Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 5, N. 2 Special Issue on Heat Transfer
213 However, due to the high temperatures of the exhaust
components and crowded engine compartment that may impede the external forced convection, one expects free
convection heat transfer to be important, though along the external exhaust system in some stagnation zones
buoyancy force could be significant.
In this paper a two-dimensional model of a section of the car underbody near to the catalyst, the most critical
component belonging to the exhaust line [6], is proposed in order to study the interactions with the road surface
and the exhaust system. The system is represented by a partially open horizontal cavity, heated by a duct placed
in the middle. The vehicle is stationary so only the natural convection is regarded as well as the radiation
mechanism.
Manca et al. [11] studied a configuration made of two horizontal parallel plates with the upper plate heated at
uniform heat flux. Results were reported for Rayleigh numbers equal to 103 and 105 and for two aspect ratios.
Koca [12] provided a numerical study about the conjugate heat transfer in partially open square cavity
with a vertical heat source for different Rayleigh numbers, conductivity ratios, opening position and open
length. Jaluria et al. [13] provided a transient analysis of natural convection in air in a horizontal open ended
cavity for a similar configuration and presented results for several significant variables, such as the penetration
length, Rayleigh numbers and aspect ratio values.
In this work a transient analysis of the interaction of a car underbody with the exhaust system and the road
surface is carried out in order to study the behavior of the system, with or without thermal shields. The vehicle is
assumed to be stationary so natural convection is the primary heat transfer mode.
II. Description of the Geometrical and
Numerical Model
The numerical model is a two-dimensional model of a car underbody section, close to the catalyst, interacting
with the road surface and the exhaust line. In order to study the influence of the introduction of the thermal
shields, a numerical model is developed. Figure 1a shows the considered geometric parameters, such as L,
the under-body length, l, the tunnel length, H, the distance from the road surface, h, the tunnel height and
D, the pipe diameter. As shown in Figure 1b, the exhaust pipe warms up the underbody wall, because its
temperature is set to 873 K and air comes in and out the channel by the bottom side walls INOUT. The
numerical analysis is carried out in laminar and transient state conditions. The considered fluid is air and all the
thermo-physical properties are assumed to be constant, except for the dependence of density on the temperature
Boussinesq approximation which gives rise to the buoyancy forces. Temperature is evaluated at an average
temperature calculated between the exhaust system value and ambient one T
a
= 300 K.
a
b Figs. 1. a sketch of the model and geometric parameters; b model
including thermal shields
The investigation is accomplished by means of FLUENT code [14]. As the car is assumed to be
stationary, the main heat transfer mechanism is represented by natural convection. However, radiative
effects are taken into account and the emissivity of the thermal shield is set to 0.13 while their thickness and
thermal conductivity are equal to 0.7x10
-3
m and 200 WmK, respectively. The temperature of road surface is
333 K. The exhaust system pipe diameter is 0.04 m and its emissivity is 0.85 while
ε for the underbody and road is
0.98 and 0.90, respectively. The base configuration of the model is characterized by H = 0.12 m, L = 0.85 m, lh
= 2.27 while the other geometric ratios and parameters considered in the investigation are shown in Table I.
TABLE I G
EOMETRIC
P
ARAMETERS
C
ONSIDERED
I
N
T
HE
I
NVESTIGATION
lh H [m]
L [m] 1.00 0.09
0.60 1.45 0.12
0.70 2.00 0.15
0.85 2.27 0.24
0.90 3.26 0.36
1.00 4.00
A transient solution and a segregrated method are chosen to solve the governing equations. A second-order
upwind scheme is chosen for energy and momentum equations. The convergence criteria of 10
-5
and 10
-7
for the residuals of the velocity components and energy ones
are assumed, respectively. It is assumed that the incoming flow is at the ambient temperature, such as T
a
Copyright © 2011 Praise Worthy Prize S.r.l. - All rights reserved International Review of Mechanical Engineering, Vol. 5, N. 2 Special Issue on Heat Transfer
214 = 300 K. The effects of radiation are taken into account,
too. The Discrete Transfer Radiation Model DTRM is employed, assuming all surfaces to be diffuse. A grid
independence analysis has been lead in order to individuate the best compromise between the accuracy
and computational time.
Four different non-structured meshes have been developed considering the model characterized by l =
0.250 m, h = 0.110 m, H = 0.120 m and L = 0.850 m without thermal shields. They have a number of nodes
equal to 10676, 17194, 25206 and 41802, respectively. The third mesh has been adopted because the comparison
of the results in terms of tunnel and side wall temperatures with a coarsen mesh has revealed a little
difference, at most equal to 0.15 as shown in Figure 2.
Furthermore, a sensitivity analysis of the solution on the time step have been accomplished, choosing a value
equal to 0.2 s, and several simulations have been carried out to set properly the radiation model parameters.
Results are presented in terms of dimensionless parameters, defined by the next relations:
. d
f
qD Nu
T T
k =
−
1
d
T T
T T
θ
− =
−
2
2
t D
ν τ =
3
t [s] T[
K ]
10 20
30 40
50 340
360 380
400 420
440 460
480 500
520
Model 1 Model 2
Model 3 Model 4
Fig. 2. Temperature profiles of the tunnel walls depending on time for the four considered mesh grids
III. Results and Discussion
