61- 71


 

 

Al-Khwarizmi Engineering Journal,Vol. 12, No. 3, P.P. 6 

 

         Experimental Simulation of 
                   Finned Vertical 
 
                                                          
              Department of Mechanical Engineering /

                                                                    

 
                                                                 (Received 20 Dec
          ___________________________________________________________________________

 
         Abstract        
    

In this work an experimental simulation
along heated finned vertical base plate 
Two types of fin arrays namely vertical fin
heights and spaces. The influence of inc
parameters such as fin height and fin spacing
and average Nusselt number have been 
between average Nusselt number versus Rayleigh number
that the configuration of V-fins array 
coefficient about 20% greater compare
present work are compared with a previous works
  
Keywords:  Natural-convection, experimental 
_______________________________________________________________________

 
1. Introduction 
  

The configurations of fins and inclinations 
play an important role in natural-convective
transfer. Fins and fin arrays are extended surfaces 
used to enhance and increase heat transfer rate and 
heat dissipation from heated surfaces to the 
surroundings in electronic devices and 
engineering applications. Many configurations of 
fin arrays like vertical fins, tri
trapezoidal fins, tree-shaped fins , pin fins ,V
shaped and V-shaped with bottom spacing. 
arrays on vertical base plates of various shapes are
of great importance in industrial applications 
as cooling of the electronic and micro
equipments , high voltage power transformers 
motors, high power chips, nuclear reactor cores ,
compact heat exchangers , radiators
the houses , energy storage system and
collectors .      

Churchill and Chu [1] deduced
correlation to predict the Nusselt number 

Khwarizmi Engineering Journal,Vol. 12, No. 3, P.P. 61- 71 (2016)

 
Simulation of Natural Heat Convection

Vertical Plate with Different Inclinations 

        Saad Najeeb Shehab       
Engineering / College of Engineering /Al-Mustansiriayah 

 E-mail:  saad_najeeb16@ yahoo.com 

eceived 20 December 2015; accepted 14 April 2016) 
___________________________________________________________________________

simulation is made to predict the performance of steady-state 
plate to ambient air with different inclination angles and config

vertical fins array and V-fins array on heated vertical base pl
of inclination angle of the plate , configuration of fins 

spacing on the temperature distribution, base convection 
have been plotted and discussed. The experimental data are correlated to a formula

versus Rayleigh number for vertical plate and vertical fins array
 gave best natural-convection heat transfer performance 

compared with vertical fins array. Experimental simulation data and correlations
previous works shows good agreement.  

xperimental simulation, finned plate, fins array. 
_______________________________________________________________________

configurations of fins and inclinations 
convective heat 

Fins and fin arrays are extended surfaces 
used to enhance and increase heat transfer rate and 
heat dissipation from heated surfaces to the 
surroundings in electronic devices and 
engineering applications. Many configurations of 

triangular fins, 
shaped fins , pin fins ,V-

shaped with bottom spacing. Fin 
s of various shapes are 

applications such 
and micro- electronic  

high voltage power transformers , 
nuclear reactor cores , 

radiators, heating of 
, energy storage system and solar 

deduced an empirical 
Nusselt number for 

steady-state free-convection heat transfer from 
vertically heated base plate 
turbulent flow conditions
Baudoin [2] obtained th
convection heat transfer 
and inclined flat plate after several experiments
They measured the temperatures by u
(IR) thermography. The results show that the
increase in convection heat transfer coefficient 
about 10% when roughness elements
used than flat surfaces. Rao et al. 
numerically the combined free
radiation heat transfer from vertical plate with fins 
array. They solved the governing equations 
Alternate Direct Implicit (ADI) method. 
noted that the convection heat transfer rate 
increasing with fin spacing decreases and fin 
length increases. Abid [4] 
the effects of fin shape on 
convection. He used vertical and pin fins array 
and developed empirical correlation
fins and pin fins array in laminar condition
Sable et al.  [5] investigated 

    
Al-Khwarizmi 
Engineering   

Journal 
(2016)

Convection from 
Inclinations  

Mustansiriayah University  

_______________________________________________________________________________________ 

state natural heat convection 
configurations of fin array. 
late are used with different 
 array and fin geometrical 

convection heat transfer coefficient 
data are correlated to a formula 

for vertical plate and vertical fins array. The results indicate 
performance as base heat transfer 

data and correlations of the 

____________________________________________________________________________________ 

convection heat transfer from 
plate in a laminar and 

conditions .Vermeulen and 
the experimental free-

convection heat transfer correlations for vertical 
and inclined flat plate after several experiments. 

the temperatures by using infrared 
(IR) thermography. The results show that the 
increase in convection heat transfer coefficient of 
about 10% when roughness elements (fins) are 

Rao et al.  [3] investigated 
numerically the combined free-convection and 
radiation heat transfer from vertical plate with fins 

governing equations using 
Direct Implicit (ADI) method. They 

noted that the convection heat transfer rate 
increasing with fin spacing decreases and fin 

] studied experimentally 
fin shape on laminar natural 

vertical and pin fins array 
and developed empirical correlations for vertical 

and pin fins array in laminar condition flow.  
] investigated enhancement of free-



Saad Najeeb Shehab                         Al-Khwarizmi Engineering Journal, Vol. 12, No. 3, P.P. 61- 71 (2016)                 
 
 

62 
 

convection heat transfer on heated vertical plate 
by multiple V-fins array. The results show that the 
V-fins array gave better heat transfer performance 
than vertical fins array and V-fins with bottom 
spacing array. Naidu et al. [6] studied the problem 
of natural convection experimentally and 
numerically by using Alternate Direct Implicit 
(ADI) method from fin arrays with different 
inclination angles of two geometric orientations, 
vertical and horizontal fins array. The results 
show that the convection heat transfer rate of 
vertical fins array is great than horizontal fins 
array for the same inclinations angles. Fahiminia 
et al. [7] presented computational analysis of the 
natural-convection on extended vertical base 
surfaces by using finite volume method (FVM). 
They concluded that the heat convection rates  
increases  with  increasing  fin  space  reaches   to   
optimum   spacing .  More et  al. [8]  presented  
review study of natural-convection from heated 
plate with different configurations of the fin 
arrays and inclinations. The results of study show 
that the all configurations of fin arrays are 
improved thermal design and heat dissipation rate 
of the heated surfaces with different percentages.  
Hireholi et al. [9] investigated experimentally and 
theoretically the heat transfer by free-convection 
of heat sink used for cooling of the electronic 
chips. They found the optimum fin spacing. They 
compared that the experimentally measured 
temperatures of heat sink with theoretically 
predicted temperatures using two-dimensional 
model and show a very good agreement. Tiwari 
and Malhotra [10] studied heat transfer of laminar 
natural-convection over a flat plate bounded by 
enclosures with effects of the surface roughness , 
ambient temperature , flow velocity and surface 
inclinations on the convection heat transfer 
coefficient at different heat source input. They 
noted that the increase in heat source input 
increases the heat transfer rates and the increase in 
surface inclination decreases the heat transfer 
coefficient. 
       The present work concentrates experimentally 
on the effects of configuration of fins array, base 
plate inclinations (ϕ), fin height (H) and fin 
spacing (S) on performance of natural-convection 
heat transfer over a heated vertical base plate. This 
is assist to predict of the temperatures distribution 
along a vertical heated base plate and to calculate 
convection heat transfer coefficient with and 
without fin arrays to choose the best configuration 
and design of fins array. 
 
 
 

2. Experimental Work 
 
2.1. Experimental Rig 
 

The experimental test rig and it’s components 
shown in Fig. 1 consists of an aluminum square 
base plate of 200 mm side has thickness 2.0 mm. 
Vertical plate and two configurations of fin arrays 
vertical fins and V-fins are joined on the base 
plate are tested as shown in Fig. 2 with different 
fin height (H) and fin spacing (S) having thickness 
2.0 mm. The vertical base plate is heated from 
backside using an electrical heater wire is coiled 
around mica sheet and then is sandwiched 
between two symmetrical square sheets of mica 
with same dimensions of the base plate and 
thickness of 0.5 mm to obtain homogeneous 
heating of the base plate and ensured the electrical 
insulation of heater wire. It’s fixed on the 
backside of base plate by thermal super glue.  The 
backside of base plate assembly is a good 
insulation using polyurethane foam layer with 60 
mm thickness to minimize the conduction heat 
loss. Also the sides are framed by plywood frame. 
The whole assembly of base plate is fixed in a 
vertical position with an adjustable support 
allowing different angles of inclination in a square 
enclosure constructed of cast acrylic sheet of 
thickness 6 mm, with dimensions (500 mm length 
× 500 mm width × 600 mm height) opened from 
upper and lower ends under guaranteed a good 
free-convection heat transfer conditions. The 
inclination angles of base plate are measured with 
vertical position by a fixed Protractor. The heating 
element is supplied up to 300 W with stabilized 
alternating current (AC) and voltage of 220 V 
through a contact type voltage regulator with 
digital reader type SAKO-TDGC2 to control on 
the electrical heat input and digital multi-meter 
type VICTOR-VC890C+ to measure voltage and 
current.  

Twelve K-type calibrated thermo-couples are 
embedded at different suitable locations in back 
surface of the vertical base plate to measure 
surface temperatures. They are matrix form 
distributed (4 rows × 3 columns) with equal 
distances. The thermocouples are connected to 
twelve channels digital temperature recorder type 
BTM-4208SD. Another two same K-type 
calibrated thermocouples are joined in digital 
multi-meter to record temperatures difference to 
evaluate the conduction heat loss from the 
backside of heated base plate. Additional two 
separate K-type digital calibrated thermocouples 
are used to measure the ambient temperature 
inside the enclosure. 



Saad Najeeb Shehab                         Al-Khwarizmi Engineering Journal, Vol. 12, No. 3, P.P. 61- 71 (2016)                 
 
 

63 
 

 
 

 
 
                        a. Front photo                                                                                    b. Side photo                         
 
1. Opened enclosure          2. Finned plate assembly.         3. Digital temperature  recorder.          4. Thermocouple wires.    
5. Adjustable support.         6. Protractor.        7. Voltage regulator.         8. Digital multi-meter. 
   
                                                  Fig. 1. Photos of the experimental rig. 
 

 
 

               a. Vertical plate                             b. Vertical fins array                            c. V-fins array 
                                   
                                         Fig.   2. Tested vertical plate and fin arrays configurations. 
  

2.2. Experimental          Procedure         and 
       Calculations 
 

Three cases are studied , vertical base plate , 
vertical base plate with vertical fins array and 
vertical base plate with V-fins array. Three angles 
of inclination with respect to vertical   position  
are  used   (ϕ= 15o , 30o and 45o). Cases of fin 
arrays  is carried  out  for  different  fin  height  
(H= 15 ,  30  and  45  mm)  and   fin   spacing   
(S= 14.5  ,  20  ,  31 and 64 mm) depending on 
numbers of fins as Table 1.  Multi- range of the 
electrical heater input Wattage namely   25 , 50 , 
75 , 100 , 125 and 150 W are used. All readings of 
the temperatures are recorded under steady-state 
conditions every 45 minutes approximately and 
when varying of the temperature readings less 
than 0.5 oC. 
 
 

Table 1, 
Number of fins against fin spacing in fins array. 
 

Number of fins, N  4  7  10 13 
Fin spacing (S), mm  64  31  20 14.5 

 
     The electrical heat input (Qin) to the heating 
element is :                 ��� = �	�																																																														…(1)   
 
It's transferred to the ambient mainly by natural-
convection (QC) in addition to radiation (QR) and 
conduction (QCd) heat transfer losses. Then, the 
rate of natural-convection heat transfe (QC) can be 
evaluated as : �
 	= �	� − �� − �
� 																																						…	(2)  
The radiation heat transfer rate (QR) is [11] : �� = �����(����� − ���)																																		…(3) 
The conduction heat transfer rate (QCd) is 
calculated by Fourier’s equation as [11,12] : 



Saad Najeeb Shehab                         Al-Khwarizmi Engineering Journal, Vol. 12, No. 3, P.P. 61- 71 (2016)                 
 
 

64 
 

�
� = �	��� 		∆�																																																	…(4) 
The radiation heat transfer (QR) from the heated 
base plate and fins array is small because the 
emissivity (ε) of bright rolled aluminum used in 
manufacturing the base plate and fins is 0.04 and 
it’s found to be less than 5% of electrical heat 
input (Qin) for all cases. The loss by heat 
conduction (QCd) is minimized using a thick layer 
of polyurethane foam with very low of   thermal   
conductivity   about   0.028 W/m.K .  It’s found to 
be approximately 2% of heat input (Qin) .     
       According to Newton’s law of cooling, the 
net heat transfer from the base heated plate by 
natural-convection is expressed as [11] : �
 = ℎ���(���� − ����)																																		…(5)                                         
Hence, the base convection heat transfer 
coefficient (hb) is : ℎ� = �	� − (�� + �
�)��(���� − ����) 																																					…(6) 
and the average convection heat transfer 
coefficient (hav) can be evaluated as follows : 	ℎ�� = �	� − (�� + �
�)�&(���� − ����) 																										…(7) 
The total surface area of free-convection heat 
transfer (At) for vertical fins array is : 	�& = (��	–*+,- + 2*.+																															…(8)  
and for V-fins array is : �& =	(��	–, ∑ +1�	2�34 - + 2. ∑ +1�2�34 									…(9)  
where , LV  is the length of V-fin. 
The average Nusselt number (Nu89) at the heated 
plate is computed by [11,12]:  	Nu89 = h89L<k 																																																		…(10) 

The average Grashof number (Grav)	can be 
defined as follows [11,12] : 	?@�� = ABCDEFGD	HC@GIJKLJGCBJ	HC@GIJ
= MNGCJO(���� − ����)+
PQR 																												…(11) 
Define Rayleigh number (Ra) as the product of 
the Grashof and Prandtl numbers [11] : SE = ?@�� T@ 																																																			…(12)  
The average surface temperature (TSav)  is: ���� = U ��F��34 																																															…(13) 
and the average of ambient temperature (TAav) is 
sum of two readings of ambient temperatures 
inside an enclosure (TA1)  and (TA2) divided by 
two to obtained a more accuracy : 	���� = ��4 + ��R2 																																													…(14) 
All properties of air are taken at film temperature 
(Tf) : 	�V = W���� + ����2 X + 273.18																						…(15) 
where, LC  is the characteristics length of 
geometry ,  LC= L  for vertical base plate, LC= S  
for vertical fins array and V-fins array 
configurations [11,12] . 
 
 
3. Results Analysis and Discussion 
 

The utilized empirical correlations for 
comparison with the experimental average Nusselt 
number (Nuav) of natural-convection heat transfer 
over heated vertical plate under steady-state and 
laminar flow conditions are listed in Table 2 . 

  
Table 2,  
Available empirical correlations.  
 

Empirical correlation     Expression with limitations 

McAdam’s   [11, 13] 			*B�� = 0.59	(SE)Z.R[ 																																																																					…(16) 
   
                                                                                    ( 10 4<  Ra  <109 ) 

Churchill and Chu’s (first 
relation) [1,11] 			*B�� = \0.825 + 0.387SE4/^{1 + `0.492T@ ab/4^}d/Ref

R
																															…(17) 

                                                                                  ( 10 -1<  Ra  <1012 ) 
 

Churchill and Chu’s 
(second relation) [1,11]  			*B�� = 0.68 + 0.67SE4/�{1 + `0.492T@ ab/4^}�/b 																																									…(18) 

                                                                                   ( 10 -1<  Ra  <109 ) 
Churchill and Usagi’s [11] 				*B�� = 0.67SE4/�{1 + `0.492T@ ab/4^}�/b 																																																								…(19) 

                                                                                   ( 10 5<  Ra  <109 ) 



Saad Najeeb Shehab                         Al-Khwarizmi Engineering Journal, Vol. 12, No. 3, P.P. 61- 71 (2016)                 
 
 

65 
 

Also the experimental simulation data of 
laminar natural heat convection from vertical fins 
array case are compared with empirical 
correlation of Abid [4] : 	*B�� = 0.045(SE′)Z.e[ 																																	…(20) 
where , SE′ = SE		Wg+X																																																		…(21) 
     Variation of the base convection heat transfer 
coefficient (hb) with average surface temperature 
(TSav) for vertical base plate , vertical fins and V-
fins array at fin heights (H) ranging  (from 15 to 
45 mm) and spacing (S= 64 mm) are  shown  in  
Figures (3) and (4). The values of base convection 
heat transfer coefficient (hb) in V-fins array are 
greater than vertical fins array case because of 
created a low pressure suction region in the 
corners of V-shaped fins on the down-stream side 
of V-fins therefore , the cold air flows into the 
separation region. It’s caused to increase the base 
convection heat transfer coefficient (hb) and the 
heat dissipation rate. 
      Figures (5-7) show variation in the base 
convection heat transfer coefficient (hb)  with  
inclination angle (ϕ) at heat input ranging from  
25 W to 150 W  when  fin height (H= 30 mm) and 
spacing (S= 64 mm)  for vertical base plate , 
vertical fins and V-fins array respectively. As the 
fin height (H) increased , the average surface 
temperature (TSav) decreased because a more of 
cold air enters between fins and the base 
convection heat transfer coefficient (hb) increased 
. In general, the base heat transfer coefficient (hb) 
decreases with inclinations (ϕ) increasing and heat 
input decreasing. 
      Figures (8) and (9) illustrate variation in the 
base convective heat transfer coefficient (hb) with 
fin spacing (S) at different fin height (H) while 
heat input kept at  100 W for vertical fins and V-
fins array respectively . The convection heat 
transfer coefficient (hb) as a function of fin 
spacing at first increases up to a peak value with 
fin spacing (S) increasing and then decreases 
gradually because the average surface temperature 
(TSav) decreases down to a minimum with fin 
spacing (S) increasing and then increases  
gradually as  shown  in  Figures (10)  and (11). 
The optimum fin spacing (Soptimum) value 
maximizing base convection heat transfer 
coefficient (hb) and minimizing average surface 
temperature (TSav)  for all three fin height is  about  
20 mm for vertical fins and V-fins array 
configurations. 
     The experimental simulation data are 
correlated to a formula between average Nusselt 
number (Nuav) versus Rayleigh number (Ra) for 

vertical plate and vertical fins array and compared 
with a previous works for same conditions as 
shown in Figures (12-14).  A correlation is 
suggested to predict the average Nusselt number 
for vertical plate : 	Nu89 = 0.563	(Ra)Z.R[ 																																	…(22) 
for  (4.3×106 < Ra < 4×107) . 

The  squared    correlation    coefficients   (R2= 
94.5%). The absolute percentage relative of error 
between suggested correlation and experimental   
data  is  (e ≤ 11%). Another experimental  
correlation  is  adopted  for  vertical  fins     array    
at      optimum      fin      spacing     ( Soptimum= 20 
mm ) and  fin  height   (H= 15 mm) : Nu89 = 0.0523	`Ra׳aZ.e[ 																														…(23) 
for (780 < Ra 2460 >׳) . 

The    squared    correlation   coefficients   
(R2= 99%) , the absolute percentage relative of 
error between suggested correlation and  
experimental  data  is  (e < 3.5%). The relative 
error between the suggested  correlation  of  
vertical    plate    with    other   correlations   is    
(e < 10%). The agreement of present work is very 
good   especially  with  McAdam’s  correlation   
(e < 5.5%), also the relative error between the 
suggested correlation of vertical fins array with 
Abid correlation is (e < 15%) at same conditions 
according to the Figures (13) and (14) . 
 

 
 
Fig. 3. Base  convection   heat-transfer      coefficient                 
versus  average   surface   temperature  for   vertical 
plate and vertical fins array. 
 



Saad Najeeb Shehab                         Al-Khwarizmi Engineering Journal, Vol. 12, No. 3, P.P. 61- 71 (2016)                 
 
 

66 
 

 
 
Fig. 4. Base heat transfer coefficient versus average 
surface temperature for vertical plate and V-fins 
array. 
 
 

 
 
Fig. 5. Base    heat       transfer     coefficient    versus 
inclination angle for vertical plate.  
 

 
 
Fig. 6. Base     heat     transfer     coefficient     versus 
inclination angle for vertical fins array. 
 
 
 

 
 
Fig. 7. Base     heat     transfer    coefficient      versus 
inclination angle for V-fins array.    
 
        



Saad Najeeb Shehab                         Al-Khwarizmi Engineering Journal, Vol. 12, No. 3, P.P. 61- 71 (2016)                 
 
 

67 
 

 
 
Fig. 8. Base   heat   transfer   coefficient    versus  fin 
spacing for vertical fins array.   
 
 

 
 
Fig. 9. Base   heat   transfer   coefficient   versus   fin 
spacing for V-fins array. 

 
 
Fig. 10. Average    surface   temperature   versus  fin 
spacing for vertical fins array.  
 
 

 
 
Fig. 11. Average   surface   temperature   versus   fin 
spacing for V-fins array.  

 
      
 



Saad Najeeb Shehab                         Al-Khwarizmi Engineering Journal, Vol. 12, No. 3, P.P. 61- 71 (2016)                 
 
 

68 
 

         
 
Fig. 12. Analysis  of   the  experimental  simulation  data  of  present  work for  vertical  base  plate  to  the power 
function fits.  
         
 

       
 
Fig. 13. Comparison   of   average   Nusselt  numbers  ( Nuav )  for  vertical  base  plate  with  available   empirical 
correlations . 
 

        
 
Fig. 14. Experimental simulation data of present work for vertical fins array compared with Abid correlation.  
 
 
 



Saad Najeeb Shehab                         Al-Khwarizmi Engineering Journal, Vol. 12, No. 3, P.P. 61- 71 (2016)                 
 
 

69 
 

4. Conclusions  
 

Natural-convective heat transfer from the 
heated vertical base plate, vertical fins array and 
V-shaped fins array are studied experimentally 
and focused on the determination of the 
geometrical configuration giving the best natural-
convection heat transfer performance. The 
following conclusions can be drawn: 
1- The type of V-fins array gave better convection 
heat transfer performance in term of base 
convection heat transfer coefficient about 20% 
bigger compared than vertical fins array.  
2- As the height of fin increased, the average 
surface temperature decreased and the base 
convection heat transfer coefficient increased.  
3- The base convection heat transfer coefficient 
decreases with inclinations increasing and heat 
input decreasing.     
4- The  optimum  value  of  fin spacing is about 
20 mm for vertical fins and V-fins arrays when 
maximizing base convection heat transfer 
coefficient.  
5- Experimental correlations are suggested to 
predict the average Nusselt number for vertical 
plate and vertical fins array.  
 
 
Nomenclature 
 
Ab                 Base area, (m

2) 
AS        Surface area of heat transfer, (m

2) 
At Total surface area of convection heat 

transfer from fin-arrays, (m2) 
F Radiation shape factor, (--) 
g Gravitational acceleration, (m/s2) 
Gr Grashof  number, (--) 
h Convection heat-transfer coefficient, 

(W/m2.K) 
H Fin height, (m) 
I Input current intensity, (A) 
k Thermal conductivity of material, 

(W/m.K) 
L Length / Height of vertical plate or fins 

array, (m) 
LC The characteristics length of geometry, 

(m) 
N Number of fins, (--) 
Nu Nusselt number, (--)  
Pr Prandtl number, (--) 
QC Convection heat transfer rate, (W) 
Ra Rayleigh number, (--)  
Ra׳ modified Rayleigh number, (--) 
S Fin spacing, (m) 
t Fin thickness, (m) 

TA Ambient temperature, (
oC) 

TS Surface temperature, (
oC) 

∆T Temperature difference,  (oC) 
V Voltage supplied, (V) 
X Thickness, (m) 

 
 

Greek Letters  
 
β Volumetric coefficient of thermal 

expansion, (1/K) 
ε Emissivity of the surface, (--) 
ϑ Kinematic viscosity of  the air, (m2/s) σ Stefan-Boltzmann constant ,                     

(σ = 5.67 × 10-8 W/ m2.K4) ϕ Inclination angle of the plate with vertical 
position, (deg) 
 

Subscript Symbols 
  
av Average 
b Base 
 
 
5. References 
  

[1] Churchill, S.W. and Chu, H. H. S.   
“Correlating   Equation    for   Laminar   and  
Turbulent Free Convection from a Vertical 
Plate  “   ,  International Journal  of   Heat and 
Mass Transfer , Vol.  18 , pp. 1323-1329 , 
1975 . 

[2] Vermeulen, J.P.  and   Baudoin  , P.   “ Study  
of  Free  Convection  by  Infrared 
Thermography over a Constant Heat-Flux 
Heated Plate “ , Eurotherm Series 27-EETI 
Edition , Paris, 1992 . 

[3] Rao, V.D. , Naidu , S.V. , Roa. B.G. and 
Sharma , K.V. “Combined Convection and 
Radiation Heat Transfer from a Fin Array with 
a Vertical Base and  Horizontal Fins”,  
Proceedings of the World Congress on 
Engineering and Computer Science  WCECS , 
San Francisco, USA, October 2007 .  

[4] Abid , W. M.  “Study of Fins Shape Efects on 
Natural Thermal Convection “, Journal of Al-
Qadisyia for Engineering Sciences, Vol. 2, No. 
2 , 2009 .  

[5] Sable, M.J.,  Jagtap, S.J. , Patil, P.S., Baviskar , 
P.R. and Barve , S.B. ”Enhancement of  
Natural   Convection  Heat  Transfer  on  
Vertical  Heated  Plate  by  Multiple  V- Fin 
Array” ,  IJRRAS , Vol. 5 (No. 2) , Nov. 2010 . 

[6] Naidu, S.V.,  Rao, V.D., Roa, B.G., Sombabu, 
A. and  Sreenivasulu, B.  “   Natural 



Saad Najeeb Shehab                         Al-Khwarizmi Engineering Journal, Vol. 12, No. 3, P.P. 61- 71 (2016)                 
 
 

70 
 

Convection Heat Transfer from Fin Arrays -
Experimental and  Theoretical   Study on 
Effect of Inclination of Base on Heat Transfer  
“,  ARPN   Journal  of   Engineering and 
Applied Sciences , Vol. 5 , No. 9 , Sep. 2010 . 

[7] Fahiminia, M. , Naserian, M.M. , Goshyeshi, 
H.R.   and   Majidian, D. “Investigation of  
Natural   Convection    Heat  Transfer   
Coefficient  on   Extended  Vertical   Base 
Plates  “ , J. of Energy and Power Engineering, 
Vol. 3, pp. 174-180 ,  2011 . 

[8] More, R.S. , Mehta, R.I. and Kakade, V.A. “  
Review  Study   of  Natural  Convection Heat  
Transfer  on Heated Plate  by  Different Types 
of  Fin  Array  “  ,  International Journal of 
Engineering Sciences and Research 
Technology , 2 (12) , Dec. 2013. 

[9] Hireholi, S.  , Shekhar , K.S.S. and  Milton , 
G.S.  “   Experimental   and   Theoretical Study 

of  Heat  Transfer by Natural Convection of  a  
Heat  Sink Used for  Cooling of Electronic 
Chip “ , International  Journal  of  Engineering 
Inventions  ,Vol. 2, Issue 2, pp. 01-09  , Jan. 
2013.  

[10] Tiwari, P. and Malhotra, V.    “Natural   
Convection Over a Flat Plate  from  Side  to 
Side   Enclosures   “    ,  International    Journal  
of   Application   or   Innovation   in 
Engineering  and Management, Vol. 3 ,  Issue 
2  , Feb. 2014 . 

[11] Lienhard, J.H. “A Heat Transfer Textbook“ , 
Phlogiston Press, 3rd Edition , USA, 2008.  

[12] Long, C. and Sayma, N. “Heat Transfer”, 
Ventus Publishing , 1st Edition , London, 
2009. 

[13] McAdams, W.H. “Heat Transmission “ , 
McGraw-Hill, New York, 1954.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 




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