Modified Matlab Simulation for a Solar System for the City of Tehran

Alberte Erantis Kofoed Lauridsen [email protected]

under the direction of Prof. Hamed Hamid Muhammed Medical Engineering School of Technology and Health, KTH

Research Academy for Young Scientists July 8, 2015 Abstract

Air pollution is the cause of numerous deaths every year and cities where the airflow is restricted by mountain ranges are especially threatened. Tehran is such a city, transcending the air quality standards many days a year. Solar chimneys are constructions which rely on wind and stack effect. Earlier studies have been made about solar chimneys for power production and room ventilation. The aim of our study is to modify a Matlab script in order to simulate a large scale sloped solar chimney with the purpose of passively ventilating the city of Tehran. The results from the study show that there is airflow through the chimneys during the sunlight hours, however it is very limited. The percentage of ventilated air per chimney is too low for it to be an effective solution to Tehrans pollution problem, but it could be valuable solution to smaller scale areas such as factories. Contents

1 Introduction 1 1.1 Solar Chimneys ...... 1 1.2 Mathematical Model ...... 3 1.3 Purpose ...... 6

2 Method 7 2.1 Topography ...... 7 2.2 Meterological Data ...... 8 2.3 Simulation ...... 9

3 Results 13 3.1 Ambient Conditions ...... 13 3.2 Volume Flow Rate ...... 14 3.3 ...... 15

4 Discussion 16

5 Acknowledgements 18

A Appedix 20

B Matlab code for linear approximation of ambient conditions 20

C Matlab code for iterative loop 21 1 Introduction

High concentrations of air pollution is the cause of numerous deaths every year. Being exposed to toxic gases can cause both acute and chronic damage [1]. An important thing to take into account when looking at health effects of air pollution is alterations in the composition and size distribution of particulate matter [2]. Tehran, the capital city of Iran, is strongly affected by pollution such as PM10,

SO2, NO2, HC, O3 and CO [2]. The topography of Tehran, surrounded by 1000- 3800 mountain ranges in the east, southeast, north, and northwest, complicates and partly restricts the airflow both in and out of the city [2]. The air is particularly constrained when there is inadequacy of wind and cold air amid the winter season. In regards to atmospheric pollution, Tehran is one of the worst areas in the world, transcending the air quality standards many days yearly and generally having higher concentrations of the aforementioned pollutants than the standard level [2]. Morbidity, mortality and other symptoms increase as an effect of the air pollution [3], hence solving this issue is essential.

1.1 Solar Chimneys

Solar chimney passive ventilation systems are environmentally friendly and easy to manage [4]. The chimneys consist of a solar collector, which is an air inlet made of glass, a chimney, and a most often a turbine as well. The chimneys rely on wind and on stack effect. As the chimney is heated by solar radiation, the temperature of the air rises and the density of the air is reduced. This causes air to flow upward through the chimney.

1 Previous studies and simulations have been made for small scale vertical chimneys used for room ventilation [5]. Larger scale chimneys have also been researched and simulated for the purpose of producing energy and electricity. A simulation of a sloped solar chimney has been made for a power plant in Lanzhou, China, [4] and in Manzanares, Spain, moreover a prototype of a vertical solar chimney for high latitudes has been constructed [6].

2 1.2 Mathematical Model

Nomenclature 2 Aab Area of absorber (m ) 2 Ac Area of cover (m ) 2 Ai Cross sectional area of chimney inlet to air flow channel (m ) 2 Ao Cross sectional area of chimney outlet to air flow channel (m ) Ar Ratio of Ao to Ai ACH Number of air changes per hour Cd coefficient of discharge of air channel inlet (0.57)) Cfl Specific heat of air (J/kg K) −2 hab Conductive coefficient for absorber (W m K) −2 hc Conductive heat transfer coefficient for cover (W m K) −2 hr,av,c Conductive heat transfer coefficient between absorber and cover (W m K) Ls Stack height (m) m˙ Mass flow rate (kg s1) −2 Sc Solar radiation heat flux absorbed by cover (W m ) − Sab Solar radiation heat flux absorbed by absorber (W m 2) T a Ambient temperature (K) Tab Mean temperature of absorber (K) Tc Mean temperature of cover (K) Tf Mean temperature of air in chimney (K) Tr (K) −2 Ub Overall heat transfer coefficient between vertical wall and room (W m K) − Ut Overall heat transfer coefficient from top of cover (W m 2) v Air velocity at outlet of chimney (m s−1) V˙ Volume flow rate (m3 s1) −3 ρf Density of air flow in chimney (kg m ) γ Constant for mean temperature approximation

According to the energy balance equation for the glass cover, the incident solar radiation and the radiative heat gained by the glass cover from the absorber wall must equal the convective heat loss to air in the flow channel and the overall heat loss coefficient from the glass to ambient. It can be presented mathematically as

[ScAc] + [hr,ab,cAab(Tab − Tf )] = hcAc(Tc − Tf )] + [UtAc(Tc − Ta)]. (1)

3 The energy balance equation for the absorber is based on that the solar radiation is equal to the to airflow, the long wave re-radiation to cover and the conduction to the main room. Similarly it can be written mathematically as

[SabAab] = [habAab(Tab − Tf )] + hr,ab,cAab(Tab − Tc)] + [UbAab(Tab − Tr)]. (2)

The energy balance equation for the airflow can be expressed as: convection from the absorber is equal to the convection from the cover added with the useful heat gained by the air. Mathematically it can be expressed as follows

hcAcTc − (hcAc + habAab +mC ˙ fl/γ)Tf + habAabTab = −(mC ˙ fl/γ)Tr, (3) where the mean temperature approximation coefficient chosen at 0.74, as suggested by Ong and Chow [7], is represented by γ.

In the simulation the Gauss Seidel method is used with Successive Over Relax- ation Method for solving linear equation systems. The codes can be found in the appendix. Different files, the main named EISCRV, are used for the code and their main functions are:

1. Implementing the calculation part of temperature, ACH, efficiency, volume flow rate, mass flow rate, and iteration performed.

2. Implementing the calculation of assorted properties of the surface of the glass surface and the absorber wall. This is done in order to retrieve the mean glass temperature, the mean temperature of air and the mean temperature of the

4 vertical wall.

3. Creating the matrix, that is to say the coefficients of temperature and right hand side vector, furthermore, some dimensional attributes.

4. Calculating the volume flow rate, mass flow rate, efficiency and number of air changes per hour (ACH), by alternating different parameters, such as the height of the wall opening and gap between the glass, and plotting them with regard of solar intensity.

For a chimney, with two openings and a consistent room air temperature, designed with the purpose of room ventilation, the mass flow rate can be written as an equation as follows,

s ρf A0 2gLs(Tf − Ta) m˙ = Cd √ . (4) 1 + Ar Ta

However, when this is calculated it is assumed that there is no effect of room volume on the volumetric flow rate obtained through the following equation,

m˙ V˙ = . (5) ρf

Calculating the number of air changes per hours is done by using the following equation, V˙ · 3600 ACH = . (6) v

The theoretical value of air velocity through Equations 5 and 6 provide the theo- retical air change rate. In order to obtain velocity of air through the flow channel, the temperatures Tf and Ta can be used together with Equation 1. The volume

5 flow rate of air and the number of air changes per hour can be obtained once the value of mass flow rate has been calculated in Equation 5 and 6.

1.3 Purpose

The purpose of this study is to simulate a sloped large scale chimney which is to rest on the surrounding mountainsides. The purpose of the chimney is to ventilate the air in the city of Tehran. The Matlab scripts and information from a former study about vertical solar chimneys for room ventilation is modified and adjusted in order to gather information about the effectiveness [5]. The purpose of our study is to evaluate whether or not a large scale sloped solar chimney ventilation system could be a possible temporary solution to Tehran’s pollution problem.

Figure 1: Desired airflow through Tehran

6 2 Method

2.1 Topography

In order to calculate the amount of solar radiation and approximate the volume of the most polluted part of the city, coordinates of were chosen, see Figure 2 and Table 1. The total area chosen was 498.6 km2. In order to estimate the volume of chosen part of the city, the height difference between the lowest and the highest coordinate, and the total area of the coordinates were multiplied.

Height differene : 1615 − 1048 = 0.567km (7)

Volume : 498.6 · 0.567 = 282, 7km3 (8)

Table 1: Coordinates of the area chosen and height of coordinates in meters above sea level (MSL).

Coordinate Height (MSL) 1 35o44’19.3”N 51o06’32.3”E 1214 2 35o47’26.6 ”N 51o23’31.6”E 1613 3 35o47’29.1”N 51o28’40.1”E 1518 4 35o43’50.3”N 51o38’06.3”E 1615 5 35o43’16.1”N 51o30’51.2”E 1287 6 35o34’49.0”N 51o26’13.6”E 1048

7 Figure 2: Sattelite image of Tehran [8], with the investigated area marked out.

2.2 Meterological Data

In order to examine whether or not the simulated chimney is effective, meteorologi- cal data is needed. The climate in Tehran varies throughout the year and therefore mean approximations were made for each season. The maximum and minimum temperatures, number of sunshine hours, which were both collected from BBC Weather[9] , and solar radiation, retrieved from the Atmospheric Science Data Center[10], were required for the simulation. The solar radiation, measured in av- erage downward longwave radiative flux was premeditated by taking the monthly mean and calculating the seasonal mean.

8 Table 2: Mean temperatures in Tehran 2011 [9]

Season Maximum [K] Minimum [K] Spring 294.8 279.5 Summer 308.8 294.2 Autumn 297.5 285.2 Winter 282.5 272.5

Table 3: Mean number of sunshine hours in Tehran 2011 [9]

Season Solar Hours [h] Spring 7.7 Summer 11.3 Autumn 8.3 Winter 6.3

Table 4: Mean downward longwave radiation flux in Tehran 2000-2005 [10]

Season Solar radiation [kWh m−2] Spring 6.814 Summer 10.102 Autumn 7.345 Winter 5.459

2.3 Simulation

In order to approximate the effectiveness of the solar chimney a simulation in

Matlab for vertical room ventilation solar chimneys was modified [11]. Since the chimneys that the experiment aims to simulate are of a larger scale than the room ventilation chimneys, the simulation represented the large chimney by using several smaller vertical segments. In this experiment there are 50 segments with a stack height of 20 m. It is assumed that the ambient conditions are identical

9 Figure 3: The segment distribution for EISCRV. throughout the chimney. Moreover, the airflow is considered to be laminar and not absorbing the radiation. The transparent cover of the chimney was assumed to be impenetrable by infrared radiation.

Since the Matlab code cannot calculate values where the solar radiation is less than 50 Wm−2, a linear approximation of the variations of ambient conditions during sunlight hours was created, using values from Table 2, Table 3, and Table 4. This was done to obtain the time interval between the two points where the solar radiation is more than 50 Wm−2, see the table for Nomenclature, to get the right amount of sunlight hours for EISCRV. EISCRV is used to predict temperature

10 Nomenclature for input w Chimney width (m) Ls Stack height (m) Lw Length of chimney (m) z Opening width (m) d Gap between cover and absorber (m) V Volume of polluted air (m3) H Incident solar radiation (Wm−2) Ta Ambient temperature (K)

Tc1i Initial temperature of cover (K)

Tf1i Initial temperature of inside airflow (K)

Tab1i Initial temperature of absorber (K) maxiter Maximum number of iterations maxerr Maximum error to be incorporated

Nomenclature for output ACH Air changes per hour V˙ Volume flow rate (m3s−1) Tf Mean temperature of inside airflow (K) Tab Mean temperature of absorber (K) m˙ Mass flow rate (kgs−1) Tc Temperature (K)

change and flow for each section. The width of the chimney were the same (w=z) in this experiment. In order to get a mean massflow and air changes per hour for each season, EISCRV was run in an iterative process for the 50 segments, four times, with values for the ambient conditions for each season.

The process of running EISCRV:

3 1. The constant input values w = z = d = 1 m, Ls = 20 m, V = 2.827 m ·

11 10 , maxiter = 1000 and maxerr = 0.0001 were inserted in the script.

11 2. The input values for H, Tc1i, Tab1i, Tf1i, and Ta are gathered for a given season and put in the script.

˙ 3. The output values for Tc, Tab, Tf , V and ACH were calculated and stored in array.

4. The steps 2-3 were repeated for each segment until the end of the time interval

with the output value for Tf as an input for Tf1i. Due to the temperature

difference as a result of altitude 0.13 K was subtracted from Ta for every new segment [12].

5. The values for V˙ and ACH were retrieved for each section and plotted as a function of time in the given time interval. The mean for V˙ and ACH are calculated.

12 3 Results

The graphs in Figure 5 and Figure 6 show a combination of 50 lines, one for each segment of the chimney. The results demonstrate that an airflow is present during sunlight hours throughout the year.

3.1 Ambient Conditions

800 900 Temperature (K) Temperature (K) 700 Solar radiation (W/m 2) 800 Incident solar radiation (W/m 2)

700 600

600 500 500 400 400 300 300

200 200

100 100

0 0 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 Time (h) Time (h) (a) Winter conditions (b) Spring conditions

1000 900 Temperature (K) Temperature (K) 900 2 800 2 Solar radiation (W/m ) Solar radiation (W/m )

800 700

700 600 600 500 500 400 400 300 300

200 200

100 100

0 0 0 2 4 6 8 10 12 0 1 2 3 4 5 6 7 8 Time (h) Time (h) (c) Summer conditions (d) Autumn conditions

Figure 4: Linnear approximation of the variations of ambient conditions during sunlight hours

13 3.2 Volume Flow Rate

1.4 1.6

1.3 1.4 1.2

1.1 1.2 1 /s) /s) 3 0.9 3 1

V (m 0.8 V (m 0.8 0.7

0.6 0.6 0.5

0.4 0.4 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 Time (h) Time (h) (a) Winter conditions (b) Spring conditions

1.6 1.4

1.3

1.4 1.2

1.1 1.2 1 /s) /s) 3 3 1 0.9 V (m V (m 0.8 0.8 0.7

0.6 0.6 0.5

0.4 0.4 0 2 4 6 8 10 12 0 1 2 3 4 5 6 7 8 Time (h) Time (h) (c) Summer conditions (d) Autumn conditions

Figure 5: Daily volume flow rate in a large scale sloped solar chimney simulation

Table 5: Daily mean volume flow for simulated sloped solar chimneys

Season V¯ [m3s−1] Winter 0.9947 Spring 1.0429 Summer 1.0863 Autumn 1.0408

14 3.3 Air Changes per Hour

× -6 10 ×10 -6 1.8 1.8

1.6 1.6

1.4 1.4

1.2 1.2 ACH ACH 1 1

0.8 0.8

0.6 0.6

0.4 0.4 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 Time (h) Time (h) (a) Winter conditions (b) Spring conditions

×10 -6 ×10 -6 2 1.8

1.6

1.4 1.5

1.2 ACH ACH 1

1 0.8

0.6

0.5 0.4 0 2 4 6 8 10 12 0 1 2 3 4 5 6 7 8 Time (h) Time (h) (c) Summer conditions (d) Autumn conditions

Figure 6: Daily air changes per hour

Table 6: Mean of daily air changes per hour conducted in a large scale sloped solar chimney simulation.

Season ACH Winter 1.2666 · 10−6 Spring 1.3281 · 10−6 Summer 1.3834 · 10−6 Autumn 1.3254 · 10−6

15 Table 7: Total amount of daily ventilated air of the chosen area in percent for one solar chimney

Season ACHTOT (%) Winter 0.0007 Spring 0.0009 Summer 0.0015 Autumn 0.0010 (K) Annual 0.001

4 Discussion

Judging from the results the simulated solar chimney in this study will not be efficient enough to ventilate a large city. In total, for a day, the amount of venti- lated air varies between the minimum of 0.0007 % and the maximum of 0.0015 % per solar chimney. An unrealistic amount of this type solar chimney would have to be installed for the effect of the chimneys to be significant. However, the study does display that there is airflow and this indicates potential for developing solar chimneys for smaller scale areas.

The results are not perfectly accurate. The gathering of data was based on rough estimations, which were not entirely up to date. Considering that the ambient conditions are not constant, the study would have been better using more rele- vant data. The estimation of the most polluted part of Tehran was also crude, since there was no data available concerning this. Furthermore, a more accurate estimation of solar radiation would have been beneficial for the study. The cho- sen measurement for the solar radiation was average downward longwave radiative flux, and more thorough estimations could have been done using radiation mod-

16 els taking the sloped angle into account. Any information during the nighttime was not either collected through this study due to the limited time interval, as a consequence of the simulation not being able to calculate for any solar radiation under 50. Moreover, by utilizing the mean temperatures, the study is neglecting any fluctuation in weather, which is not realistic. Similarly the airflow is expected to be exclusively laminar, neglecting any turbulent flow which may occur.

Additionally, the entire study is based on a rather simple mathematical model which does not allow changes of the dimensions of the chimney, when it comes to the width of the chimney, opening width, and the gap between the absorber and the cover.To study the effects more thoroughly the gathering of more accu- rate data would be necessary. And the development of a completely new code, custom made for a larger scale sloped ventilation chimney would be necessary for improving this study. The code should allow different dimensions and shapes to be investigated in order to estimate the most efficient type of solar chimney. It would also be necessary to take turbulence, viscosity and general interaction of air with the surroundings, in this case the walls of the chimney, into account. The absorbtion properties of the cover and the conduction properties of the mountains would also need to be included to achieve a more realistic result.

In conclusion the simulated sloped solar chimney would not be a solution to such a large scale polluted area as Tehran. However, solar chimneys could be beneficial in smaller scale such as for factories. For example, if a factory is located close to a mountain range, by the means of a sloped solar chimney, the pollution could be lead further away from the city than for a factory with vertical non-solar chimneys.

17 By the solar chimney on the mountain range it would be possible to build longer chimneys functioning as outlets, and the pollution would be lead up and over the mountain range, instead of being retained in the city.

5 Acknowledgements

First of all I would like to thank my colleague Alexandra Polyakova for a fantastic collaboration. Secondly, I would like to thank Prof. Hamed Hamid Muhammed for counseling and support throughout the project. Furthermore, I would like to thank the counselors at Rays for proofreading and help with writing the report. Finally I would like to thank project leader Philip Frick and Research Academy for Young Scientists for the opportunity.

18 References

[1] World Health Organization, Ambient (outdoor) air quality and health, (2014), 2015-07-08. http://www.who.int/mediacentre/factsheets/fs313/en/ [2] Naddafi, K., Hassavand, M.S., Yunesian, M., Momeniha, F., Nabizadeh, R., Faridi, S., Gholampour, A. Health impact assessment of air pollution in megacity of Tehran, Iran Iranian J Environ Health Sci Eng. (2012); 9(1): 28. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3561072/ [3] U.S. Environmental Protection Agency,Health Effects of Ozone in the General Population,(2015), 2015-07-08. http://www.epa.gov/apti/ozonehealth/ population.html [4] Cao, F., Zhao, L., Guo, L.Simulation of a sloped solar chimney power plant in Lanzhou, Energy conversion and management, (2011), 2015-06-27 [5] Mathur, J., Bansal, N.K., Mathur, S., Jain, M., Anupma, Experimental inves- tigations on solar chimney for room ventilation, (2005), 2015- 06-27 [6] Bilgren, E., Renault, J., Solar chimney power plants for high latitudes, Solar Energy, 2005-10-01, 2015-06-23 [7] Ong, K.S., Chow, C.C., Performance of a solar chimney, Solar Energy, 74, 1–17, (2003), 2015-07-08. http://www.researchgate.net/publication/ 222580259_Performance_of_a_solar_chimney [8] Google Earth, "Tehran", 2015-06-23 [9] BBC weather, Tehran- Average Conditions (2011), 2015-06-25. http://www. bbc.com/weather/112931 [10] Atmospheric Science Data Center, NASA Surface meteorology and Solar Energy: Interannual Variability (2015), 2015-07-03. https://eosweb.larc. nasa.gov/cgi-bin/sse/interann.cgi [11] Meshram A., Experimental Investigation on Solar Chim- ney for room ventilation, Matlab Central (2013), 2015-06- 26. http://www.mathworks.com/matlabcentral/fileexchange/ 41731-experimental-investigation-on-solar-chimney-for-room-ventilation [12] Portland State Aerospace Society, A Quick Derivation relating altitude to air pressure, (2004), 2015-07-07. http://psas.pdx.edu/RocketScience/ PressureAltitude_Derived.pdf

19 A Appedix

B Matlab code for linear approximation of ambi-

ent conditions

Downward radiative flux and temperature variation during sunlight hours are the ambient conditions which are approximated. The time interval between the two points where H>50 are calculated. The input values for the code below are esti- mations for spring.

% linear approximation of solar radiative flux and temperature variation % with graph % s p r i n g

Hsp1 = linspace(0,870,13860); % increase radiation Hsp2 = linspace(870,0,13860); % decrease radiation Hsp = [Hsp1 Hsp2]; % radiation change vector

Tsp1 = linspace(279.48,294.82,2 ∗ length(Hsp)/3); % increase temperature Tsp2 = linspace(294.82,279.48,length(Hsp)/3); % decrease temperature Tsp = [Tsp1 Tsp2]; %temperature change vector

tsp = linspace(0,27720,length(Hsp)); % time vector

indsp=find(Hsp>=50); % start index tsp(indsp(1)); % start time tsp(indsp(end)); % end time tintsp = tsp(indsp(end))− tsp(indsp(1)) % time interval Tsp(indsp(1)) % start temperature Tsp(indsp(end)) % end temperature

20 C Matlab code for iterative loop Iterative loop for calculating air changes per hour and the volume flow rate. Values are plotted. The input values for the code below are estimations for spring.

%[T,M,V,ACH] = EISCRV(H,T,Ta,Ls ,W,z ,d,Vr, maxiter ,maxerr) c l o s e a l l c l e a r a l l h1=1400; %lowest altitude h2=2400; %highest altitude

Tmax=282.48; %max temp of day Tstart=272.98; %start temp of day Tend=273.48; %end temp of day

t=linspace(0,5.88); % time vector

TT1 = linspace(Tstart ,Tmax,round(2∗ length(t)/3));%[Tstart :1:Tmax]; TT2 = linspace(Tmax,Tend,round(length(t)/3)); %[Tmax: −1:Tend ] ; TT = [ TT1 TT2 ] ;

H1 = linspace(50,750,length(t)/2); H2 = linspace(750,50,length(t)/2); %max and min solar radiation H = [ H1 H2 ] ;

Hlen=length(H); ndx=1; %round(length(tt )/2); Ttub=TT(ndx)+2; % initial warm up of air in tube by two degrees

antal_steg = round((h2−h1 )/20) antal_temp = length(TT) kk = 0 ; for ii= 1:antal_temp k=0; i f i i == 1 T=[(TT(ndx)+Ttub)/2; Ttub; TT(ndx)]; e l s e

21 T=[(TT(ndx)+mtris ((ndx −2)∗50+1,2))/2; mtris((ndx −2)∗50+1,2)+2; TT(ndx)]; end %T=[(TT(ndx)+TT(ndx)+2)/2; TT(ndx)+2; TT(ndx )]; i i for i = 1:antal_steg [T,M,V,ACH] = EISCRV(H(ndx) ,T,TT(ndx)−k ∗ 0.13, 20, 1, 1, 1, 2827000000, 1000, 0.0001); k=k+1; kk = kk +1; mtris(kk,:)= [T(1) T(2) T(3) M V ACH]; T=[((TT(ndx)−k ∗0.13)+T(2))/2; T(2); TT(ndx)−k ∗ 0 . 1 3 ] ; end

if ndx==length(TT) ndx=1; e l s e ndx=ndx+1; end end

f i g u r e plot(t,TT, ’b’) hold on plot(t,H,’r’) %title({’Temperature and solar radiation change ’; ’Linear approximation ’; ’Autumn conditions ’},’Interpreter ’,’latex ’) legend({’Temperature (K)’,’Solar radiation (W/m^{2})’}) xlabel(’Time (h)’) meanV=mean(mtris (: ,5) , ’omitnan ’) meanACH=mean(mtris (: ,6) , ’omitnan ’)

f i g u r e y1 = reshape(mtris(: ,6) ,[antal_steg ,antal_temp]); plot(t,y1’) %plot of ACH %title({’Number of air changes per hour (ACH)’;’Chimney width = 2 m’; ’Autumn conditions ’},’Interpreter ’,’latex ’) ylabel ( ’ACH’) xlabel(’Time (h)’)

22 f i g u r e y2 = reshape(mtris(: ,5) ,[antal_steg ,antal_temp]); plot(t,y2’) %plot volume flow rate %title({’Volume flow rate (V)’; ’Chimney width = 2 m’; ’Autumn conditions ’},’Interpreter ’,’latex ’) ylabel(’V (m^{3}/s)’) xlabel(’Time (h)’)

23