A parametric approach for the study of heat flow between street canyon and the atmosphere

Abstract

This paper presents the investigation results of the convective heat flow behaviour among the top of an urban street canyon and overlying atmosphere using a numerical model together with available field measurement data in variable geographical and meteorological conditions. It finds that the heat flow structure characterizes the street canyon have a strong relationship with narrowness index, outside wind velocity and latitude of the study area. The increase of the narrowness index and consequently, reduction of the sky-view factor leads to the diminution of heat flow exchange. The temperature of canyon surfaces in smaller narrowness index (n) decreases quickly to the lower degree than the temperature of the surface with larger (n) one. The increase of wind velocity outside of canyon makes this convective heat exchange flow higher, and cooler the street canyon. A parametric approach was established to evaluate this convective heat exchange flow based on the narrowness index, the latitude of the city and outside wind velocity.

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1Associate Professor at International Islamic University Malaysia. Email: eusuf2005@gmail.com
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PLANNING MALAYSIA:
Journal of the Malaysian Institute of Planners
VOLUME 16 ISSUE 2 (2018), Page 63 – 74
A PARAMETRIC APPROACH FOR THE STUDY OF HEAT FLOW
BETWEEN STREET CANYON AND THE ATMOSPHERE
Muhammad Abu Eusuf1, Wira Mohd. Noor Salleh2, Abdullah Al Mamun3,
Adnan M.4, MSR Sabeek Eusuf5, Ataur Rahman6, & Mansor Ibrahim7
1,2,3,4,6Kulliyyah of Engineering
INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA
5,7Kulliyyah of Architecture and Environmental Design
INTERNATIONAL ISLAMIC UNIVERSITY MALAYSIA
Abstract
This paper presents the investigation results of the convective heat flow behaviour
among the top of an urban street canyon and overlying atmosphere using a
numerical model together with available field measurement data in variable
geographical and meteorological conditions. It finds that the heat flow structure
characterizes the street canyon have a strong relationship with narrowness index,
outside wind velocity and latitude of the study area. The increase of the
narrowness index and consequently, reduction of the sky-view factor leads to the
diminution of heat flow exchange. The temperature of canyon surfaces in smaller
narrowness index (n) decreases quickly to the lower degree than the temperature
of the surface with larger (n) one. The increase of wind velocity outside of canyon
makes this convective heat exchange flow higher, and cooler the street canyon.
A parametric approach was established to evaluate this convective heat exchange
flow based on the narrowness index, the latitude of the city and outside wind
velocity.
Keyword: street canyon, narrowness index, convective heat flux

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INTRODUCTION
Urban climate research has been carried out in two distinct scales: urban
boundary layer (UBL) and urban canopy layer (UCL) (Oke, 1981). At the
mesoscale, the UBL derives many of its characteristics from the interaction with
the UCL beneath (Swaid, 1990), which extends vertically between the levels of
zero net heat flux in the ground up to an arbitrary upper level, which is a fictitious
surface, known as an urban lid and situated slightly above the roof level (Swaid
& Hoffman, 2010). Within this level, all the structures at the urban surface
contribute to the energy storage.
The complexity of the UCL generates an unlimited number of
microclimates that prevents its study at city-scale. Thus, instead of studying the
whole UCL, in the microscale the smallest division, which has common structural
characteristics known as urban street canyon, is investigated. Fig. 1 shows the
different geometrical aspects. Some studies have addressed the problem of
heating characteristics of the canopy layer; especially the street canyon and then
significant results have achieved (Yoshida, Tominga, & Watatani, 1990; Mills,
1993; Oke, 1981; Nunez & Oke, 1977; Sharlin & Hoffman, 2004; Swaid &
Hoffman, 2011; Swaid & Hoffman, 2010).
The top of UCL yields the lower boundary conditions for any model of
the overlying UBL. To study the thermal characteristics at city-scale, heating
characteristics of the canopy layer and heat exchange between this layer and the
overlying atmosphere must be well understood. However, in a numerical model
for the urban climate, to give a detail resolution in the canopy layer, the grid
meshes in the horizontal direction must be much smaller than the width of the
urban canyon. This usually prohibits the application of the model to a large scale
due to the limitation of computational facilities. Thus, large grid meshes in the
horizontal direction and enables the study of the urban thermal climate at the scale
of a city. It is, therefore, evident that the quantification of the exchange processes
between the top of the UCL and the overlying atmosphere at the lowest
computational cost is of vital importance.
This study also attempts to provide a quantitative estimate of the
convective heat exchange between the smallest division of the urban canopy layer
and the overlying atmosphere through a parameterization scheme based on
observed data and a numerical model.

Muhammad Abu Eusuf, Wira M.N.S, Abdullah A.M, Adnan M., Sabeek E., Ataur R., & Mansor I.
A Parametric Approach for The Study of Heat Flow Between Street Canyon and The Atmosphere
© 2018 by MIP
52
HEAT FLOW AND CHARACTERIZATION ON STREET CANYON
Studies have revealed that the main reason for the modification of heat flow is
the reduction of the fraction of the bare soil surface and the increase of paved or
covered surfaces in the urban area (Yazid, Sidik, Salim, & Saqr, 2014). Generally,
for an unpaved natural ground surface, a significant portion of the net incoming
radiation is converted into latent heat by evaporation & evapotranspiration
(Asaeda & Vu, 2000) and as consequences minimal heating of the soil surface
and that influence the reduction of subsurface heat storage and then convective
heat exchange between the soil surface and atmosphere is small. In this case, the
reheating of the atmosphere by convective heat released from the ground surface
is present only during the solar hour. After sunset, surface temperature decreases
quickly and soon becomes lower than that of the atmosphere. Nocturnally, the
downward transfer of the convective heat from the atmosphere to the ground
surface leads to the cooling of the atmosphere by the ground surface (Asaeda &
Vu, 2000). But the situation is entirely different for a paved or covered surface.
During the solar heating time, paved surface absorb a huge amount of solar
insolation and since no evaporation can occur, the surface temperature becomes
significantly higher than that of the overlying atmosphere. Due to higher surface
temperature created more convective heat exchange between the canyon surface
and the atmosphere and emitted higher net upward infrared radiation from the
surface, modifying air temperature in the urban area compared with that in the
rural area. Besides, the high conductivity of the pavement material helps to store
a significant amount of heat flow (Asaeda & Vu, 2000).
Figure 1: Different Urban geometrical aspects in studies
Source: Toparlara, Blockena, Maiheub, & van Heijstd (2017)
The subsurface storage heat is released to the atmosphere nocturnally in
the form of convective heat and upward infrared radiation. The complexity of the

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urban surface represented by urban structures can reduce the sky-view from the
surface, thus trapping portion of infrared radiation emitted by the surface, and
making surface temperature even higher. Hence the temperature of the
atmosphere above an urban surface is higher than that above the rural surface not
only during the day, but also at night.
Figure 2: Geometry and flow characterization of Urban Street Canyon
Source: Yazid et al. (2014)
This phenomenon is known as the urban heat island (Oke, 1981;
Toparlara et al., 2017) and the difference of the air temperature with surrounding
rural area is called urban heat island intensity the underground heat storage, and
paved surface temperature is different for different pavement materials and
canyon geometries (Vu, Asaeda, Ito, & Armfield, 1994; Oke, 1981; Nunez &
Oke, 1977; Swaid & Hoffman, 2011; Yazid et al., 2014) (Figure 2). Heating
processes in a street canyon area very complicated due to the complexity of the
wind field and the radiation condition due to the change of skyline and which
affects the duration of sunshine and radiate interaction occurs between a building
and front streets. Also, surfaces in a street canyon can absorb the incoming direct
and diffuse solar radiation together with short-wave radiation reflected and
infrared radiation emitted by the surrounding environments. This interaction is
determined by narrowness index of a street canyon, which is the ratio between
the average high of buildings at both sides of the street canyon and width of the
street. The physical environment can change with the narrowness index, and this
leads to alterations of heat energy exchange and thermal conditions. The increase
of the narrowness index leads to: (i) a smaller fraction of a surface sunlit; (ii)
smaller downward diffused short-wave; (iii) reduction infrared radiation to the
surface in a street canyon. Consequently, the canyon surface becomes cooler
during the day, which results in it smaller convective heat flow interchange
among the street canyon and the overlying atmosphere. However, a street canyon
with high narrowness index can trap massive portion of the infrared radiation
emitted by its surfaces and slow down cooling processes after sunset. Studies
have revealed that wind blowing over a street canyon creates eddies inside the
street canyon whose number and intensity depends on the narrowness index (Vu

Muhammad Abu Eusuf, Wira M.N.S, Abdullah A.M, Adnan M., Sabeek E., Ataur R., & Mansor I.
A Parametric Approach for The Study of Heat Flow Between Street Canyon and The Atmosphere
© 2018 by MIP
54
et. al., 1994). It is clear that all of the factors as mentioned above must consider
for the study of the canyon heating processes.
FLOW OF MATERIALS
Field Observations
Field observations were carried out at IIUM Gombak campus, Selangor,
Malaysia, 3.2513oN, 101.7362°E, to study the heating characteristic of street
canyons. The observational site was near the Rectory building (known as Imam
Gazzali Street - a street canyon). The narrowness index of street canyons varies
between 2 to 3.0, with the North-south orientation.
During the observation, the metrological parameters were measured at
2m height using hand-held KANOMAX CLIMOMASTER 6511 with the
accuracy of ± 1%. The sampling and recording rate for the sensor is 1 minute.
Other parameters such as Albedo, surface temperature, etc. were also measured.
Observations were carried out from January to December 2014. The weather
conditions were varying from sunny, cloudy and rainy days. Since the purpose of
this paper is to validate a numerical model and construct a Parametric approach
between Street Canyon and the Atmosphere and the data observed from July 7th
were used to attain this validation
A sketch of the observational area and points are represented as shown
in Figure 1 and Figure 2, were different geometry and flow characteristics are
with various narrowness indices and orientation. Figure 2 depicts geometry and
flow characteristics urban street canyon include upwind and backwind building,
x-y-z flow.
As can be seen in the figure, the day was hot and sunny where air
temperature and solar influx reaching more than 33°C, close to 800 W/m2 and
150 W/m2 as incident and reflected radiation at noon, respectively. The
meteorological conditions from 8 a.m. to 8 p.m. varies in the range from 23- 33o,
85.4% to 82.8%. This hot and humid weather is typical during the tropical (dry)
Kuala Lumpur area. Figure 3 describes the observed diurnal solar influx: incident
(Si) and reflected radiation (Sr).
In order to investigate the behavior of convective heat exchange between
the street canyon and the boundary layer above, heating characteristics of street
canyons with different narrowness indices must be investigated. However, a huge
amount of observational data would be needed for this purpose. Being, a very
costly and time- consuming task and basically challenging to implement in
practice.
Numerical Model Description
The numerical model employed in this study is the same as that of Vu et al.
(1994). In this model the temperature of walls and road surfaces in a long, straight
street canyon is computed by solving the one-dimensional heat conduction

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equation (1) as follows:
(1)
The boundary conditions at outsides surfaces of walls and road are the
energy balance equation:
(2)
Where, ρc is the volumetric heat capacity of the surface material; k is the
thermal conductivity of the surface material; T is the surface temperature; S is the
total short-wave radiation to the surface; α is the canyon surface albedo; RLn is
the net infrared radiation to the surface and H is the convective heat flux. The
temperatures inside the buildings and at depth are considered constant.
To compute the fabric (walls and road) temperature, the street canyon is
divided into many horizontal and vertical elements4. Then, for each element,
equation 1 is discretized in the normal direction to the element surface using a
finite difference Crank-Nicholson scheme. RLn is estimated from the following
equation (3)9.
(3)
Where i is the receiving surface temperature, j and k are the emitting
surface elements to i, Tj, Ti, Tk and εi, εj, εk are the temperature and emissivity of
surfaces of elements i, j, k respectively, and εa is the atmospheric apparent
emissivity, Ta is the temperature outside the canyon and ψsky-I is the view factor
of ith element for the sky and ψji is the view factor of surface element i for surface
element j. The last term of the eqn. (3) is assumed to be negligible in the 2-D
canyon analysis; the first and second terms are incoming infrared radiation from
the surface; and the last term is that of alternate regions. The convective heat flux
H from an element i is estimated by the equation 43,
(4)
In equation 4, the convective heat transfer coefficient hc is estimated as3:
(5)
Since the purpose of this work is to establish a parameterization scheme
which permits the evaluation of convective heat exchange between the street
canyon and outside atmosphere, wind velocity outside the street canyon u should
be used in equation 5 (Nunez & Oke, 1977).
To verify the applicability of the model for the simulation of the heating
processes in a street canyon, the model was used to compute temperature at wall

Muhammad Abu Eusuf, Wira M.N.S, Abdullah A.M, Adnan M., Sabeek E., Ataur R., & Mansor I.
A Parametric Approach for The Study of Heat Flow Between Street Canyon and The Atmosphere
© 2018 by MIP
56
and road surface at the observational site. The model has also been used to
compute surface temperature in an east-west oriented street canyon for the
observations reported in Yoshida et al. (1990).
RESULTS AND DISCUSSION
Diurnal Variation of Heat Influx
Figures 3 depicts the comparison between computed and observed diurnal
variations of heat fluxes within the North-South oriented street canyons with the
conditions reported in Yoshida et al. (1990). The convective heat flux at the top
of the canyon Ht is estimated using equation 9 in the next section; the net radiation
flux Q* is estimated based on the computed net short-wave and infrared radiation
to the street canyon; and the conductive heat flux Qg is the difference between the
net radiation (Vu et. al., 1994). Figure 5 also confirms that there is a satisfactory
agreement between the computed and observed heat fluxes.
All above-mentioned facts prove that the numerical model can simulate
the heating processes in a 2D street canyon with reasonable accuracy.
Figure 3: The observed diurnal solar influx: incident (Si-eqn 6) and reflected
radiation (Sr-eqn 7)

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𝑆𝑖 = 0.51 × 102 + 0.16 × 103𝑡 − 0.945 × 102𝑡2
+ 0.196 × 102𝑡3 − 0.164 × 10𝑡4
+ 0.06𝑡5 − 0.8032 × 10−3𝑡6
Root mean square (RMS)=90% (A)
𝑆𝑟 = 0.088 × 102 + 0.301 × 102𝑡 − 0.182 × 102𝑡2
+ 0.037 × 102𝑡3 − 0.031 × 10−1𝑡4
+ 0.1136 × 10−1𝑡5 − 0.1522
× 10−3𝑡6 RMS=91% (B)
Σ 𝑆𝑟
𝑆𝑖 (C)
Where 𝛼 in equation 8 is the albedo or solar reflectivity coefficient for
urban canyon and that 𝑆𝑟 is multiple in characteristics, but for plane location 𝑆𝑟 is
single. Figure 4 describes the meteorological condition of the observed area. The
figure also depicts the tropical characteristics of the experimental field. In
general, it is expected that air temperature at a specific point in a city influences
not only by physical structures immediately surrounding but also by the heating
processes at more remote locations due to heat advection by local wind. Since the
wind velocity at the area mentioned above is in the range of 0.3-2 m/s, thermal
advection is expected in this case.
Convective Heat Flow at the Fictitious Level
Assuming that the energy involved in advection, canyon air temperature change
and radioactive flux divergence is small in comparison with the surface sources.
𝛼 =

Muhammad Abu Eusuf, Wira M.N.S, Abdullah A.M, Adnan M., Sabeek E., Ataur R., & Mansor I.
A Parametric Approach for The Study of Heat Flow Between Street Canyon and The Atmosphere
© 2018 by MIP
58
Figure 4: The meteorological conditions of the observed area
The convective heat flux through the top of the canyon can be evaluated
using the convective heat fluxes at the vertical and horizontal surface as
(Toparlara et al., 2017)
(9)
Where He, Hw and Hƒ are the convective heat flux at the east & west wall and the
canyon, n is the narrowness index of canyon which is estimated as follows (Oke,
1981; Nunez & Oke, 1982)
(10a)
Where, ws is the width of the canyon (m). zb is the height of the building and it is
estimated as follows (Yoshida et al., 1990)
(10b)
Where b is the height of the building in meters, xp is the number of stories and c
is the height of basement floor (m).
Parameterization of Heat Flow Structure
As presented in previous section, for a clear summer day, the convective heat flux

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at the top of a street canyon strongly depend on the narrowness index, outside
wind velocity, latitude o the place and time of the day, and the difference between
air temperatures inside the street canyon and outside (Figure 5).
Parameterization For parametrization of Ht all factors must consider. A
generalized equation for the evaluation of Ht is proposed as follows-
(11)
In equation 11, ∆T is the air temperature difference between the
imaginary surface at the top of the canyon and outside atmosphere. This
temperature difference decrease to a minimum at around 06:00 and its magnitude
increases rapidly during the morning hours peaking at about 13:00-14:00 near the
maximum of net solar radiation.
Figure 5: Parametrized the heat flow in urban canyon system
RLn to the surface; α and β are the parametric coefficients with
is a function of latitude, narrowness index, time and outside wind
velocity, and is a function of narrowness index and latitude; is the
narrowness index where convective heat flux is equal to zero.
It is seen that parameterized results the best fit with the model and is
closer to the field data than the results of equation 9 and Figure 5. This
parameterization equation may apply to the real situation.
CONCLUSION
The formulae obtained for the convective heat exchange are ready for use in any
numerical model for the urban climate. Heating processes inside a street canyon

Muhammad Abu Eusuf, Wira M.N.S, Abdullah A.M, Adnan M., Sabeek E., Ataur R., & Mansor I.
A Parametric Approach for The Study of Heat Flow Between Street Canyon and The Atmosphere
© 2018 by MIP
60
are very complicated and a numerical model for their study must account for all
factors. The heat flow among the urban canyon and overlying atmosphere
strongly depends on the narrowness index, latitude, time of the day and outside
mean wind velocity. Our parameterization scheme has been established to
formulate the relationship between these quantities. The results of computation
using this functional relationship reveal that t can give a reasonable estimate of
convective heat exchange between the canyon and overlying boundary layer.
Since this relationship is rather simple it might be applicable for the real situation
and convenient for practical use.It is expected that, in the evening, the
temperature of a street canyon with small narrowness index may become lower
than those in street canyon with large narrowness index. However, since no
measurements were made at night, hence this assumption cannot be verified
experimentally.
ACKNOWLEDGEMENT
This work was supported by Research Management Centre, International Islamic
University Malaysia and Grant Nos. EDW-B14-175-1060.
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