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Al-Khwarizmi 

  Engineering  
Journal 

Al-Khwarizmi Engineering Journal,Vol. 13, No. 3, P.P. 10- 17 (2017) 

 

 

Numerical Investigations on Heat Flow of Nanofluids in Ribs Tube 

Configurations 

 
Sami D. Salman*             Ramzi Ata Abd Alsaheb**  

*,** Department of Biochemical Engineering/ Al-khwarizmi College of Engineering/ University of Baghdad 

*E-mail :sami.albayati@gmail.com 

**E-mail: ramzi_eng_1981@yahoo.com 

 
(Received 20 June 2017; accepted 24 July 2017) 

https://doi.org/10.22153/kej.2017.07.002 

 
 

Abstract 
 
In this paper presents two dimensional turbulent flow of different nanofluids and ribs configuration in a circular tube 

have been numerically investigation using FLUENT 6.3.26. Two samples of CuO and, ZnO nanoparticles with 2% v/v 

concentration and 40 nm as nanoparticle diameter combined with trapezoidalribs with aspect ratio of p/d=5.72 in a 
constant tube surface heat flux were conducted for simulation. The results showed that heat flow as Nusselt number for 
all cases raises with Reynolds number and volume fraction of nanofluid, likewise the results also reveal that ZnO with 
volume fractions of 2% in trapezoidal ribs offered highest Nusselt number at Reynolds number of Re= 30000. 

 
Keyword: Heat transfer augmentation, Friction factor, Thermal performance factor, Ribs configuration, CFD 

simulation, Fluent. 

 

 

1. Introduction 
 

Heat exchangers as convective heat transfer 

equipment are widely used in various engineering 
applications. Heat rate enhancement in all types of 
heat apparatus is one of the great significance for 

the industry. Besides the energysaving, it also 
leads to minimize the size and weight. In general, 
the enhancement techniques may be categorized 

into two kinds; first one is the active techniques 

which required an external power and second one 
is the passive techniques which do not required an 

external power source. Several attempts on heat 

augmentation techniques using roughen surfaces 
or tabulators such as groove and rib to disturb the 

flow and break the thermal boundary layer and 

consequently increase the heat transfer coefficient. 

Different configuration of channels with rib–
grooves had been investigated in the antecedent 

decades considering different combinations of the 

ribs configurations and temperature gradients. 
The ordinary ribsgeometries including circular 

rectangular, square and triangular, all these 

geometries of channels with rib–grooves were 
utilized in various engineering applications; gas 
turbines heat exchanger with cross-flow, 

aircooling system and gas cooled nuclear power 

reactor [1]. On the other hand, Nanofluidsas heat 
transfer enhancement technique has bring 

significant interesting the past years as applicable 

and alternative coolants for many fields such as 
power generation, automotive electronics, air 

conditioning and nuclear applications [2]. 

Different types of nanoparticles have been utilized 
for nanofluid preparation, including metals such 

as silver (Ag), copper (Cu), gold (Au), and also 

metal oxides such as Fe3O4,TiO2,CuO and 

Al2O3[3–9]. Due to their sufficient low cost, metal 
oxides are more enticing for heat transfer 

augmentation applications compared to metals. 

Simultaneously, nanofluids were combined with 
other heat transfer enhancing techniques [10, 11, 

and 12]. 
Ahmed et al. [10], reported numerical 

simulation of the heat and friction characteristics 
of Copper/water nanofluid with various volume 



Sami D. Salman                                Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 10- 17 (2017) 
 

11 

 

fraction range (0 to 0.05)through isothermally 
heated corrugated channel under laminar flow 

condition ( Re = 100-1000).It was found that the 

heat transfer augmented as nanoparticle volume 
fraction of increases. Likewise, the pressure drop 

somewhat increases with the volume fraction 

increases, for all Reynolds number. In addition, 

the highest value in heat transfer enhancement 
was obtained at Re= 200 and 5% v/v nanoparticle 

with 43.9% enhancement compared with base 

fluid. Mohammed et al. [11], has conducted 
numerical study on the turbulent heat transfer and 

friction factor of different nanoparticles CuO, 

Al2O3,ZnO and SiO2, with different concentration 

(1% to 4% ) and different nanoparticle size (25 
nm to 80 nm), with different base fluids (glycerin, 

water, engine oil) in channel with rib–groove.  

Their results showed that SiO2-glycerin produce 
highest Nusselt number followed by SiO2- engine 

oil while SiO2- water produce the lowest value of 

Nusselt number.  
Salman et al. [12] reported a numerical 

simulation on heat transfer enhancement of 

nanofluids in circular micro tube using different 

nanoparticles CuO, Al2O3, ZnO and SiO2, with 
different concentration (1% to 4% ) and different 

nanoparticle size (25 nm to 80 nm with ethylene 

glycol base fluid. Their results showed that 
SiO2nanoparticles with particle size (dp) of 25 nm 

and particle concentration 4% at Re = 1500 gives 

the highest value of Nusselt number. It is evident 

from the recent studies that the simultaneous use 
of turbulators with nanofluids efficiently gives 

further improvement in heat transfer rate as 

compared with the individual uses of nanofluids 
or of ribs configuration. In the present research 

the effects of  two types of nanoparticles; CuO 

and ZnO with 2% volume fractions and 

nanoparticles size of 40nmwith Reynolds number 
ranging from 10000 to 30000in constant tube 

surface heat flux with trapezoidal ribs 

configurations have been investigated 
numerically. 

 

 

2. Numerical Model 
2.1. Geometry Model and the Governing 

Equations 
 

Two dimensions of governing equations have  

been used to characterize the fluid flow and heat 

transfer in the circular tube with different ribs 
configurations as shown in Figures1a-b.The 

diameter of tube d=10mm and length of rib tube 

L2=100mm and the high and width of ribs is 

H=1.2mm and W=1.2mm respectively. The pitch 
of ribs is P=10mm.the entrance tube length 

L1=50mm in order to achieve the fully develop 

flow in the tube. 

 

 

 
(a) 

 
(b) 

 

Fig. 1. Schematic diagram of (a) Tube geometrical model, (b) Trapezoidal ribs. 

 

 
The assumptions below have been adopted for 

numerical simulation: (i) Nanofluid is considered 

as Newtonian and incompressible fluid, (ii) Flow 

is turbulent, (iii) Heat flux is constant with 
negligible radiation effects (iv) Nanoparticles is 

regarded as spherical shape and nanofluid is used 

as single phase model (v) The rmophysical 

properties of nanofluidsare considered as constant 

values. The governing equations in Cartesian form 

are illustrated as follows [13]: 
Equation of Mass Conservation: 



Sami D. Salman                                Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 10- 17 (2017) 
 

12 

 

0
u v

x y

∂ ∂
+ =

∂ ∂
                                                  …(1) 

Equation of momentum Conservation: 
2 2

2 2

1
( )

eff

eff

pu v u u
u v

x y x x y
µ

ρ

∂∂ ∂ ∂ ∂
+ = − + +

∂ ∂ ∂ ∂ ∂
 

                                                                        …(2) 
2 2

2 2

1
( )

eff

eff

pu v v v
u v

x y y x y
µ

ρ

∂∂ ∂ ∂ ∂
+ = − + +

∂ ∂ ∂ ∂ ∂
 

                                                                        …(3) 

Equation of Energy Conservation: 
2 2

2 2
( )

eff

eff

eff eff

kT T T T
u v

x y Cp x y

∂ ∂ ∂ ∂
+ = + +

∂ ∂ ∂ ∂
µ

ρ
                                                                

                                                                       …(4)  
 

2.2. Simulation Boundary Conditions 
 

Various inlet velocities in the tube with 

constant temperature (T=300 K) and constant heat 
flux (200,000 W/m

2
) were used for simulation. 

 

 

2.3. Nanofluids Thermophysical Properties 
 

The physical properties of nanofluids for CuO 
and ZnO nanoparticles are estimated using the 

following equations [14] and [20]:  

(1 )
n f f n p

= − +ρ ϕ ρ ϕ ρ                                  …(5) 

( ) (1 )( ) ( )
n f f n p

C p C p C p= − +ρ ϕ ρ ϕ ρ          …(6) 

Where��,���are densities of the base fluid and 
nanoparticles, ϕ represents volume fraction of 

nanoparticle,�������and ������ are heat 

capacities of nanoparticles and base 

fluid,respectively. 

e f f B row n ian S tatic
K K K= +                         …(7) 

( 2 ) 2 ( )

( 2 ) ( )

np f f npS tatic

f np f f np

K K K KK

K K K K K

 + − −
=  

+ + +  

φ

φ
  …(8) 

           

50000 ( , )
2

b
Brownian f f

np np

k T
K Cp f T

R
= ϕρ β ϕ

ρ
   

                                                                                …(9) 
 

Where; 

( , ) (0.28217 0.003917) (0.03669
o

T
f T

T

 
ϕ = + + ϕ 0.00339112) 

 
−

  

T is the fluid temperature, K is the Boltzman 
constant and T0 is the reference temperature, β 
values of two types nanoparticles with their 

boundary conditions are illustrated in Table 1. 
 

Table 1, 

β values of of CuO and ZnO nanoparticles material [14]. 
Nano particles β Concentration Temperature (K) 
CuO 0.9446

9.881(100 )
−

φ  
1% ≤ ϕ ≤ 6% 298 ≤ T ≤ 263 

ZnO 1.07304
8.4407(100 )

−
φ  

1% ≤ ϕ ≤ 7% 298 ≤ T ≤ 263 

  
 

The effective viscosity can be obtained by 
using the following mean empirical correlation 

[15]: 

1.03 0.3

1

(1 34.87 ( / 6 ) )

eff

f fo
dpN M

−
=

−

µ

µ ϕ πρ
    …(10) 

 

Where;  

M is the base fluid molecular weight,  

N is the Avogadro number 
ρfo base fluid  density  
2.4. Grid testing and codes validation 

Finite volume was used to solve the equations of 

continuity, momentum and energy with their 
corresponding boundary conditions. The 

turbulences model was very important to describe 

the flow characteristics for each application. The 
standard k-ε turbulence model and the 
Renormalized Group (RNG) k-ε turbulence model 
were selected in order to reach accurate prediction 

for simulation. The Navier-Stokes equations with 
time-independent for incompressible turbulence 

model were solved for analysis. The SIMPLE 

algorithm was selected to evaluate the pressure 
field, the velocity profile at the inlet assumed as 

fully developed and the inlet turbulence intensity 

was selected as 1%. Three different mesh spacing 

sizes (0.01,0.02,0.03) was selected for grid size 
effect on Nusselt number values at 10000 

Reynolds number including plain tube and 

trapezoidal ribs tube configurations. The results 



Sami D. Salman                                Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 10- 17 (2017) 
 

13 

 

show that the mesh spacing of 0.01 give the 
optimum values of Nusselt number with 

maximum deviations up to 3% as elaborated in 
the Table 2. 

 

Table 2, 

Mesh dependence 

Configuration Mesh spacing size % Nudeviations % 
 0.01 0.02 0.03 0.02     0.03 

Plain tube 89 87 86 2%       3% 

Trapezoidal ribs Tube 115 113.5 111 1%       3% 

 

 

3. Results and Discussion 
3.1.  Local and Average Nusselt Number 

 
The variations of the local Nusselt number 

versus position x-direction of top wall and 

average Nusselt number for circluar tube with 
trapezoidal ribs and Reynolds number ranging 

from 10000 to 30000 using water as a working 

fluidare shown in Figures 4 and 5.Its be noted that 

the Nusselt number increases with the increase of 
the Reynolds number and the highest Nusselt 

number obtained at Reynolds number of 30000. 

This implies that The use of the ribs in the circular 
tube produce (i) good turbulence flow with good 

mixing after the ribs leading to thermal boundary 

layer desolation and (ii) the strong flow vortices 
conducte better mixing between the fluid near the 

tube wall and the tube center. The highest heat 

transfer enhancement was achieved for the 

trapezoidal ribs due to the increase of strong 
turbulence intensity. 

 

 
 
Fig. 4.Varation of local Nusselt number with x-

position with trapzoidal ribs 

 

 

 

 
 

Fig. 5. Variation of average Nusselt number with 

trapezoidalat different Reynolds number. 

 

 

3.2. Skin Friction Factor 
 

The friction coefficient variations with 

Reynolds number for trapezoidal of ribs is 
presented in Figure 6. From this figure it is clearly 

seen that the skin friction factor constrict with 

Reynolds number the rises and maximum value of 
skin friction coefficient can be achieved by using 

trapezoidal ribs, whereas the minimum values of 

friction coefficient was found for smooth tube.  

 

 

X(m)

L
o

c
a
l

N
u

s
s
e
lt

N
u

m
b

e
r

0.06 0.075 0. 09 0. 105 0.12 0.135 0. 15

100

150

200

250

300

350

400

450 Re=30000

Re=25000

Re=20000

Re=15000

Re=10000



Sami D. Salman                                Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 10- 17 (2017) 
 

14 

 

 

Fig. 6. Variation of skin friction coefficient with 
trapezoidal at different Reynolds number. 

3.3. The Effect of Nanoparticles 
 

Two types of nanoparticles namely CuO and 
ZnO with 2% volume fraction and pure water as 

base fluid for trapezoidal ribs were used in this 

investigation. The Nusselt number and skin 
friction friction versus different Reynolds number 

are shown in Figure.7 and 8.From Figure 7, its 

clearly noticed that the nanofluid Nusselt number 

was higher than that obtained by base fluid 
(water), this is result in due to the presence of 

nanoparticles increase of thermal conductivity and 

due to nanoparticles collision oneself and between 
the tube wall and nanoparticles, which increase 

the energy rate exchange. Among test fluids, it is 

clearly noted that ZnO nanofluid offered highest 
Nusselt number, followed by CuO and pure water, 

respectively. This is due to the lower thermal 

conductivity of ZnO as compared with CuO nano 

fluids, From Figure 8, its clearly seen that the 
friction factor decreases with the rising of the 

Reynolds number, while no effect was distinguish 

with different nanofluids. 
 

 
 

Fig. 7. Variation of average Nusselt number for 

pure water and different nanofluids types with 

trapezoidal ribs. 

 

 
 
Fig. 8. Skin friction factorvariation of for pure 

waterand different nanofluids types with 

trapezoidal ribs 

 

 

4. Conclusions 
 

Forced convection for turbulent flow heat 
transfer simulation in a constant heat flux tube 

with trapezoidal ribs configurations were carried 

out using FLUENT 6.3.26.The effect of this 

configuration with aspect ratio of p/d=5.72 with 
water, CuO and, ZnO nano fluids with 2% volume 

fractions as a single-phase model were reported 

for Reynolds number variation from 10000 to 
30000. The results in forms of heat transfer 

coefficient (Nu) and skin friction factor (f) are 

reported as follow; 

• The local and average Nusselt number are 
augmented for trapezoidal ribs tube than that 

of the plain tube and maximum Nusselt 

number was obtained with Reynolds number 

equal to 30000, while the maximum friction 
factor obtained at Reynolds number equal to 

10000.  

• The ZnO nanofluid gives highest values of 
Nusselt number and skin friction factor, 
followed by CuO and pure water gives the 

lowest values of Nusselt number. However no 

effect was distinguish with different nanofluids 

and pure water. 
 

 

 

 

 

 

 

 

 



Sami D. Salman                                Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 10- 17 (2017) 
 

15 

 

Nomenclature 
 
keff Thermal conductivity in Energy 

equation, W/m K  

Re   Reynolds number, dimensionless 

Nu    Nusselt number, dimensionless 
p   Pressure, N/m2 

u   Velocity m/s 

T    Temperature. °C. 

 

Greek symbols 

 
ρ             Density, Kg/m3 

eff
τ
uuur

        Stress, N/m
2
. 

 

 

Acknowledgment 
 

We wish to specially acknowledge the 
assistance offered by the University of Baghdad 

AL Khwarizmi College of Engineering for 

carrying our this investigation. 
 

 

5. References 
 
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Sami D. Salman                                Al-Khwarizmi Engineering Journal, Vol. 13, No. 3, P.P. 10- 17 (2017) 
 

16 

 

[16] Jung-Yang San (2006), Wen-Chieh Huang 
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[18] Usui, H., Y. Sano, Iwashita, K. &Isozaki, A.   
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 )2017(10-17 ، صفحة 3د، العد13دجلة الخوارزمي الهندسية المجلم                                                              سامي داود سلمان

17 

 

 

 

اتءالنتو ينبوب ذاألفي للموائع لتدفق الحراري لعددية  دراسة  
 

**عبد الصاحب سامي داود سلمان*            رمزي عطا  
 / جامعة بغدادالخوارزمي الهندسة كلية /األحيائية كيميائيةالقسم الهندسة *،**

sami.albayati@gmail.com :البريد اإللكتروني* 
   ramzi_eng_1981@yahoo.comااللكتروني:**البريد 

 

  

  الخالصة
  

 FLUENTبرنامجعدديا باستخدام األبعاد  ةثنائيات ءنتوال يتم دراسة تأثيرالجريان المضطرب للموائع النانوية في انبوب دائري ذالبحث في هذا 
 فيالنانوية نانومتر قطر الجسيمات  ٤٠و  ٢%كأوكسيد الزنك وأوكسيد النحاس بتركيز حجمي يصل الى  الجسيمات النانوية أستخدام نموذجين تم. 6.3.26
لحرارة السطحية للمحاكاة. وأظهرت ثابت ل تدفقتحت p / d = 5.72 تصل الى الى قطر األنبوب ءطول ضلع النتوشبه منحرف نسبةنتوؤات بشكل  يانبوب ذ

بتركيز كسيد الزنك والنتائج أيضا أن أ كما أظهرتللموائع النانوية  حجميالبتركيز رينولدز وزداد بزيادة نسلت لجميع الحاالت ي احرارة عددالنتائج أن تدفق ال
نسلت العدد لفي األضالع شبه منحرف عرضت أعلى  ٪٢مع حجم الكسور من أعلى قيمة في انبوب ذو نتوؤات بشكل شبه منحرف  ٢حجمي يصل الى %

  .٣٠٠٠٠ الىرينولدز عدد  عندما يصل