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A thesis submitted for the degree of Doctor of Philosophy

by

Louis Demetriou

School of Engineering and Design

March 2006

ABSTRACT Thermal analysis of buildings was carried out using simplified design tools, prior to the widespread use of computers. Since the early 1980' s, the rapid growth of computational power has lead to the introduction of many building dynamic thermal simulation software programs. The accurate performance of many of these programs has lead to the view that manual calculation methods should only be used as indicative design tools. The cmSE admittance method is based on the fundamentals of building heat transfer, its calculations procedures being simplified for use on hand held calculators. Manual calculation methods must be developed for use on more powerful calculators, if greater accuracy is required. Such calculators are available in the form of computer spreadsheet programs. The computational power of the computer spreadsheet program, combined with suitable mathematical thermal modelling techniques, has thus far, remained unexploited. This thesis describes the development of a powerful manual thermal design method, for application on a computer spreadsheet program. All the modes of building heat transfer are accurately modelled. Free-running or plant-controlled spaces can be simulated. In the case of a single zone, the accuracy of the new manual dynamic thermal model is comparable with commercially available software programs. The level of mathematical modelling complexity is limited only by computer power and user ability. The Iterative Frequency Domain Method (IFDM) and the Adiabatic Iterative Frequency Domain Method (AIFDM) are alternative mathematical simulation techniques developed to form the core of the Thermal Analysis Design Method. In the IFDM and AIFDM, the frequency domain and numerical iteration techniques have been integrated to produce a thermal simulation method that can model all non-linear heat transfer processes. A more accurate formulation of sol-air temperature, a window sol-air temperature and an accurate reduced internal long-wave radiant exchange model is a sample of further innovations in the thesis. Many of the developments described in the thesis, although designed for the computer spreadsheet environment, may also be employed to enhance the performance of some of the current dynamic thermal models of buildings.

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ACKNOWLEDGEMENTS

I would like to express my gratitude to my supervisor Professor Savvas A Tassou for his expert guidance, encouragement and support during the period of this research thesis.

I wish to express my deep appreciation to my wife Ellen, for understanding, encouragement and patience.

I would like to thank my children, Lara, Michael, Matthew and Anna for their support and for the sacrifices they had to make in keeping the number of house parties to a mInImum.

I acknowledge and appreciate the financial support afforded me, during this thesis, by the Dublin Institute of Technology.

Finally I wish to acknowledge the many useful discussions I had with colleagues, Michael Crowley and Ben Costelloe, in particular.

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NOMENCLATURE General symbols A

Surface area (m 2)

a

Solar altitude angle CO)

c

Constant

C

Air flow or pressure coefficient or fractional cloud cover

d

Declination angle CO)

D

Diurnal range

E

Illuminance (Lux)

F

View factor between surfaces

H, z or Z

Height (m)

I

Solar radiation 0V m-2)

IG ( or)

Global solar irradiance CW m- 2) for a plane of slope 0 CO) and orientation r CO)

k

Air flow coefficient (L

h

Surface heat transfer coefficient 0V m-2 K- I ) or hour angle (Degrees)

L

Latitude CO)

LF

Lamp luminous flux (Lumens)

I

Perimeter length or element thickness (m)

MF

Maintenance factor of lighting system

N

Number of lamps

m

Coefficient

n

Wall-solar azimuth angle CO)

p

Pressure (pa)

q

Surface heat flow

Q

Total surface heat flow (W)

R

Long-wave radiation (W)

T

Temperature (K)

S-I

m- I Pa-D )

CW m-2)

t

Time (s) or temperature in Celsius COC)

T or q etc.

Fluctuating thermal component or thermal complex quantity

t or q etc.

Mean thermal component

IV

L1T or L1t

Temperature difference (K)

UF

Utilisation factor of luminaire

v

Velocity (m S-l)

Subscripts Inside air ao

Outside air

bId

Building

eo

Sol-air

C

Convective

Cl

Internal convection

co

External convection

d

Direct

g or grd

Ground

G

Global

h

Horizontal

1

Identification number of surface being evaluated

j

Designating room surfaces 1 to N

m

Mean value

pf

Parallel flow

r

Reflected

s or sur

Surface

v

Vertical surface

Superscripts n

Air flow exponent

v

G reek letters a

Thermal diffusivity (m2/s)

8

Surface emissivity

(J

Stepfan-Boltzmann constant = 5.67xlO-8 W m-2 K-4