heat sinks: Multiphase Eulerian-
Lagrangian modeling,” Case Stud. Therm. Eng., vol. 31, p. 101806, Mar. 2022, doi: 

10.1016/j.csite.2022.101806. 

 
[9] R. Ray, A. Mohanty, P. Patro, and K. C. Tripathy, “Performance enhancement 

of heat sink with branched and interrupted fins,” Int. Commun. Heat Mass Transf., 

vol. 133, p. 105945, Apr. 2022, doi: 10.1016/j.icheatmasstransfer.2022.105945. 
 

[10] Y. Ding et al., “Experimental and numerical investigation on natural 
convection heat transfer characteristics of vertical 3-D externally finned tubes,” 

Energy, vol. 239, p. 122050, Jan. 2022, doi: 10.1016/j.energy.2021.122050. 

 
[11] D. Hithaish, V. Saravanan, C. K. Umesh, and K. N. Seetharamu, “Thermal 

management of Electronics: Numerical investigation of triangular finned heat sink,” 

Therm. Sci. Eng. Prog., vol. 30, p. 101246, May 2022, doi: 
10.1016/j.tsep.2022.101246. 

 

[12] S. H. Yu, K. S. Lee, and S. J. Yook, “Natural convection around a radial heat 

sink,” Int. J. Heat Mass Transf., vol. 53, no. 13–14, pp. 2935–2938, Jun. 2010, doi: 

10.1016/j.ijheatmasstransfer.2010.02.032. 
 

 

 

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