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Journal of Engineering Science and Technology Vol. 12, No. 12 (2017) 3251 - 3273 © School of Engineering, Taylor’s University

3251

USE OF WAISTED TRIANGULAR-SHAPED BAFFLES TO ENHANCE HEAT TRANSFER IN A CONSTANT TEMPERATURE-

SURFACED RECTANGULAR CHANNEL

YOUNES MENNI*, AHMED AZZI, CHAFIKA ZIDANI

Unit of Research on Materials and Renewable Energies - URMER - Department of Physics,

Faculty of Sciences, Abou Bekr Belkaid University, BP 119-13000-Tlemcen, Algeria

*Corresponding Author: [email protected]

Abstract

The purpose of the present computational fluid dynamic analysis is to investigate

the turbulent flow and heat transfer characteristics of air inside a constant

temperature-surfaced rectangular cross section channel, where two waisted

triangular-shaped baffles (WTBs) were placed in opposite walls. The aim at using

the left and right wall-mounted solid-type WTBs is to create recirculation cells

having a significant influence on the flow field leading to higher thermal transfer

rate in the whole domain investigated. The governing equations with the

associated boundary conditions were discretized using the Finite Volume Method

(FVM). The SIMPLEC-algorithm was used for the convective terms in the

solution equations. As expected, the largest variations in the Nusselt number and

friction loss occur in the regions near to the WTBs, due to the strong velocity

gradients in those regions. Some numerical results were compared with those

obtained by the experiment in the literature. This comparison shows that there is a

qualitative agreement as well as a very good concordance between the two results.

The current originality lies in the geometric shape of the baffles inside the

channel. This study can be a real application in the field of shell-and-tube heat

exchangers and air plan solar collectors.

Keywords: Aerodynamics, CFD, Fluid dynamics, Engineering and industrial

applications, Heat exchangers, Waisted baffles.

1. Introduction

Heat exchangers are used in several sectors and in very diverse fields. In general, in

order to achieve high energy performances, it is essential to install rows of baffles

within the flow channel in the heat exchangers so as to create turbulence and also to

3252 Y. Menni et al.

Journal of Engineering Science and Technology December 2017, Vol. 12(12)

Nomenclatures

AR Channel aspect ratio (W/H = 1.321)

BR Blockage ratio (h/H = 0.547)

Cp Specific heat at constant pressure, kJ/kg K

Cf Skin friction coefficient

Dh Aeraulic diameter of rectangular channel (= 0.167), m

f

h

hx

H

k

L

Lin

Lout

Nu

Nux

P

Patm

Pi

Pr

Re

T

Tin

Tw

u

Uin

w

W

Friction factor

Baffle height (= 0.08 ), m

Local convective heat transfer coefficient, W/m K

Channel height (= 0.146), m

Turbulent kinetic energy, m² s-²

Length of rectangular channel in x-direction (= 0.554), m

Distance upstream of the first baffle (= 0.218), m

Distance downstream of the second baffle (= 0.174), m

Average Nusselt number

Local Nusselt number

Pressure, Pa

Atmospheric pressure, Pa

Axial pith (= 0.142), m

Molecular Prandtl number (μCp/λf)

Reynolds number (ρUDh/μ)

Temperature, K

Inlet temperature, K

Temperature at the wall, K

Fluid velocity in x-direction, m s-1

Inlet velocity, m s-1

Thickness of basis baffles (= 0.01), m

Channel width (= 0.193), m

Greek Symbols

Angle of triangular-baffle tip (= 7.152), deg.

r

Angle of waisting the baffles (=50), deg.

Ray of waisting the baffles (= 0.03), m

ε

ρ

λf

μ

μt

τw

ΔP

ϕ

Turbulent dissipation rate, m² s-3

Fluid density, kg/m3

Fluid thermal conductivity, W m-1

K-1

Dynamic viscosity, kg/m s

Turbulent viscosity, kg/m s

Wall shear stress, Pa

Pressure drop, Pa

Universal variable representing u, v, k, ε and T

Subscript

atm

f

in

t

w

x

Atmosphere

Fluid

Inlet

Turbulent

Wall

Local

Use of Waisted Triangular-Shaped Baffles to Enhance Heat Transfer 3253


Abbreviations

CFD Computational Fluid Dynamics

FVM

QUICK

RANS

SOU

Finite Volume Method

Quadratic Upstream Interpolation for Convective Kinetics

Reynolds-Averaged Navier-Stokes

Second Order Upwind

WTB Waisted Triangular Baffles

lengthen the trajectory of fluids by promoting a better convective heat exchange.

Consequently, a remarkable improvement in the thermal efficiency is obtained.

Baffles and fins submitted to laminar and turbulent heat transfer flows have

being analyzed in the recent years by several authors, using numerical and

experimental methods. Kelkar and Patankar [1] numerically studied the heat

transfer in a parallel plate channel with staggered fins and found that the heat

transfer increases with the rise in baffle height and with the decrease in baffle

spacing. Habib et al. [2] experimentally investigated the characteristics of the

turbulent flow and heat transfer inside the periodic cell formed between

segmented baffles staggered in a rectangular duct and showed that the heat and

pressure drop characteristics increase with the baffle height. Flow visualization

techniques, manometry, and laser-Doppler anemometry were applied by Berner et

al. [3] to approximately two-dimensional flow around segmented baffles in order

to simulate important aspects relating to shell side flow in shell-and-tube heat

exchangers. They suggested that the laminar flow occurred for Reynolds number

below 600. Experimental data on velocity and wall pressure fluctuations in the

turbulent flow through a simulated tube bank with square arrangement between

two baffle plates were reported by Möller et al. [4].

In general, the results of wall pressure and wall pressure fluctuations showed

higher values than in pure cross flow. By means of hot wire experiments and

numerical simulation, Demartini et al. [5] presented the analysis of velocity and

pressure fields in the same channel as Möller et al. [4]. The geometry of this

problem is a simplification of the geometry of baffle plates found in shell-and-

tube heat exchangers. The results showed that the airflow is characterized by

strong deformations and large recirculation regions, and in general, the largest

variations in the pressure and velocity fields occur in the regions near to the

deflectors. A numerical analysis of laminar forced convection heat transfer in a

three-dimensional channel with baffles for periodically fully developed flow and

with a uniform heat flux in the top and bottom walls was conducted by Lopez et

al. [6]. The simulation focused on the influence of Reynolds number, baffle height

to channel width ratio, Prandtl number, and wall thermal conductivity to fluid

thermal conductivity ratio on the local and global heat transfer coefficients, and

pressure drop measurements.

Characteristics of the laminar forced convection heat transfer flow in a three-

dimensional channel with a single baffle in the entrance region were numerically

studied by Guo and Anand [7]. The heat flux was uniform in both upper and lower

walls. The parameters of the numerical work were the Reynolds number, the Prandtl

number, the baffle height, and the thermal conductivity. In general, separation

length upstream of the baffle and recirculation length downstream of the baffle

increased with an increase in the flow Reynolds number and baffle height, and the



averaged Nusselt number increased with an increase in the thermal conductivity of

the wall. A detailed numerical study of the flow and conjugate heat transfer through

two wall-mounted obstacles placed in lower and upper walls was carried out by

Mohammadi Pirouz et al. [8] using Lattice Boltzmann Method (LBM). In that

study, various parameters were investigated, such as Reynolds number, the thermal

diffusivity ratio of solids and fluids, and horizontal distances between obstacles.

Aiming to enhance the heat transfer characteristics of backward-facing step flow in

a channel, Tsay et al. [9] propose a method to install a baffle onto the channel wall.

The effects of the dimensionless baffle height, baffle thickness, and distance

between the backward-facing step and baffle on the flow structure, temperature

distribution, and Nusselt number variation were numerically studied in detail for a

range of Reynolds number varying from 100 to 500.

Nasiruddin and Kamran Siddiqui [10] numerically investigated the effect of

baffle size and orientation on the heat transfer enhancement in a heat exchanger

tube with a single transverse flat-baffle. In that study, three different baffle

arrangements were considered. In the first case, a tube with a vertical baffle was

examined. In the second case, the same tube with a baffle inclined towards the

downstream end was investigated. In the third case, the same tube with a baffle

inclined towards the upstream end was analyzed. They found that a significant

heat transfer enhancement in a heat exchanger tube can be achieved by

introducing a baffle inclined towards the downstream side, with the minimum

pressure loss. Another way for improving the heat transfer characteristics in the

industrial heat exchanger is the use of porous medium. Several forced convection

studies in channels with wall-mounted porous baffles were conducted. Dutta and

Dutta [11] first reported the enhancement of heat transfer with inclined solid and

perforated baffles. In that study, the effects of baffle size, position, and orientation

were studied for internal cooling heat transfer augmentation.

Karwa and Maheshwari [12] presented results of an experimental study of

heat transfer and friction in a rectangular section duct with fully perforated baffles

(open area ratio of 46.8%) or half perforated baffles open area ratio of 26%) at

relative roughness pith of 7.2-28.8 affixed to one of the broader walls. In general,

the half perforated baffles are thermo-hydraulically better to the fully perforated

baffles at the same pitch. In a series of studies, Dutta [13, 14], Dutta and Hossain

[15], Dutta et al. [16], Santos and De Lemos [17], Yang and Hwang [18], Da

Silva Miranda and Anand [19], and Tsay et al. [20] investigated the effects of

different aspect ratio channels and different porosity baffles on internal heat

transfer enhancement. They found that judicious choices of these parameters can

lead to high heat transfer rates with a moderate increase of pressure drop. A

numerical study was reported by Sahel et al. [21] to investigate the turbulent

flows and heat transfer characteristics in a rectangular channel fitted with two

baffles placed on the upper and lower walls. These baffles were perforated by a

row of four holes at three different positions. Three values are taken for the PAR

and which are 0.190, 0.425 and 0.660, respectively. The obtained results showed

that the Pores Axis Ratio (PAR) of 0.190 is the best design that eliminates

significantly the LHTAs, giving thus an increase in the heat transfer rate from 2%

to 65% compared with the simple baffle.

Other similar works can be found in literature such as Siba et al. [22], Chikhi

et al. [23], Menni [24], Menni and Saim [25], Menni and Azzi [26], Adegun et al.

[27], Pakdee et al. [28], Hachemi [29], Moummi [30], Gbaha [31], Chaudry [32].



The baffle shape is also a necessary parameter for the generation of vortex. For

this context, the several works proposed several shapes, for example, flat

rectangular [33-35], rounded [35], graded [36], corrugated [37, 38], diamond [39],

arc [40], ꞌLꞌ [41], cascaded [42], ꞌVꞌ [43], double ꞌVꞌ [44], and ꞌZꞌ-shaped [45]. In

those studies, different geometry parameters and different operating conditions

were used. In those studies, different geometry parameters and different operating

conditions were used.

In this present study, two waisted triangular-shaped baffles (WTBs) are

installed in the rectangular channel on both the upper and lower isothermal walls

in a periodically staggered manner and each WTB-tip pointing downstream. The

Finite Volume Method (FVM), by means of Commercial CFD software

Fluent14.0 is applied in this research work.

2. Mathematical Formulation

2.1. Geometrical model

The system of interest, shown in Fig. 1, is a two-dimensional horizontal

rectangular cross section channel with two-waisted triangular-shaped baffles

(WTBs) placed in a staggered manner on the top and bottom channel walls as

presented in more detail in Demartini et al. [5], used for validation.

(a) Configuration of the problem.

(b) Configuration of the problem.

Fig. 1. Physical model.

This is an important problem in the scope of heat exchangers where the

characterization of the flow field, heat and pressure loss characteristics, as well as

the existence and the extension of possible vortices need to be identified [5].



The numerical simulation is conducted in a two-dimensional domain, which

represents a waisted triangular-shaped baffled channel of 0.167 m aeraulic diameter,

Dh, and 0.554 m length, L. The fluid enters the channel at an inlet temperature, Tin,

and flows over a staggered WTB pair where h is the baffle height, H set to 0.146 m,

is the channel height and h/H is known as the blockage ratio, BR. The axial pith, Pi

or distance between both the considered baffles is set to 0.142 m in which Pi/H is

defined as the pith spacing ratio, PR = 0.972, and the width of the channel, W is

equal to 0.193 m for the channel aspect ratio, AR, of 1.321. The employment of two

staggered transverse WTB elements fitted in the given computational domain is to

create recirculation zones in order to prolong the resistance time of the fluid flow

leading to higher heat transfer rate in the test channel [43].

The form of the baffles varies from the triangular form, Fig. 2(a), to the

waisted triangular form, Fig. 2(b), without changing the geometrical dimensions a

and b, but their size is variable. In this computation, two identical WTBs pointed

towards the downstream end are treated. This baffle form reduces the resistance to

the flow and so leads to a decrease of the pressure drop in the channel [46].

Fig. 2. Shape of baffles treated.

The geometry parameters are listed in Table 1.

Table 1. Dimensions of WTBs used.

Parameter Value

Angle of triangular-baffle tip, α (degree) 7.152

Angle of waisting the baffles β (degree) 50

Ray of waisting the baffles, r (m) 0.030

Baffle height, h (m) 0.080

Thickness of basis baffles, w (m) 0.010

Spacing, Pi (m) 0.142

Inlet distance, Lin 0.218

Exit distance , Lout 0.174

The waisting of the triangular-baffles to obtain WTBs is such that the ray (r)

and angle (β) is equal to 50°, as presented in more detail in Abene et al. [46]. In

the dynamic fluid vein of the channel, the upstream face of the first WTB

mounted on the upper wall of the channel is located at Lin = 0.218 m. The

downstream face of the second WTB is located at Lout = 0.174 m. The WTBs

obtained by waisting the triangular-baffles are slightly inclined as compared to the

h

w w

r

Center

Sense of air flow β

α

(a) Baffle before the waisting. (b) Baffle after the waisting.



entire wall of the computational domain, and the fluid flow is directly guided to

the heated wall surfaces, with less effectiveness when considering the fluid

trajectory between two successive elements of baffles [46].Air is selected as

working fluid, and the parameters are given in Table 2 [47].

Table 2. Thermo-physical data of air at 300K [47].

Parameter Value

Density, ρ (kg/m3) 1.225

Specific heat at constant pressure, cp (J/kg K) 1006.43

Thermal conductivity, λf (W/m s) 0.0242

Dynamic viscosity, μ (kg/m s) 1.7894×10-5

2.2. Numerical model

The mathematical formulations for air flow and forced-convection heat transfer in

the given computational domain was developed under the following assumptions:

(i) Steady two-dimensional fluid flow and heat transfer; (ii) The flow is turbulent

and incompressible; (iii) The thermal-physical properties of fluid such as ρ, μ, cp,

and λf are constant; (iv) Body forces and viscous dissipation are ignored; (v)

Negligible radiation heat transfer; and (vi) The standard k-ε model, proposed by

Launder and Spalding [48], is used for the closure of the system under study.

Based on the above assumptions, the flow in the given computational domain

is governed by the steady two-dimensional form of the Reynolds-averaged

Navier-stokes (RANS) and the energy equations. The detail on mathematical

modelling can be found in similar work by Xie et al. [49].

2.3. Boundary conditions

The aerodynamic boundary conditions are set according to the experimental work

of Demartini et al. [5] while the thermal boundary conditions are chosen

according to the numerical work of Nasiruddin and Kamran Siddiqui [10]. In the

entrance region, a uniform one-dimensional velocity profile (Uin) was prescribed,

as shown in Fig. 1(b). The turbulence intensity (TI) was set equal to 2%.The

pressure-inlet was set equal to the zero (gauge). The temperature of the working

fluid (Tin) was set equal to 300K at the inlet of the channel. A constant

temperature (Tw) of 375K was applied on the channel walls and WTB sides as the

thermal boundary condition. Impermeable boundary and no-slip wall conditions

are implemented over the channel walls as wells as the WTB surfaces. In the

channel outlet it is prescribed the atmospheric pressure, and the derivations of all

the variables, ϕ ≡ (u, v, T, k, ε), along the x-direction were set to zero.

The flow Reynolds number Re, based on channel hydraulic diameter,

Dh = 2HW/(H+W) (1)

is given by

hDURe (2)

The skin friction coefficient, Cf can be written as



2

2

U

C wf

(3)

The friction factor, f is computed by

2

2

U

DLPf h

(4)

The local Nusselt number, Nux is estimated as follow:

f

hx

hD

Nu (5)

The average Nusselt number, Nu is obtained by

xL

xNu1

Nu (6)

where U is the mean air velocity of the channel; h the local convective heat

transfer coefficient, and ΔP is the pressure drop across the test channel

3. Numerical Approach

The Computational Fluid Dynamics (CFD) software Fluent14.0 [47] was used to

capture the thermal and hydrodynamic fields in the whole domain investigated. As a

part of the same package, a pre-processor Gambit was used to generate the required

mesh for the solver [10]. It was first attempted to use a mesh with regular space

steps, but the results obtained were not very satisfactory. Moreover, knowing the

boundary layer phenomena, it seemed quite evident to use a finer mesh on the walls

[50] (Fig. 3). This type of mesh was then used for the rest of our study. Several

grids were tested in order to check whether the solution is independent of the mesh.

Fig. 3. Mesh generated on the upper wall-mounted WTB with refinements

near the solid boundary to resolve velocity and temperature fields.

The wall functions given by Launder and Spalding [48] were employed to

prescribe the boundary conditions along the faces of the WTBs and the channel

walls in the computational domain.

The two-dimensional channel flow model was governed by the Reynolds

Averaged Navier-Stokes (RANS) equations with the standard k-ε turbulence

model [48] and the energy equation. The Finite Volume Method (FVM) [51] is

used in the present study because it offers considerable advantages in terms of

simplicity, reliability of results, and can easily be adapted to the physical problem.

Moreover, it guarantees the conservation of mass, momentum and any

transportable scalar on each control volume throughout the entire computational

domain. This is not the case for the other numerical methods [50]. The SIMPLEC



(Semi-Implicit Method for Pressure-Linked Equation Consistent) algorithm [52]

was adopted for the discretization, and all the variables were treated with the

QUICK-scheme [53], except the pressure term with Second-Order Upwind (SOU)

[51].To control the update of the computed variables in each iteration; under-

relaxation was varied between 0.3 and 1.0 [10].The CFD solution is assumed to

converge when the relative error on ϕ is smaller than δ as [54]

*

*

max (7)

here (*) denote values of the previews iterations; ϕ is a generalized variable that

represents the component velocity u and v, the temperature T, the turbulence kinetic

energy k, and the turbulence kinetic energy dissipation rate ε and δ is a prescribed

error. Here, we select δ = 10-7

for ϕ ≡ (u, v, k and ε) and δ = 10-9

for ϕ ≡ (T).

4.1. Mesh verification

The grid independence was examined by conducting simulations in the whole

domain investigated with upper and lower wall-mounted solid-type WTBs, using

different structured grids with the number of nodes ranging from 220 to 420 along

the length (in X-direction) and 75-160 along the depth (in Y-direction). Table 3

shows the percent errors δ’ and ɛ

’ defined as [17]

100'

ref

ref

Nu

NuNu (8)

and

100'

ref

ref

f

ff (9)

for grids of seven sizes in x and y directions with 220 × 75, 270 × 75, 320 × 95,

370 × 115, 370 × 145, 370 × 160 and 420 × 160 cells, and a near wall elements

spacing of y+ ≈ 2. The number within brackets gives the percentage deviation

relative to the 420 × 160 cells.

Table 3. Effect of node density on the CFD solution

at the surface of the upper channel wall for Re = 8.73 × 104.

x y Nu /Nu0 δ’ (%) f/f0 ɛ (%)

220 75 10.499 11.435 94.116 -03.835

270 75 11.024 07.003 92.462 -02.011

320 95 11.143 05.999 91.753 -01.229

370 115 11.477 03.187 91.521 -00.973

370 145 11.718 01.155 90.050 00.650

370 160 11.607 02.090 89.731 01.002

420 160 11.855 00.000 90.640 00.000



It is found that the variations in Nu and f values at the surface of the upper

channel wall for the Reynolds number of 8.73×104 is less than 1.25% when rising

the number of cells from (370×145) to (420×160) in X and Y directions,

respectively. Thus the final selected grid system is applied with the number of

nodes equal to 145 and 370 along the channel depth and the length, respectively.

It was necessary to refine the mesh near the walls in order to account for the flow

variations in the near-wall region. For the regions more distant from the walls, the

mesh is uniform, as presented in more detail in Demartini et al. [5] and

Nasiruddin and Kamran Siddiqui [10].

4.2. Numerical verification

To validate the present computational fluid dynamic analysis, the axial velocity

profiles obtained from the present simulation were compared with the one

obtained from the numerical and experimental work of Demartini et al. [5] for the

air flow inside a horizontal channel at W/H = 1.321, L/Dh = 3.317, S/H = 0.972,

h/H = 0.547 and Re = 8.73×104. Both the numerical and experimental velocity

profiles were computed along the depth of the channel at axial stations given by

x= 0.189 m and x = 0.525 m, 0.365 m and 0.029 m before the exit, respectively.

The results are presented in Figs. 4 and 5, and as can be seen, there is a good

agreement between the numerical and experimental data which indicates that the

present CFD scheme and the calculation are feasible and accurate.

Fig. 4. Validation of u/uin with reported data [5] for x = 0.189 m.

x = 0.189 m, Re = 8.73 × 104

Vitesse axiale adimensionnelle U/Uin

0,0 0,5 1,0 1,5 2,0

Ch

an

nel

heig

ht

(m)

-0,08

-0,06

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

Present CFD

Numerical [5]



Fig. 5. Validation of u profiles with reported data [5] for x = 0.525 m.

The validation of the Nusselt number and friction factor of the smooth

rectangular channel is performed by comparing with the values from Dittus-

Boelter and Petukhov correlations [55] under a similar operating condition as

shown in Figs. 6 and 7, respectively.

Correlation of Dittus-Boelter,

44.08.0

0 10ReforPrRe023.0 Nu (10)

Correlation of Petukhov,

62

0 105Re3000for64.1Reln79.0

f (11)

As it can be shown in Figs. 6 and 7, the present CFD simulation agrees well

with the available correlations with ±6.5% and ±1.15% in comparison with

empirical correlations of Dittus-Boelter and Petukhov, respectively.

Fig. 6. Verification of Nu0 for smooth channel.

Reynolds number

10000 15000 20000 25000 30000 35000

Av

era

ge N

uss

elt

nu

mb

er

30

40

50

60

70

80

90

Smooth channel

Dittus-Boelter correlation

Ch

an

nel

heig

ht

(m)

Our numerical simulation

Numerical data [5]

x = 0.525 m, Re = 8.73×104

-0,08 -10 0 10 20 30 40

-0,06

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

Axial velocity (m/s)

Experimental data [5]



Fig. 7. Verification of f0 for smooth channel.

4. Results and Discussion

Numerical results of turbulent forced-convection heat transfer and friction loss

behaviors for air flow through a constant temperature-surfaced rectangular cross

section channel fitted with two WTBs are presented for W/H = 1.321, L/Dh =

3.317, S/H = 0.972, h/H = 0.547, and Re = 5,000-8.73×104. Both the WTBs are

placed on both two opposite walls of the channel with staggered arrangement and

each WTB-tip pointing downstream. The streamlines, the velocity and

temperature fields, the dimensionless axial velocity profiles, the temperature

profiles, the skin friction coefficients, and the local and average Nusselt number

distributions were obtained for all the investigated whole domain and for different

stations selected, upstream, downstream and between the two baffles. For the

representation of the figures, Re = 5,000 is chosen as base case.

4.1. Flow topology

The impact of the waisted triangular-shaped baffles (WTBs) on the structure of

the near wall flow is shown in Fig. 8. The field in Fig. 8 presents the stream

function around the baffle module at w = 0.01 m, r = 0.03 m, β= 50°, Pi = 0.142

m, and Re = 5,000. The distance between the upper edge of the baffle and the

wall was kept constant at 0.08 m. This corresponds to the area reduction of 54.794

% at the baffle edge.

Fig. 8. Contour plot of stream function for staggered

WTBs at Re = 5,000. Stream function values in kg/s.

Reynolds number

10000 15000 20000 25000 30000 35000

Ch

an

nel

heig

ht

(m)

0,022

0,024

0,026

0,028

0,030

0,032

Smooth channel

Petukhov correlation



As seen from the figure, a strong recirculation zone is generated downstream of

the top wall-mounted WTB, which was induced due to the flow separation [10].

The zone of recycling was formed in the vicinity of the upper right corner and its

height was approximately equal to the extent of the flow blockage by the WTB,

which is equal to 0.08 m for the whole domain investigated. In the lower part of the

channel, as a result of sudden expansion in the cross-section, the air flow separates,

a larger recirculation zone is formed behind the lower wall-mounted WTB and flow

reattachment is then established [8]. These recirculation zones cause the air to

strongly rotating motion. This motion causes the air near the walls to flow in the

core region and vice versa [56]. It is concluded that the presence of these baffles has

a significant impact on the fluid flow structure by formatting vortices downstream

from each WTB. This observation is confirmed by Demartini et al. [5], Mohammadi

Pirouz et al. [8], Nasiruddin and Kamran Siddiqui [10], Sripattanapipat and

Promvonge [56], and Guerroudj and Kahalerras [57].

The distribution plot of the axial velocity field along the axial length in the

case of Re = 5,000 is shown in Fig. 9. The largest variations in the velocity field

occur in the regions near to the WTBs, as expected [5].

Fig. 9. Distribution of the Axial velocity field in the investigated whole

domain with two staggered WTBs for Re = 5,000. Velocity values in m/s.

The acceleration and expansion of the working fluid are clear when it flows

cross WTBs, and the flow direction varies, which generates longitudinal vortices

behind the WTBs and results in the turbulence enhancement, due to the decreased

flow area effects [58]. The highest velocity value can be observed where the flow

impinges the channel walls while the lower one is found at the WTB corner area

where the corner recirculation zone occurs, especially area behind the WTBs. The

most intense recirculation zone is that occurring downstream of the bottom wall-

mounted WTB, responsible for high flow velocities observed at the region

opposite the second WTB, creating a negative velocity profile which introduces

mass inside the test section through the outlet [5].These results showed the same

behavior as Demartini et al. [5], Mohammadi Pirouz et al.[8], Nasiruddin and

Kamran Siddiqui [10], Sripattanapipat and Promvonge [56], and Guerroudj and

Kahalerras [57], and except for flow areas around the baffle corners.

Figure 10 shows the axial velocity profile distribution plot in the case of Re =

5,000 at transverse positions given by x = 0.159, 0.174, 0.189 and x = 0.204 m,

respectively 0.059, 0.044, 0.029, and 0.014 m before the top wall WTB, located at

a distance of x = 0.218 m from the entrance.




0,0 0,2 0,4 0,6

Ch

an

nel

heig

ht

(m)

-0,08

-0,06

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

x = 0.159 m

x = 0.174 m

x = 0.189 m

x = 0.204 m


-0,4 -0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2

Ch

an

nel

heig

ht

(m)

-0,08

-0,06

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

x = 0.315 m

x = 0.33 m

x = 0.345 m

x = 0.36 m

Fig.10. Profiles of axial velocity

upstream of the top wall-mounted

WTB for Re = 5,000.

Fig.11. Profiles of axial velocity

between the first and the second

WTBs for Re = 5,000.

In these locations, the plot shows that as the air flow approaches the first

WTB, its velocity is reduced in the upper part of the channel while in the lower

part is increased. Between the WTBs, at locations x = 0.315, 0.330, 0.345 and x =

0.360 m from entrance, respectively 0.055, 0.04, 0.025 and 0.01 m before the

second WTB, the air flow is characterized by very high velocities at the lower

part of the channel, respectively, approaching 275.555, 266.666, 248.888 and

240.000% of the inlet velocity, which is 0.45 m/s, as shown in Fig. 11. In the

upper part of the channel, negative velocities indicate the presence of

recirculation behind the first WTB. Its velocity is reduced in the higher half of the

channel, while in the lower half the air flow starts to accelerate toward the gap

above the second WTB as indicated and confirmed by Demartini et al. [5].

Axial distributions of velocity profiles for transverse stations x = 0.390, 0.405,

0.420 and x = 0.435 m, measured downstream of the entrance are shown in Fig.

12. These locations are situated behind the second WTB, located at x = 0.370 m

from the entrance. In the figure, the trends of velocity profiles are similar in all

locations. The second WTB was installed 0.142 m downstream of the first WTB

where the influence of the zone of recycling generated by the bottom wall-

mounted WTB, is very large as seen in Fig. 12.


-0,6 -0,4 -0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6

Ch

an

nel

hei

gh

t (m

)

-0,08

-0,06

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

x = 0.39 m

x = 0.405 m

x = 0.42 m

x = 0.435 m


-0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4

Ch

an

nel

hei

gh

t (m

)

-0,08

-0,06

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

x = 0.525 m

Fig. 12. Profiles of axial velocity

downstream of the bottom wall-

mounted WTB for Re = 5,000.

Fig. 13. Profiles of axial velocity near

the channel outlet for Re = 5,000.



Due to the change in the air flow direction produced by the lower wall WTB, the

highest velocity values appear neat the top face of the WTB with an acceleration

process that starts just after the second WTB [5]. The maximum velocity is obtained

at x = 0.435 m while the lowest one is for x = 0.390 m. At positions x = 0.390,

0.405, 0.420 and x = 0.435 m after channel inlet, the value of the velocity,

respectively, reaches 1.185, 1.240, 1.320 and 1.445 m/s, respectively, 2.633, 2.755,

2.933 and 3.211 times higher than the entrance velocity.

A representation of numerical results of axial velocity after the second WTB,

near the channel outlet is shown in Fig. 13. The greatest values occur, as

expected, after the considered WTB, near the upper channel wall. In this area, the

value of the velocity reaches 1.36 m/s, 3.02 times higher than the entrance

velocity. In the lower part of the channel, velocity profiles present negative

values, meaning that the pressure in that location is below atmospheric pressure as

reported by Demartini et al. [5]. These negative velocities indicate the presence of

recirculation behind the bottom wall-mounted WTB, near the channel exit. These

recirculation cells are produced by introducing two WTBs in the dynamic air vein

of the rectangular channel, known as vortex generators, as indicated by

Nasiruddin and Kamran Siddiqui [10]. The pressure difference across the vortex

generators causes flow separation and induces vortices downstream. The vortex

creates a rotating motion within the flow stream, which causes a rapid transfer of

fluid parcels to and from the heat transfer wall surface [10].

4.2. Heat transfer

The presence of the WTBs influences not only the velocity field but also the

temperature distribution in the computational domain examined. The contour plot

of temperature field along the axial length at a Reynolds number of Re = 5,000 is

shown in Fig. 14. It can be seen that there is a major change in the temperature

field along both channel walls, especially in the region opposite the WTBs [56].

Fig. 14. Temperature field distribution in the channel

with two staggered WTBs for Re = 5,000. Temperature values in K.

The higher temperature gradient can be observed where the air flow impinges

the channel walls while the lower one is found at the WTB corner area, especially

at the locations corresponding to the zones of counter rotating flow as seen in the

figure [56].The figure also shows that the fluid temperature in the recirculation

region is significantly high as compared to that in the same region of no WTB

case, due to the insertion of the baffles [10]. Due to the changes in the flow

direction produced by the WTBs, the highest temperature values appear behind

the WTBs in the vicinity of right faces with an acceleration process that starts just

after the second WTB as shown in Fig. 8.



The fluid temperature profiles are shown in Fig. 15 in different sections of the

channel are identical to those shown in the figures above. Fig. 15(a) shows the

temperature profiles upstream of the first WTB for two transverse positions at x

=0,159mandx = 0,189m. We note that the presence of the first WTB which is in

the upper half of the channel induces a strong increase in temperature,

paradoxically in the lower half, where we find significantly lower values.

In the intermediate zone, at transverse positions x = 0.255 m and x = 0.285 m

downstream of the first WTB, Fig. 15(b) shows that the flow is characterized by

high temperatures in top part of the channel. In part again stand inversely at the

lower part, there is a temperature reduction in the free segment located between

the top of the first baffle and the bottom wall of the channel. We also note that the

nearest section of the fin is the best heated section away.

Figure 15(c) shows the total temperature profiles upstream of the second WTB

for two transverse positions at x = 0.315 m and x = 0.345 m. It is noted that the

flow approaching the second WTB, the temperature is increased in the bottom of

the channel, while in the upper part; the temperature is reduced compared with the

previous two sections. At the channel output, for x = 0.525m, the profiles of total

temperature was presented in Fig. 15(d). The values of temperature decrease

significantly in both high and low regions of the channel, since it was near the

exit of channel, where this section is removed plenty relative to the fins.

It addition, according to analysis of our numerical results on axial velocity profiles

(Figs. 8-12), and the total temperature profiles (Figs. 13 and 14) for different sections

of the channel, it is found that the temperature of the fluid is related to the velocity of

flow. It is clear that for high velocity values, temperatures drop significantly. In other

words, it exists an inverse proportionality between increasing velocity value and the

total temperature in each channel cross section.

The heat transfer coefficient characterized by the local number of convective

Nusselt, Nux, is then determined by Eq. (5)and presented along the upper wall of

the channel, as shown in Fig. 16. The Nux shows the largest value in the region

opposite the second WTB, and the smallest value in the region around the first

WTB due to the strong velocity gradients in that region as indicated by

Sripattanapipat and Promvonge [56].As expected, the local Nusselt number is

high at the start of the heating section due to the development of the thermal

boundary layer [15]. In the figure, the Nux values tend to drop considerably to

almost zero when it reaches and passes the first WTB [56]. The placement of the

first WTB at the beginning of the channel (Lin = 0.218 m) disturbs the boundary

layer formation and contributes to higher heat transfer as reported by Dutta and

Hossain [15]. The plot shows that in the region downstream of the considered

WTB, x ˃ 0.228 m, the local Nusselt number is enhanced. This enhancement is

due to the intense mixing by the vortex. This result shows the same behavior as

Nasiruddin and Kamran Siddiqui [10] results. The plot shows that the maximum

Nux occurs in the lower wall WTB regime that has the maximum velocity [10].

These local peaks are certainly due to the jet impingement from the lower waisted

section [10]. In the region downstream of the lower wall WTB, the value of the

Nusselt number decreases gradually, where the effect of the vortex mixing is

diminishing [10]. They concluded that the appearance of the vortex flows can

help to increase higher the heat transfer in the WTB channel because of highly

transporting the fluid from the core to the near wall regimes [59].



Total Temptrature (K)

300 320 340 360 380

Ch

an

ne

l h

eig

ht

(m)

-0,08

-0,06

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

x= 0.159 m

x= 0.189 m

(a)

Total Temperature (K)

300 320 340 360 380

Channel h

eig

ht (m

)

-0,08

-0,06

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

x= 0.255 m

x= 0.285 m

(b)

Total Temperature (K)300 320 340 360 380

Cha

nnel

hei

ght (

m)

-0,08

-0,06

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

x= 0.315 m

x= 0.345 m

(c) Total Temperature (K)

300 320 340 360 380

Channel h

eig

ht (

m)

-0,08

-0,06

-0,04

-0,02

0,00

0,02

0,04

0,06

0,08

x=0.525 m

(d)

Fig. 15. Distribution of fluid temperature profiles in different axial stations

of the channel: (a) upstream of the first WTB at x = 0.159 m and x = 0.189 m,

(b) between the WTBs at x = 0.255 m and x = 0.285 m, (c) upstream of the

second WTB at x = 0.315 m and x = 0.345 m, and (d) after the second WTB,

near the exit, Re = 5,000. Temperature values in K.

Axial position (m)

0,0 0,1 0,2 0,3 0,4 0,5 0,6

Loca

l N

uss

elt

nu

mb

er [

-]

0

200

400

600

800

1000

1200

1400

1600

1800

Top channel wall

Reynolds number [-]

0 5e+4 1e+5 2e+5 2e+5

Av

era

ge

Nu

ssel

t n

um

ber

[-]

0

1000

2000

3000

4000

5000 Bottom channel wall

Top channel wall

Fig. 16. Axial variation of Nux along

the upper channel wall for Re = 5,000.

Fig. 17. Effect of Re number on Nu

at the surface of lower and upper

channel walls.

In thermal point of view, it is interesting to study the influence of the variation

of the Reynolds number on the evolution of the average Nusselt number along the

top and bottom walls of the channel, Fig. 17 shows this dependence. It was found

that the highest rate of heat transfer is achieved by increasing the Reynolds

number where the flow structure very disturbed which promotes mixing of the

fluid. On each wall, when the Reynolds number increases, the Nusselt number



believed, where we also find that the temperature gradient at the level of the

heated walls decreases with increasing flow rate. This is because the introduction

of the negative velocity of the turbulent flow, forced convection reduces the level

of turbulence intensity within the boundary layer. For a Reynolds number

between 5,000 and realized 2×105, it is clear that there is a direct proportionality

between the increase in average Nusselt number and the increase of Reynolds

number where the heat transfer rate reaches its maximum on the top wall.

4.3. Friction loss

Waisted triangular-shaped baffles play an important role in the dynamics of the

air flow through the whole domain investigated. For the better comprehension of

the phenomena produced by these devices, the search of detailed information

about the friction loss characteristics is necessary.

The skin friction coefficient, as seen in Eq. (3), was adopted to evaluate the local

resistance loss in the given computational domain. Figure 18 presents the variation in

the local skin friction coefficient along the top wall. It can be clearly seen that the

values of the coefficient of friction is very low near the first WTB especially in

upstream areas, this may be caused by the absence of WTB as obstacles. We also note

the increased friction in the intermediate zone due to the recirculation of the fluid

which then results in an abrupt change indirection of flow. We also note that the

highest values of friction coefficient are situated in the output of the channel; these

values correspond to significant pressure drops which are caused by the effect of the

expansion of the air leaving the section formed by the second WTB and the top wall.

The two minimum Cf values are generated by the separation of the air flow through

the upper wall WTB. One is around the baffle and the other is at reattachment point

behind the baffle. This observation is confirmed by Sripattanapipat and Promvonge

[56]. The pressure drop is also affected by the Re number.

Figure 19 illustrates the variation of the average skin friction coefficient, f

calculating along both top and bottom walls, corresponding to radial positions y =

0.073 m and y =-0073 m respectively, and for a Reynolds number range from

5000 to 2×105. It is clear that there is proportionality between the increase in

coefficient of friction and the elevation of the Reynolds number. Similarly to the

results in Fig. 16, the highest friction loss values are found at the heated top

channel surface, due to the high velocities in that region.

Axial position (m)

0,0 0,1 0,2 0,3 0,4 0,5 0,6

Sk

in f

ric

tio

n c

oeff

icie

nt

[-]

0,00

0,02

0,04

0,06

0,08

0,10

0,12

0,14

Top channel wall

Reynolds number [-]

0 5e+4 1e+5 2e+5 2e+5

Aver

age

fric

tcoef

fici

ent

[-]

0

2

4

6

8

Bottom channel wall

Top channel wall

Fig. 18. Axial variation of Cf along the

top channel wall for Re = 5,000.

Fig. 19. Effect of Re number

on f at the channel walls.



5. Conclusion

A numerical analysis has conducted to examine the flow and heat transfer in a

two-dimensional constant temperature-surfaced rectangular channel fitted with

waisted triangular-shaped solid-type baffles (WTBs) for the turbulent flow

regime, Reynolds number of 5,000 to 2×105. The computational fluid dynamic

analysis shows a fairly complex flow disorganized where the fluid is deflected

towards the top and bottom walls with high velocities. This aeraulic structure has

significantly influenced the repair of the temperature field which explains the high

heat transfer in the areas of recycling, and the distributions of the Nusselt number

varies with the geometry of the WTBs. The analysis results also showed inverse

proportionality between the increase in the rate of flow and the total reduction in

the fluid temperature in each channel cross-section, this means that the

temperature gradient at the heated wall decreases with increase in the flow

velocity. Weal souses large Reynolds numbers and thus the high velocities;

significantly improve the coefficient of friction and the rate of heat transfer. The

current originality lies in the geometric shape of the baffles inside the channel.

Acknowledgments

This research was funded by the Unit of Research on Materials and Renewable

Energies, Abou Bekr Belkaid University, Republic of Algeria. The authors would

like to thank Associate Prof. Dr. Ahmed AZZI for suggestions.

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