Journal of Applied Mathematics and Physics, 2013, 1, 65-73
Published Online November 2013 (
Open Access JAMP
Numerical Study of Turbulent Periodic Flow and He at
Transfer in a Square Channel with Different Ribs
Ahmed M. Bagabir, Jabril A. Khamaj, Ahmed S. Hassan
Faculty of Engi neering, Ja zan University, Jazan, Saudi Arabia
Received July 2013
A numerical investigation has been carried out to examine turbulent flow and heat transfer characteristics in a
three-dimensional ribbed square channels. Fluent 6.3 CFD code has been used. The governing equations are discretized
by the second order upwind differencing scheme, decoupling with the SIMPLE (semi-implicit method for pressure
linked equations) algorithm and are solved using a finite volume approach. The fluid flow and he at tran sfer char acter is-
tics are presented for the Reynolds numbers based on the channel hydraulic diameter ranging from 104 to 4 × 104. The
effects of rib shape and orientation on heat transfer and pressure drop in the channel are investigated for six different rib
configurations. Rib arrays of 45˚ inclined and 45˚ V-shaped are mounted in inline and staggered arrangements on the
lower and upper walls of the channel. In addition, the performance of these ribs is also compared with the 90˚ transverse
Keywords: Ribs; Square Channel; Heat Transfer; Numerical Simulation; Turbulent Flow; Periodic Flow
1. Introduction
Heat transfer enhancement is an active and important
field of engineering research since it increases the effec-
tiveness of heat exchangers. Suitable heat transfer aug-
mentation techniques may achieve considerable technical
advantages and savings of costs. There are various kinds
of available techniques adopted in many applications as
gas turbine, heat exchanger, nuclear reactors, process
industry and solar heater. The use of ribs mounted in the
cooling or heating channels has been found to be an effi-
cient technique of enhancing heat transfer by several
investigators. The periodically positioned ribs in a chan-
nel interrupt hydrodynamic and thermal boundary layers.
Ribs break the laminar sub-layer and create local wall
turbulence due to flow separation and reattachment,
which reduce thermal resistance and greatly augment the
heat transfer. It is found that if ribs are placed at an in-
clination angle with respect to the axial direction, sec-
ondary flows are induced over the channel, resulting in
the rise in the heat transfer rate towards the upstream
region with respect to the downstream one [1,2]. Al-
though heat transfer is increased through the use of ribs,
the pressure drop of the channel flow is also increased
due to the decreased flow area effects. Therefore, the
shape, spacing, height and orientation of ribs are among
the most important parameters used in the design of the
channel of heat exchangers. Thus, it is difficult to realize
the adva nt a ge of the ri b geomet ry and arrangements.
Flow and heat transfer characteristics inside a ribbed
channel depend on flow conditions and geometric confi-
gurations of the system. Many experimental and numeri-
cal investigations were carried out to determine configu-
rations that produce optimum results in terms of both
heat transfer and pressure loss. Previous studies show
that there are many parameters involved in such studies.
channel shape (e.g. [1]);
channel aspect ratio, H/W (e.g. [1]);
rib shape (e.g. [3-6]);
rib angle of attack, α (e.g. [2-5]);
rib width to rip height ratio, e/h (e.g. [7]);
rib pitch to rib ratio, P/e (e.g. [7]);
rib height to channel height ratio (blockage ratio), h/H
(e.g. [1]);
number of ribbed walls (e.g. [3]); and
The manner by which ribs are positioned with respect
to each other (inline/staggered) (e.g. [4]).
It is found that the increase in rib width has an adverse
effect on the heat transfer performance. The square rib
produced the best heat transfer performance [7]. From
the hydrodynamic point of view, since the pressure drop
is raised as the rib height increases, the optimum block-
age ratio, h/H, is known to be ar ound 0.1 [8,9]. Th e pitch
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also has an o ptimum, because it should be longer than the
recirculation zone formed behind the rib. The recom-
mended ratio of the rib pitch to height is about 10 for the
Reynolds number range of interest [8,9]. Flow parame-
ters such as the Reynolds number are also of critical im-
portance. The Reynolds number, Re, based on the bulk
velocity and hydraulic diameter, ranges from 104 to 105
in the internal cooling channel of turbine blade.
On the other hand, many studies have been conducted
to examine thermal and flow characteristics for using r ibs
to promote heat transfer in the channel walls. An expe-
rimental study of Han et al. [3], on heat transfer beha-
viors in a square channel with different inline inclined
ribs, showed that the inclined and V-shaped ribs provide
higher heat transfer enhancement than transverse rib. For
heating either one of the ribbed walls only or both of
them, or all four channel walls, they [3] reported that the
former two conditions resulted in an increase in the heat
transfer with respect to the latter one. Khamaj [1] expe-
rimentally investigated the internal cooling channel of a
turbine blade. He developed heat transfer correlations for
turbulence air flow in static and rotating rectangular
channels with 45o inclined ribs on two opposite wall. A
numerical investigation of Murata and Mochizuki [10] on
heat transfer characteristics in a ribbed square channel
with 60˚ orientation showed that the flow reattachment
caused a significant increase in the local heat transfer.
Patankar et al. [11] introduced the concept of periodical-
ly fully developed flow to investigate numerically the
flow and heat transfer characteristics in a channel and
since then, periodic channel flows have been applied
The present work extends the experimental investiga-
tion of internal cooling channel of a turbine blade carried
out in the previous study of Khamaj [1]. The aim of the
present analysis is to investigate the flow and the heat
transfer characteristics of a rib-roughened square channel
with the upper and bottom walls subjected to uniform
heat flux by means of Fluent 6.3 code [12]. The numeri-
cal simulations have been applied to help in the interpre-
tation and to gain a more solid understanding of these
complicated flow fields and to achieve a better under-
standing of the ongoing processes. The objective of this
study is to compare the heat transfer characteristics, the
friction losses and the thermal performance for different
rib shapes and orientations for both inline and staggered
arrangements with varying Reynolds numbers in the
range between 104 and 4 × 104. The numerical computa-
tions are performed for three-dimensional turbulent pe-
riodic channel flows over 90˚, 45˚ inclined and 45˚
V-shaped ribs m ount e d pe r iodica lly.
2. Flow Configuration
The flow is computed in a square cross-sectioned chan-
nel with a 45˚ inclined and 45˚ V-shape ribs. This geo-
metry is representative of a high pressure turbine blade
cooling channel. The ribs are placed on the upper and
lower channel walls for both inline and staggered ar-
rangements as shown in Figure 1. Ribs are provided on
the heated walls. For rib pairs arranged in staggered
manner, the upper surface is moved to the right by half
the inter-rib spacing (see Figure 1). The computational
domain and the grid size for both inline and staggered
configurations are similar. The flow under consideration
is expected to attain a periodic flow condition in which
the velocity field repeats itself [11]. As a result, the si-
mulation is limited to a single pitch. The upstream and
downstream boundaries have the same inclination angle
as the rib (see Figure 1).
Figure 1. Computational domains of periodic channel flow for inline and staggered ribs.
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The air enters the channel at an inlet temperature and
flows over square rib of length, h = e = 2.5 mm. The
channel height, H, is set to 0.014 m, and the pitch, p, or
distance between ribs is set to 0.02 m. The pitch to rib
ratio (P/e) is 8 and the ratio between rib height and hy-
draulic diameter of the channel (h/D) is 0.1786. Also, a
typical transverse r ib (
= 90˚) is introduced for compar-
Periodic boundar ies are used for the inlet and outlet of
the flow domain. Th e inlet and outlet profiles for the ve-
locities must be identical. Constant mass flow rate of air
is assumed in the flow direction due to the periodic flow
conditions. Also a mean bulk temperature of 300 K is
applied at the inlet. The physical properties of the air
were assumed to remain constant at average bulk tem-
perature. Impermeable boundary and no-slip wall condi-
tions were implemented over the chann el walls as well as
the ribs. The two opposite walls with the ribs are as-
sumed heated surfaces with constant heat flux of 17,577
W/m2, while the other two walls are kept adiabatic. The
ribs are assumed at conjugate wall (low thermal resis-
tance) conditions. To simplify the calculations, a sym-
metry condition is applied. The computational domain is
resolved by regular Cartesian elements. The grids are
refined near the wall surfaces using grid adaption tech-
nique employed by Fluent 6.3 which refines the grid
based on geometric and numerical solution data [12].
Considering both convergent time and solution precision,
the grids shown in Table 1 are adopted for the current
computational models using similar grid density.
3. Mathematical Modelling
The numerical model for fluid flow and heat transfer in a
channel i s developed under the following as sumpti ons .
Steady three-dime ns ional fluid flow a nd heat transfer.
Periodic, fully developed, turbulent and incompressi-
ble flow.
Consta nt fluid pro pe rties.
Ignore d bo dy forces.
Negligible radiation heat transfer.
Subsequently, the channel flow is governed by the
Table 1. Grid details for different cases.
Case No. of cells symmetry plane(s)
Inline 90˚ 39,315 xy and xz planes
Inline 45˚ 104,840 xz plane
Inline 45˚ V 52,420 xy and xz planes
Staggered 90˚ 78,630 xy plane
Staggered 45˚ 209,680 -
Staggered 45˚ V 104,840 xy plane
continuity, the Reynolds aver aged Navier-Stokes (RANS)
equations and the energy equation. In the Cartesian ten-
sor system these equations can be written as follows.
Continuity equation.
( )
Momentum equation.
( )
iji j
jij j
uuu u
xxx x
ρ µρ
∂ ∂∂′′
∂∂∂ ∂
is the density of fluid, and ui is the mean com-
ponent of velocity in xi direction, p is the pressure, μ is
the dynamic viscosity, and u' is a fluctuating component
of velocity. Repeated indices indicate summation from
one to three for three-dimensional problems. The Rey-
nolds-averaged approach of turbulence modelling utilizes
the Boussinesq hypothesis to relate the Reynolds stresses
in the above equation to the mean velocity gradients as.
where k is the turbulent kinetic energy defined by
, and δij is th e Kronecker delta.
Energy equation.
( )()
t are molecular thermal diffusivity and
turbulent thermal diffusivity, respectively and are given
ttt Pr ,Pr
The selection of the suitable turbulence model is very
important in any computational analysis to predict the
accurate results. The analysis consists of flow with low
Reynolds number. The standard k -
and realizable k -
turbulence model are generally used for low Reynolds
number analysis. However, three turbulence models are
investigated, namely the renormalization group (RNG) k
[13], realizable k -
[14] and shear-stress transport
(SST) k -
[15]. The k -
turbulence models are in-
corporated with a well-established non-equilibrium wall
function for the near wall treatment. The equations go-
verning the turbulence models will not be given here.
Readers who are interested in these models are advised to
refer to the above mentioned studies.
The commercial Fluent 6.3 CFD code has been used in
this work [12]. The governing equations are discretized
by the second order upwind differencing scheme, de-
coupling with the SIMPLE algorithm and are solved us-
ing a finite volume approach. The energy equations are
solved after the flow and turbulence equations in a se-
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gregated fashion. The y+ value of the near-wall nodes is
kept, in all computations, to less than 10. The solutions
are considered to be converged when the normalized
residual values are less than 106 for all variables but less
than 108 only for the energy equation. Four parameters
of interest in the present work are the Reynolds number,
Nusselt number, friction factor and thermal enhancement
factor. The Reynolds number, Re, is based on the bulk
velocity, Um, and hydraulic diameter, D. The thermal
performance is measured by the heat transfer coefficient,
h, and Nusselt number, Nu, which can be written as.
khDNu =
where, TB is the bulk temperature of fluid over the cross
section, TS is the channel wall temperature, q is the heat
flux and k is the thermal conductivity. The Nu is norma-
lized by Nusselt number for a smooth channel, Nu0,
which is given by Dittus-Boelter formula operated at the
same Reynolds number.
PrRe.Nu =
The friction factor, f, is computed by pressure drop, p,
across the length of the periodic channel, l (=rib pitch
spacing) as.
( )
pl D
The relative importance of the pumping power can be
assessed by comparing the friction factor with the one
associated with the flow in a smooth pipe, f0, which is
given by the Blasius correlation.
The thermal enhancement factor, TEF, is defined as
the ratio of the heat transfer coefficient of an augmented
surface to that of a smooth surface at an equal pumping
power. It is given by.
() ( )
TEFNu Nuff=
4. Results and Discussions
4.1. Code Validation
The present numerical method is validated by comparing
its results with the corresponding experimental data of
Khamaj [1] for the average Nusselt numbers at wall sur-
face. The calculations are performed in a double wall
ribbed square channel with inline 45˚ inclined rib arrays.
The computed average Nusselt numbers using different
turbulence models are shown in Figure 2. The percen-
tage error is very high for realizable k -
(RKE) model
which is about 20%. The percentage error is 12% for
SST k -
turbulence model. It is clear that the RNG k -
Figure 2. Average Nusselt number for different turbulence
models compared with the experimental results [1] at dif-
ferent Reynolds numbers.
model exhibits best results and predicts the overall heat
transfer rate in excellent agreement with the experimental
results of Khamaj [1]. It shows less than 6% deviation
from experimental results. The difference in the averaged
heat transfer predictions is related to the large scale mo-
tion of the flow field (e.g. reattachment lengths) which is
not properly reflected in the realizable k -
and SST k -
models. Although the RNG k -
turbulence model
reveals the best accuracy of heat transfer, the other tur-
bulence models ensure better convergence performance
and less computational time. However, the agreement
found between the measured value and the numerical
computations using RNG k -
model is rather encourag-
ing. Therefore, the RNG k -
model is used for the rest
of the calculations in the present study. On the other hand,
the standard k -
model is also investigated. Its outcome
displays a solution almost identical to the SST model.
This is expected because the SST k -
model incorpo-
rates a blending function that allows it to switch from the
standard k -
model in the near-wall region to a high
Reynolds number version of the k -
model in the free
stream. Therefore, it is omitted from the comparisons.
4.2. Flow Structure
It is necessary to understand the flow structure and beha-
vior in the ribbed channel before discussing the results.
The flow structure in the channel mounted periodically
with various ribs can be displayed by considering the
streamtraces as depicted in Figure 3 for 90˚ transverse,
45˚ inclined and inline 45˚ V-shaped ribs, respectively.
The streamtraces are presented at Reynolds number of Re
= 3 × 104. As shown in Figure 3, the flow field is do
dominated by large-scale and small-scale vortex struc-
tures. The large-scale coherent structure initiates at up-
stream and presents above the upstream and on the
downstream part of the rib. The large vortex which
arches through the channel is twice the length of the
010000 20000 30000 40000 50000
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Figure 3. Streamtraces for transverse, inclined, and V-shaped rib arrays arranged in the inline configurati on at Re = 3 × 104.
pitch and has a major influence on the flow.
For the transverse rib, the large vortex appears at side
walls and small structure on the downstream is also visi-
ble. Only two transverse vortices moved towards the side
walls are found and trapped behind each rib. Moreover,
for 90o rib, the flow moves upwards by the secondary
flow near side walls. The presence of inclined and
V-shaped ribs creates two main counter rotating vortices
resulting in longer flow path and high strength of vortex
due to changing in its orientation (see Figure 3). The
most notable characteristics of the effects of the inclined
and V-shaped ribs on the mainstream flow are flow se-
paration, recirculation, and inclined secondary flow (see
Figure 3). As the mainstream flow passes over the 45˚
and 45˚ V-shaped ribs, it separates and creates vortex
flow behind the rib due to high pressure difference across
the rib before moving helically along the rib downstream,
then rolling up. Also the mixing of the streamtraces in-
itialized from various positions can be followed clearly
in the cases of inclined and V-shaped ribs. This flow
mixing between the main and the wall regions leads to
relatively high heat transfer.
4.3. Heat Transfer
Figure 4 displays contour maps of normalized tempera-
ture, T/Tin, for 90˚, 45˚ and 45˚ V-s haped ribs arr anged in
the inline and staggered arrays at Reynolds number of Re
= 3 × 104. Similar contour levels and numbers are applied.
The contour maps show that there is a major change in
the temperature field over the ribbed channels.
The contour map of normalized temperature field for
the 90˚ ribs shows that the higher temperature gradient
can be observed almost in the downstream and over the
rib where the lower one can be found in the upstream
region (see Figure 4). The major change in the tempera-
ture field is found in the upstream and over the rib, while
in the downstream, there is a minor change. The contour
maps and the average normalized temperature values,
shown in a bracket above the contour legend, reveal that
the inline and staggered orientations of the transverse rib
generate almost similar results (see Figure 4). For the
fully developed flow, hot spots exist in the recirculation
region immediately downstream the square 90˚ ribs be-
cause the fluid flow is nearly stagnantly relative to the
mainstream in this region (see Figure 4). The hot spots
lead to lower heat transfer coefficient from the surface.
This implies that the transverse recirculation zone up-
stream of the rib provides a significant influence on the
temperature field while th e flow in the rib downstr eam is
not affected by the presence of the 90˚ rib. Therefore, it
is of interest to know whether the channel roughened with
ribs of different shape can improve the heat transfer rate.
It appears that, in comparison with the 90˚ case, the
lower temperature values over the heated surface with
the inclined and V-shaped ribs are seen in a larger area,
except for small regions near the sidewalls (Figure 4).
This indicates the merit of employing such ribs over a
smooth channel for enhancing heat transfer. For inclined
and V-shaped rib cases, the vortex flows provide a sig-
nificant influence on the temperature field, because it can
induce better fluid mixing between the wall and the main
flow. The higher temperature gradient can be observed
where the flow impinges the side channel wall. It is ob-
vious that the 45˚ V-shaped ribs orientation enhances the
heat transfer better than 45˚ inclined ribs. For the
V-shaped rib, two pair of large-scale counter-rotating
secondary flows are induced in the channel [3]. For the
V-shaped rib configurations, the temperature maps show
the minimum values at the centre region, and increases
gradually along the ribs towards sidewalls due to the two
pairs of counter-rotating secondary flows generated in
the channel. Moreover, the temperature maps and the
average normalized temperature values of V-shaped ribs
illustrate that when the ribs are arranged in the inline
orientation, they produce better rate of heat transfer than
staggered ribs (see Figure 4 ). This could be attributed to
the stronger counter-rotating secondary flows in the case
of the inline rib configuration which reduces the size of
the devel o ped boundary layer.
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Figure 4. Normalised temperature (T/Tin) maps for different ribs at Re = 3 × 104.
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On the other hand, the local variation of the norma-
lized Nusselt number, Nu/Nu0, in the streamwise direc-
tion at three spanwise locations (centreline and side walls)
in between the ribs, is shown in Figure 5. The consi-
dered cases are 90˚, 45˚ and 45˚ V-shaped ribs arranged
in the inline configuration at Reynolds number of Re = 3
× 104. Heat transfer enhancements along the streamwise
direction are attributed to the flow separation and reat-
tachment. The presence of ribs locally reduces the chan-
nel area resulting in the acceleration of the flow around
the ribs. The acceleration and sudden expansion of this
flow separates it which again reattaches further down-
stream. The 90˚ case shows the highest Nu/Nu0 values at
the sidewalls and the lowest at the centre region. Al-
though, the 45˚ V-shaped rib reveals the highest Nusselt
number values at the centre region, it shows big varia-
tions between the upstream and downstream sides of the
rib. Moreover, the plots of Figure 5 indicate that the heat
transfer is reduced downstream of the rib near back wall
of 45˚ case and near the sidewalls of the 45˚ V-shaped rib.
The heat transfer in these zones is even lower than the
heat transfer of a smooth channel with no rib. However,
when compared with the 45˚ layout, the 45˚ V-shaped rib
shows improvement of heat transfer at the upstream of
the rib.
When the solutions are averaged over appropriate
areas, they provide engineering information about the
heat transfer and friction. The variation of the average
normalized Nusselt number, Nu/Nu0, with the Reynolds
number for ribs of various shapes and arrangements is
depicted in Figure 6. In general, as the Reynolds number
increases, the average Nusselt number, Nu, for a channel
increases. This is due to the increase in velocity which
causes turbulence. Since the rate of increase in Nusselt
number is low, the Nu/Nu0 values have a negative slope
as the Reynolds number increases. Therefore, as shown
in Figure 6, the average normalized Nusselt number,
Nu/Nu0, decreases as the Reynolds number increases.
For the considered cases, the analysis of Figure 6 re-
veals that the introducing of ribs yields heat transfer rate
about 2.3 - 5.8 times higher than the smooth channel with
no rib. Thus, the generation of vortex flows from using
rib as well as the role of better fluid mixing and the im-
pingement are the reason for the augmentation of heat
transfer in a ribbed channel. The 45˚ and 45˚ V-shaped
ribs perform much better than the 90˚ rib for enhancing
heat transfer. Moreover, the Nusselt number values for
both the 45˚ and 45˚ V-shaped ribs are found to be about
17% - 50% over that for the rib placed transversely to the
main stream direction. On the other hand, the inline and
staggered rib orientations of 90˚ and 45˚ cases reveal
identical heat transfer performance for all considered
Reynolds number. However, for the 45˚ V-shaped ribs, it
is noted that the inline performs 15% better than the
staggered arrangement. The inline and staggered inclined
ribs perform nearly the same heat transfer rate as the
staggered V-shaped ribs at Reynolds number greater than
2 × 104 (see Figure 6). It is clear that the inline 45o
V-shaped rib represents the best rib shape and orien tation
for heat transfer augmentation. This indicates that this
case produces strong vortex which yields a mixing inten-
sity of the flow.
4.4. Pressure Loss
In general, the heat transfer augmentation is concerned
with penalty in terms of increased friction coefficient
resulting in higher pressure drop. It is found that the fric-
tion factor follows a different pattern from Nusselt num-
ber. The average normalized friction factor, f/f0, increas-
es as the Reynolds number increases for various rib
shapes and orientations as depicted in Figure 7. It is ob-
vious that all considered ribs create friction factor h igher
than smooth channel with no rib. Figure 7 illustrates that
the staggered orientation generates lower friction factor
Figure 5. Normalized local Nusselt number along streamwise for 90˚, 45˚ and 45˚ V-shaped ribs ar ranged in the inl ine confi-
guration at Re = 3 × 104.
00.2 0.4 0.6 0.81
90 (centre line)
45 (centre line)
V-shape (centre line)
00.2 0.4 0.6 0.81
90 (side walls)
45 (front-side wall)
45 (back-side wall)
V-shape (side walls)
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Figure 6. Variation of average normalized Nusselt number,
Nu/Nu0, with Rey nolds number for di f f erent ribs.
Figure 7. Variation of average normalize friction factor, f/f0,
with Reynolds number for di f fe rent ribs.
for 90˚ and 45˚ V-shaped ribs than their inline arrange-
ment. The staggered 90˚ rib offers the lowest flow resis-
tance among all configurations. In contrast, it reveals
friction factor of about 150% lower than its correspond-
ing inline orientation.
For the 45˚ V-shaped rib, the staggered configuration
provides about 10% lower friction factor than the inline
one. On the other hand, as depicted in Figure 7, it is
found that the inline configuration is preferable for the
45˚ rib.
4.5. Performance Evaluation
Figure 8 exhibits variation of the thermal enhancement
factor, TEF, for air flowing in square channels of two
ribbed walls. The thermal enhancement factor tends to
decrease with the rise of the Reynolds number. Mean-
while, it shows an increase trend for the inline 45˚
V-shaped rib for the Reynolds number greater than 3 ×
104. The enhancement factors of the ribs considered in
this study are seen to be above unity. They vary between
1.3 and 4.2 per unit pumping power, depending on the
Figure 8. Variation of thermal enhancement factor, TEF,
with Reynolds number for di f fe rent ribs.
Reynolds number. This indicates that these cases are ad-
vantageous with respect to smooth channel with no rib. It
is found that the inline 90˚ rib yield the lowest thermal
enhancement factor.
This is the reason why it is not used a lot to enhance
heat transfer in many thermal engineering applications in
comparison with other orientations. It seems that the in-
line configuration is preferable for the inclined and
V-shaped ribs especially at low Reynolds number of Re =
104. At Reynolds number of Re = 104, the inline 45˚ rib i s
found to have the highest channel heat transfer per unit
pumping power.
5. Conclusions
Turbulent periodic flow and heat transfer characteristics
in a square channel fitted with 45˚ inclined and 45˚
V-shaped ribs in tandem have been investigated numeri-
cally. The rib arrays are set in inline and staggered ar-
rangements on two opposite walls. The vortex flows
created by using such ribs help to induce strong rotation-
al momentum of the secondary flows leading to drastic
increase in heat transfer in the square channel compared
with 90˚ transverse ribs. However, the temperatures maps
demonstrate that the 45˚ V-shaped rib improve the heat
transfer rate better than 45˚ inclined rib especially near
side walls. It is apparent that the main flow induces two
impinging flows on each sidewall of V-shaped rib lead-
ing to an increase in heat transfer rate over the channel.
In general, the order of heat transfer enhancement in
the channel with two ribbed walls is abo ut 230% - 580%
higher than the smooth channel with no rib. However, the
heat transfer augmentation is associated with enlarged
friction loss ranging from 2.0 to 6.2 times above the
smooth channel. Moreover, the inclined and V-sha pe d rib
pairs arranged in the inline manner reveal heat transfer
improvement of about 17% - 50% higher than that for the
90˚ rib; whereas the pressure loss can be reduced at about
010000 20000 30000 40000 50000
90 (inline)
45 (inline)
V (inline)
90 (staggered)
45 (staggered)
010000 20000 30000 40000 50000
90 (inline)
45 (inline)
V (inline)
90 (staggered)
45 (staggered)
010000 20000 30000 40000 50000
90 (inline)
45 (inline)
V (inline)
90 (staggered)
45 (staggered)
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4% - 38% depending on Reynolds number. It is found
that the staggered inclined ribs produce similar thermal
profile as inline orientation but with higher friction factor.
The staggered orientation lowers the thermal perfor-
mance of 45˚ V-shape and reduces the friction factor. On
the contrary, the staggered 90˚ transverse rib reveals
thermal enhancement factor similar to inclined and
V-shaped ribs for Reynolds number equal or higher than
2 × 104. For Reynolds number of 104, the inline 45˚ rib
reveals the optimum thermal enhancement factor.
[1] J. Khamaj, “An Experimental Study of Heat Transfer in
the Cooling Channels of Gas Turbine Rotor Blades,” PhD
Thesis, University Wales, 2002.
[2] O. Manca, S. Nardini and D. Ricci, “Numerical Study of
Air Forced Convection in a Channel Provided with In-
clined Ribs,” Frontiers in Heat and Mass Transfer, V ol. 2,
[3] J. C. Han, Y. M. Zhang and C. P. Lee, “Augmented Heat
Transfer in Square Channels with Parallel, Crossed and
V-Shaped Angled Ribs,” ASME, Journal of Heat Transfer,
Vol. 113, 1991, pp. 590-596.
[4] H. Liu and J. Wang, “Numerical Investigation on Synthe-
tical Performances of Fluid Flow and Heat Transfer of
Semiattached Rib-Channels,” International Journal of
Heat and Mass Transfer, Vol. 54, 2011, pp. 575-583.
[5] P. Promvonge, W. Changcharoen, S. Kwankaomeng and
C. Thianpong, “Numerical Heat Transfer Study of Tur-
bulent Square-Duct Flow Through Inline V-Shaped Dis-
crete Ribs,” International Communications in Heat and
Mass Transfer, Vol. 38, 2011, pp. 1392-1399.
[6] R. Kamali and A. R. Binesh, “The Importance of Rib
Shape Effects on the Local Heat Transfer and Flow Fric-
tion Characteristics of Square Ducts with Ribbed Internal
Surfaces,” International Communications in Heat and
Mass Transfer, Vol. 35, 2008, pp. 1032-1040.
[7] A. R. Sampath, “Effect of Rib Turbulators on Heat Tran-
sfer Performance in Stationary Ribbed Channels,” PhD
Thesis, Cleveland State University, 2009.
[8] J. C. Han, “Heat Transfer and Friction in Channels with
Two Opposite Rib Roughened Walls,” ASME Journal of
Heat Transfer, Vol. 106, 1984, pp. 774-781.
[9] T. M. Liou and J. J. Hwang, “Turbulent Heat Transfer
and Friction in Periodically Fully Developed Channel
Flows,” ASME Journal of Heat Transfer, Vol. 114, 1992,
pp. 56-64.
[10] A. Murata and S. Mochizuki, “Comparison between La-
minar and Turbulent Heat Transfer in a Stationary Square
Duct with Transverse or Angled Rib Turbulators,” Inter-
national Journal of Heat and Mass Transfer, Vol. 44,
2001, pp. 1127-1141.
[11] S. V. Patankar, C. H. Liu and E. M. Sparrow, “Fully De-
veloped Flow and Heat Transfer in Ducts Having Stream-
wise-Periodic Variations of Cross-Sectional Area,” ASME
Journal of Heat Transfer, Vol. 99, 1977, pp. 180-186.
[12] Fluent Corporation, “Fluent v6.3 User Guide,” 2006.
[13] V. Yakhot and S. A. Orszag, “Renormalization Group
Analysis of Turbulence: I. Basic Theory,” Journal of
Scientific Computing, Vol. 1, No. 1, 1986, pp. 1-51.
[14] T. H. Shih, W. W. Liou, A. Shabbir, Z. Yang and J. Zhu,
“A New k-
Eddy-Viscosity Model for High Reynolds
Number Turbulent Flows-Model Development and Vali-
dation,” Computers Fluids, Vol. 24, No. 3, 1995, pp. 227-
[15] F. R. Menter, “Two-Equat ion Eddy -Viscosity Turbulence
Models for Engineering Applications,” AIAA Journal,
Vol. 32, No. 8, 1994, pp. 1598-1605.
D: Hydraulic diameter of channel width (m)
e: Rib width (m)
f: Friction factor for a ribbed channel
f0: Friction factor for a smooth channel
h: Rib height (m) or heat transfer coefficient
H: Channel height ( m)
k: Thermal conductivity (W/mK)
Nu: Nusselt nu mber of a ribbed channel
Nu0: Nusselt number of a smooth channel
p: static pressure (pa) or rib pitch spacing (m)
Pr: Prandtl number
q: Heat flux (W/m2)
Re: Reynol ds number
TB: Bulk tem pe rature of flow (K)
TS: Surface temperature (K)
Tw: Wall temperature (K)
TEF: Thermal enhancement factor
u: Velocity (m/s)
Um: Bulk velocity (m/s)
W: Channel wi dth (m)
: Density (kg/m3)