Calculation of below-grade residential heat loss: low-rise residential building

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Calculation of below-grade residential heat loss: low-rise residential

building

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CALCULATION OF BELOW-GRADE

1 RESIDENTIAL HEAT LOSS:

LOW-RISE RESIDENTIAL BUILDING

G.P.

Mitalas,

P.E.

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CALCULATION OF BELOW-GRADE

RESIDENTIAL HEAT LOSS:

LOW-RISE RESIDENTIAL BUILDING

G.P. Mitalas,

P.E.

ASHRAE Fellow

ABSTRACT

A s i m p l e c a l c u l a t i o n makes i t p o s s i b l e t o d e t e r m i n e t h e maximum r a t e of below-grade h e a t l o s s from a basement and t h e t o t a l h e a t l o s s o v e r t h e h e a t i n g s e a s o n . The p r o c e d u r e a c c o u n t s f o r t h e v a r i a t i o n of below-grade h e a t l o s s d u r i n g t h e y e a r . T h i s i s a s i g n i f i c a n t f a c t o r i n t h e h o u s e h e a t b a l a n c e . A n a l y t i c a l a s w e l l a s e x p e r i m e n t a l d a t a a r e u s e d t o d e v e l o p a s e t of f a c t o r s t h a t a r e t h e n u s e d i n t h e c a l c u l a t i o n of below-grade h e a t l o s s . T h i s n o t e i s a

r e v i s e d and e x t e n d e d v e r s i o n of a n ASHRAE p a p e r ( M i t a l a s 1983). T h i s r e v i s i o n e x t e n d s t h e f u l l basement c a l c u l a t i o n p r o c e d u r e t o i n c l u d e slab-on-grade and s h a l l o w basement h e a t l o s s c a l c u l a t i o n s .

INTRODUCTION

E x p e r i m e n t a l and a n a l y t i c a l s t u d i e s were c a r r i e d o u t t o d e v e l o p a method f o r c a l c u l a t i n g d e e p basement* h e a t l o s s . The d e t a i l s of t h e s e s t u d i e s a r e r e p o r t e d i n M i t a l a s ( 1 9 8 2 ) , and t h e f i n a l v e r s i o n of t h e c a l c u l a t i o n p r o c e d u r e i s p r e s e n t e d i n M i t a l a s (1983). T h i s p r o c e d u r e u s e s basement h e a t l o s s f a c t o r s (BHLF) t h a t r e l a t e basement i n t e r i o r s u r f a c e h e a t f l u x t o v a r i o u s t e m p e r a t u r e s t h a t g o v e r n basement h e a t l o s s . BHLFs a c c o u n t f o r t h e basement i n s u l a t i o n s y s t e m , s o i l t h e r m a l c o n d u c t i v i t i e s , and basement g e o m e t r y , a s w e l l a s t h e a n n u a l v a r i a t i o n of ground s u r f a c e t e m p e r a t u r e s . I t was r e c o g n i z e d t h a t a s i n g l e c a l c u l a t i n g p r o c e d u r e f o r a l l t y p e s of h o u s e

foundations--deep basement, s h a l l o w basement, and s l a b on grade--would be a d v a n t a g e o u s f o r t h e f o l l o w i n g r e a s o n s :

1. P r e s e n t a t i o n and i m p l e m e n t a t i o n of t h e method i s s i m p l i f i e d b e c a u s e one c a l c u l a t i n g p r o c e d u r e (computer program o r manual c a l c u l a t i o n ) h a n d l e s a l l t y p e s of h o u s e f o u n d a t i o n s . 2. I n c a s e s where t h e g r a d e l e v e l , i n s u l a t i o n c o v e r a g e of t h e w a l l , a n d / o r s o i l c o n d u c t i v i t i e s d i f f e r s u b s t a n t i a l l y from t h e " s t a n d a r d " f o u n d a t i o n s y s t e m s u s e d f o r BHLF c a l c u l a t i o n s , t h e below-grade h e a t l o s s e s c a n b e e s t i m a t e d by i n t e r p o l a t i o n of t h e h e a t l o s s c a l c u l a t e d f o r t h e two " s t a n d a r d " f o u n d a t i o n s y s t e m s t h a t b r a c k e t t h e f o u n d a t i o n c o n f i g u r a t i o n u n d e r c o n s i d e r a t i o n .

3. A more a c c u r a t e comparison c a n b e made of t h e below-grade h e a t l o s s from v a r i o u s t y p e s of h o u s e f o u n d a t i o n s and t h e i r i n s u l a t i o n s y s t e m s u s i n g a s i n g l e c a l c u l a t i n g p r o c e d u r e r a t h e r t h a n a s p e c i a l p r o c e d u r e f o r e a c h c a s e .

C o n s e q u e n t l y a p r o c e d u r e was d e v e l o p e d and u s e d t o c a l c u l a t e below-grade h e a t l o s s from s h a l l o w basements and s l a b on g r a d e . The c a l c u l a t i n g p r o c e d u r e , b a s e d on t h e p r e v i o u s l y

--

*The terms "deep basement," " s h a l l o w basement," and " s l a b on g r a d e " a r e u s e d t o d e n o t e t h e t h r e e t y p e s of house basements: _{( 1 ) "deep basement" d e n o t e s a basement where t h e basement} f l o o r i s a t l e a s t 1.0 m below g r a d e ; ( 2 ) " s h a l l o w basement" d e n o t e s a basement where t h e basement f l o o r i s 0.25 m t o 1.0 m below g r a d e (e.g., " c r a w l s p a c e " ) ; ( 3 ) " s l a b on g r a d e " d e n o t e s a basement where t h e s l a b i s l e s s t h a n 0.25 m below t h e s u r r o u n d i n g g r a d e .

G.P. M i t a l a s i s a R e s e a r c h O f f i c e r , I n s t i t u t e f o r R e s e a r c h i n C o n s t r u c t i o n , N a t i o n a l Research C o u n c i l Canada, O t t a w a , Canada, K 1 A OR6.

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r e p o r t e d d e e p basement work

i it alas

1 9 8 3 ) , i s d e s c r i b e d i n t h i s paper. The n e c e s s a r y m o d i f i c a t i o n s of t h e deep basement c a l c u l a t i n g p r o c e d u r e t o e x t e n d i t t o slab-on-grade and s h a l l o w basement h e a t l o s s c a l c u l a t i o n s a r e p r e s e n t e d h e r e .

The aim of t h i s p a p e r i s t o o u t l i n e t h e a p p r o a c h u s e d t o g e n e r a t e t h e basement h e a t l o s s f a c t o r s (BHLFs) and t h e u s e of t h e BHLFs i n c a l c u l a t i o n s of house f o u n d a t i o n h e a t l o s s . More s p e c i f i c a l l y , t h i s p a p e r d e s c r i b e s : 1. M a t h e m a t i c a l model f o r c a l c u l a t i o n s of h o u s e f o u n d a t i o n h e a t l o s s e s . 2. R e p r e s e n t a t i v e p h y s i c a l house f o u n d a t i o n models of t h e t h r e e f o u n d a t i o n t y p e s t h a t were u s e d f o r BHLF c a l c u l a t i o n s . 3. A l g o r i t h m s f o r f o u n d a t i o n h e a t l o s s d e t e r m i n a t i o n b a s e d on BHLFs (Appendix A). 4. Sample c a l c u l a t i o n (Appendix B). M a t h e m a t i c a l Model

F i g u r e s . 1 , 2, and 3 show r e p r e s e n t a t i v e p r o f i l e views of p h y s i c a l models of a d e e p basement, a s h a l l o w basement, and a s l a b o n g r a d e , r e s p e c t i v e l y . F i g u r e 4 shows a p l a n v i e w . common t o a l l t h r e e t y p e s .

The main f a c t o r s and v a r i a b l e s t h a t d e t e r m i n e t h e below-grade h e a t l o s s from d e e p

basements, s h a l l o w basements, and s l a b o n g r a d e a r e ( 1 ) ground s u r f a c e t e m p e r a t u r e around t h e f o u n d a t i o n , ( 2 ) l o w e r t h e r m a l boundary r e p r e s e n t e d by a c o n s t a n t t e m p e r a t u r e , ( 3 ) i n t e r i o r s p a c e t e m p e r a t u r e , ( 4 ) basement d i m e n s i o n s and i n s u l a t i o n system, and

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t h e t h e r m a l c o n d u c t i v i t y of t h e s o i l s u r r o u n d i n g t h e f o u n d a t i o n .

Based on t h e d e e p basement h e a t l o s s c a l c u l a t i n g a p p r o a c h of M i t a l a s (1982) and t h e p h y s i c a l models d e s c r i b e d above, t h e i n s t a n t a n e o u s h e a t l o s s f r o m t h e below-grade s e c t i o n of a house f o r a l l t h r e e f o u n d a t i o n t y p e s c a n be e x p r e s s e d a s

where

A = a r e a of segment, n

q n ( t P = i n s t a n t a n e o u s h e a t f l u x a t time, t , a v e r a g e d o v e r t h e segment a r e a ,

h.

.

Note t h a t summation b e g i n s w i t h n = l i f above-grade f o u n d a t i o n h e a t l o s s i s i n c l u d e d i n t h e summation. The i n s t a n t a n e o u s h e a t f l u x , q n ( t ) , c a n be approximated by

q n ( t ) = qa,, + qV,, s i n ( w ( t

+

~ t , ) ) where

qa,, = a n n u a l mean v a l u e of q (t)

q,,. = a m p l i t u d e of t h e annua? h e a t f l u x v a r i a t i o n

o

= a n g u l a r v e l o c i t y of t h e v a r i a b l e component,

i.e.,

30°/month

t = t i m e (month)

A t n = t i m e l a g of t h e h e a t f l u x harmonic r e l a t i v e t o t h e s u r f a c e t e m p e r a t u r e

v a r i a t i o n .

The a m p l i t u d e v a l u e s f o r t h e a n n u a l and s e m i a n n u a l harmonics of t h e ground s u r f a c e t e m p e r a t u r e f o r s e v e r a l l o c a t i o n s i n Canada a r e g i v e n i n T a b l e 2, d e r i v e d from t h e d a t a g i v e n i n P h i l l i p s and Aston (1979). A s t h e a m p l i t u d e of t h e two c y c l e s p e r y e a r component of ground s u r f a c e t e m p e r a t u r e i s r e l a t i v e l y small a n d t h e h i g h e r h e a t f l u x harmonics a r e a t t e n u a t e d more t h a n t h e f i r s t , t h e a n n u a l ground s u r f a c e t e m p e r a t u r e v a r i a t i o n c a n be approximated u s i n g o n l y t h e o n e c y c l e p e r y e a r component.

The h e a t c o n d u c t i o n t h r o u g h a l i n e a r t h e r m a l s y s t e m i s a f u n c t i o n of t h e t e m p e r a t u r e d i f f e r e n c e a c r o s s t h e s y s t e m and t h e o v e r a l l conductance. The two components of q n ( t ) g i v e n by E q u a t i o n 2 c a n t h e r e f o r e be e x p r e s s e d a s

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and q v , , ( t ) = V n an Ov s i n ( w ( t + b t n ) ) where Sn

_--

= BHLF f o r t h e s t e a d y - s t a t e h e a t l o s s component = o v e r a l l c o n d u c t a n c e between t h e b o u n d a r i e s a t t e m p e r a t u r e s Op and

_"

0, U = S + S n and

S n P s and S = f o r d k e a d y - s t a t e h e a t l o s s component t o t h e ground s u r f a c e and l o w e r n ' g boundary, r e s p e c t i v e l y

QB = i n t e r i o r a i r t e m p e r a t i r e (assumed t o b e c o n s t a n t t h r o u g h o u t t h e e n t i r e y e a r ) OG = ground s u r f a c e t e m p e r a t u r e a v e r a g e d o v e r t i m e and a r e a , which e q u a l s mean

ground t e m p e r a t u r e

Vn = BHLF f o r t h e p e r i o d i c h e a t l o s s an = a m p l i t u d e a t t e n u a t i o n f a c t o r

Qv = a m p l i t u d e of t h e o n e c y c l e p e r y e a r component of t h e ground s u r f a c e t e m p e r a t u r e .

Thus E q u a t i o n s 3 and 4 a r e t h e b a s i c h o u s e f o u n d a t i o n m a t h e m a t i c a l models: h e a t f l u x e s a r e e x p r e s s e d i n t e r m s o f BHLFs, (Sn, V n ,

an,

and Atn) and t h e t e m p e r a t u r e s . It i s assumed t h a t t h e f o u n d a t i o n ' s t h e r m a l s y s t e m c h a r a c t e r i s t i c s d o n o t s i g n i f i c a n t l y change w i t h t i m e and t e m p e r a t u r e .

F o u n d a t i o n Heat Loss F a c t o r s (BHLFs) f o r R e p r e s e n t a t i v e House F o u n d a t i o n s

BHLFs a r e s p e c i f i c s e t s of f a c t o r s t h a t a r e u s e d i n E q u a t i o n s 3 and 4 t o r e l a t e below-grade h e a t l o s s and boundary t e m p e r a t u r e s f o r s p e c i f i c f o u n d a t i o n s y s t e m s . The a v a i l a b l e number of BHLF s e t s , t h e r e f o r e , w i l l d e t e r m i n e t h e r a n g e of a p p l i c a b i l i t y of t h i s method f o r p r e d i c t i n g s p e c i f i c h o u s e f o u n d a t i o n h e a t l o s s . The number of BHLF s e t s , however, must be b a l a n c e d a g a i n s t t h e c o s t t o c a l c u l a t e them and t h e t a b u l a t i o n and c o n v e n i e n c e of u s i n g t h e s e f a c t o r s .

F o r t h e s e r e a s o n s , S n ' s and V n ' s w e r e c a l c u l a t e d f o r t h e c r o s s - s e c t i o n a l models of t h e basement and s u r r o u n d i n g ground shown i n F i g u r e s 1, 2, 6nd 3 w i t h t h e f o l l o w i n g p e r t i n e n t d i m e n s i o n s t h a t a r e deemed t o b e r e p r e s e n t a t i v e of common h o u s e f o u n d a t i o n s y s t e m s : a ) Deep basement: H e i g h t of a r e a A 2 = 0.6 m H e i g h t of a r e a A3 = 1.07 m Width of a r e a A4 = 1.0 m Width of a r e a A5 = 3 . 6 m

A v e r t i c a l d i m e n s i o n of 0.6 m f o r A2 was s e l e c t e d b e c a u s e t h a t i s the e x t e n t of basement i n s u l a t i o n recommended i n s e v e r a l p r o v i n c i a l b u i l d i n g c e d e s . b) S h a l l o w basement: H e i g h t of a r e a A2 = 0 m H e i g h t of a r e a A3 = 0.85 m Width of a r e a A4 = 1.0 m Width of a r e a A5 = 3 . 6 m

F o r s h a l l o w basements, a l l a b o v e - g r a d e w a l l area i s d e s i g n a t e d

as

A l and a l l below-grade w a l l a r e a i s d e s i g n a t e d a s A3. c ) S l a b on g r a d e H e i g h t of a r e a A2 = 0 m H e i g h t of a r e a A3 = 0 m Width of a r e a A4 = 1.0 m Width of a r e a A5 = 3 . 6 m For s l a b on g r a d e t h e e n t i r e w a l l a r e a i s d e s i g n a t e d a s A l .

The basement f l o o r was d i v i d e d i n t o a p e r i m e t e r and a c e n t r a l r e g i o n , b e c a u s e

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from t h a t t h r o u g h t h e r e m a i n d e r of t h e f l o o r , and b e c a u s e s u c h a d i v i s i o n makes i t p o s s i b l e t o a c c o u n t f o r a s t r i p of f l o o r i n s u l a t i o n a d j a c e n t t o t h e w a l l .

It i s assumed t h a t two-dimensional h e a t c o n d u c t i o n p r e v a i l s around t h e f o u n d a t i o n and t h a t t h e t h r e e - d i m e n s i o n a l h e a t f l o w due t o c o r n e r s c a n be a c c o u n t e d f o r by s p e c i a l c o r n e r a l l o w a n c e f a c t o r s , Cn.

The c a l c u l a t i o n s of S 's and V n l s a l l o w f o r s p a t i a l v a r i a t i o n s i n s o i l t h e r m a l p r o p e r t i e s

_*

by a s s i g n i n g d i f f e r e n t s o i l c o n d u c t i v i t i e s above and below t h e f o u n d a t i o n f l o o r l e v e l .

S n 1 s and V ' S f o r s l a b on g r a d e were c a l c u l a t e d f o r t h r e e s l a b l w a l l c o n f i g u r a t i o n s t o a c c o u n t f o r d i f p e r e n t w a l l / s l a b j u n c t i o n s ( s e e T a b l e 1 )

,

namely,

1. The c o n c r e t e f l o o r s l a b i s i n good t h e r m a l c o n t a c t w i t h t h e c o n c r e t e w a l l and t h e s l a b i s i n s u l a t e d o n t h e i n t e r i o r o r e x t e r i o r .

2. The w a l l i s i n s u l a t e d (U=0.31 w / ( m 2 * ~ ) ) t o a d e p t h of 0.2 m below g r a d e and t h e f l o o r s l a b i s i n s u l a t e d on t h e i n t e r i o r o r e x t e r i o r . 3. The d e p t h of i n s u l a t i o n on t h e w a l l below g r a d e i s a v a r i a b l e ( i . e . , 0.5 m , 1.0 m, o r 1.5 m below g r a d e ) and t h e f l o o r s l a b i s n o t i n s u l a t e d . Sn and Vn, n u m e r i c a l l y e q u a l t o t h e a v e r a g e h e a t f l u x e s t h r o u g h i n t e r i o r s u r f a c e segments d u e t o a p p r o p r i a t e u n i t t e m p e r a t u r e d i f f e r e n c e s , were c a l c u l a t e d u s i n g f i n i t e - e l e m e n t n u m e r i c a l methods f o r h e a t c o n d u c t i o n ( M i t a l a s 1982).

A n a l y s i s of t h e c a l c u l a t e d S n ' s and V n V s i n d i c a t e s t h a t , i n most c a s e s , t h e basement i n s u l a t i o n t h e r m a l r e s i s t a n c e , R , and t h e S n l s and V n ' s f o r t h e r a n g e 1

<

R

<

5 c a n be r e l a t e d by e q u a t i o n s of t h e form: and C o n s e q u e n t l y , S n and V n a r e p r e s e n t e d i n T a b l e 1 a s f u n c t i o n s of t h e basement i n s u l a t i o n t h e r m a l r e s i s t a n c e , R , i n t h e f o r m of E q u a t i o n s 5 and 6 o r a s c o n s t a n t s f o r s p e c i f i c i n s u l a t i o n s y s t e m (e.g., nonuniform i n s u l a t i o n c o v e r ) . T a b l e 1 p r e s e n t s BHLFs f o r d e e p , s h a l l o w , and slab-on-grade f o u n d a t i o n s , v a r i o u s i n s u l a t i o n s y s t e m s and g e o m e t r i e s , and a r a n g e of s o i l t h e r m a l c o n d u c t i v i t i e s .

The a t t e n u a t i o n f a c t o r ,

an,

and t h e t i m e - l a g f a c t o r , A t n , have been d e t e r m i n e d by

c a l c u l a t i n g h e a t f l u x of i n t e r i o r s u r f a c e s , u s i n g a s i n e wave v a r i a t i o n of t h e ground s u r f a c e t e m p e r a t u r e ( M i t a l a s 1982). C a l c u l a t e d a t t e n u a t i o n and t i m e - l a g f a c t o r s a r e l i s t e d i n T a b l e 1. Based on t h e i n s i d e s u r f a c e h e a t f l u x v a l u e s c a l c u l a t e d a t a c o r n e r f o r two l e v e l s of f o u n d a t i o n i n s u l a t i o n and u s i n g a t h r e e - d i m e n s i o n a l model ( M i t a l a s 1 9 8 2 ) , a s e t of c o r n e r a l l o w a n c e f a c t o r s , Cn, were d e r i v e d f o r a l l of t h e f o u n d a t i o n i n s u l a t i o n s y s t e m s and a r e l i s t e d i n T a b l e 1.

House F o u n d a t i o n Heat L o s s C a l c u l a t i n g P r o c e d u r e and A p p l i c a t i o n i n P r a c t i c e The c a l c u l a t i n g p r o c e d u r e b a s e d o n BHLFs c o n s i s t s of f o u r d i s t i n c t s t e p s :

1. D e t e r m i n a t i o n of S

,

V n ,

an,

At,, and C f a c t o r s f o r a f o u n d a t i o n t y p e , f o u n d a t i o n g e o m e t r y , ground t E e r m a l p r o p e r t i e s , a n 8 i n s u l a t i o n s y s t e m u n d e r c o n s i d e r a t i o n , u s i n g T a b l e 1.

2. C a l c u l a t i o n of f o u n d a t i o n w a l l and f l o o r i n t e r i o r s u r f a c e segment a r e a s and c o r n e r a l l o w a n c e f o r t h e f o u n d a t i o n i n q u e s t i o n .

3. C a l c u l a t i o n of 1 2 monthly v a l u e s of below-grade h e a t l o s s u s i n g ground s u r f a c e , ground mean, and i n t e r i o r t e m p e r a t u r e a p p r o p r i a t e f o r t h e l o c a t i o n i n q u e s t i o n , BHLFs d e t e r m i n e d i n S t e p 1 , and a r e a s c a l c u l a t e d i n S t e p 2.

4 . C a l c u l a t i o n of t h e h e a t i n g s e a s o n below-grade h e a t l o s s u s i n g t h e monthly h e a t l o s s v a l u e s c a l c u l a t e d i n S t e p 3.

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C a l c u l a t i o n of below-grade h e a t l o s s becomes more i n v o l v e d when t h e f o u n d a t i o n d i f f e r s c o n s i d e r a b l y from t h e f o u n d a t i o n s l i s t e d i n T a b l e 1. I n t h i s c a s e , t h e h e a t l o s s c a n be d e t e r m i n e d u s i n g a s i m p l e i n t e r p o l a t i o n p r o c e d u r e : s e l e c t two f o u n d a t i o n s l i s t e d i n T a b l e 1 t h a t " b r a c k e t " t h e a c t u a l f o u n d a t i o n , c a l c u l a t e below-grade h e a t l o s s f o r t h e s e two c a s e s , and t h e n , u s i n g t h i s d a t a , i n t e r p o l a t e t o d e t e r m i n e h e a t l o s s of t h e a c t u a l f o u n d a t i o n .

I f i t i s known t h a t t h e groundwater l e v e l i s j u s t below t h e f o u n d a t i o n f l o o r , and t h a t a p o t e n t i a l e x i s t s f o r g r o u n d w a t e r Elow a r o u n d and u n d e r t h e f o u n d a t i o n , t h e RHLFs f o r t h e s t e a d y - s t a t e h e a t l o s s component t h r o u g h t h e f l o o r s h o u l d be a r b i t r a r i l y i n c r e a s e d by 30% t o 70% t o a c c o u n t f o r a d e c r e a s e d ground t h e r m a l r e s i s t a n c e b e n e a t h t h e f l o o r d e p e n d i n g on t h e p e r c e i v e d s e v e r i t y of t h e g r o u n d w a t e r e f f e c t . I n c a s e s of p o o r l y i n s u l a t e d f o u n d a t i o n s i n which s o i l p r o v i d e s t h e m a j o r p o r t i o n of t h e t o t a l t h e r m a l r e s i s t a n c e , a n a c c u r a t e v a l u e of s o i l t h e r m a l c o n d u c t i v i t y i s r e q u i r e d t o e s t a b l i s h t h e BHLFs a p p r o p r i a t e f o r t h e c a s e u n d e r c o n s i d e r a t i o n . I n a d d i t i o n , t h e f o l l o w i n g may have a s i g n i f i c a n t i n f l u e n c e o n t h e h e a t l o s s f r o m a p o o r l y i n s u l a t e d f o u n d a t i o n :

-

The t i m e v a r i a t i o n i n g r o u n d w a t e r t e m p e r a t u r e and l e v e l ;

-

The f l o w of r a i n o r melt-water i n t o s o i l s u r r o u n d i n g t h e basement;

-

The s p a c e v a r i a t i o n of ground t e m p e r a t u r e a r o u n d t h e f o u n d a t i o n due t o s o l a r e f f e c t s , a d j a c e n t b u i l d i n g s , and v a r i a t i o n i n t h e snow c o v e r ;

-

Changes i n s o i l t h e r m a l c o n d u c t i v i t y due t o m o i s t u r e and t e m p e r a t u r e changes.

The d e t a i l s of t h e a p p l i c a t i o n of BHLFs f o r c a l c u l a t i o n of below-grade h o u s e f o u n d a t i o n h e a t l o s s a r e g i v e n i n Appendix A and a s a m p l e c a l c u l a t i o n i n Appendix B.

A s a m a t t e r of i n t e r e s t , t h e measured basement h e a t l o s s a t t h e t e s t basement and t h e c o r r e s p o n d i n g c a l c u l a t e d v a l u e s a r e p r e s e n t e d i n Appendix B and p l o t t e d i n F i g u r e 4. I n t h i s p a r t i c u l a r c a s e , t h e c a l c u l a t e d a n n u a l basement h e a t l o s s of 24 G J compares w e l l w i t h t h e measured 23.3 G J h e a t Loss. A more e x t e n s i v e comparison of c a l c u l a t e d and measured d e e p basement h e a t l o s s i s g i v e n i n M i t a l a s ( 1 9 8 2 ) .

OBSERVATIONS

V a r i o u s a s s u m p t i o n s h a v e been made i n d e r i v i n g a s i m p l e method of c a l c u l a t i n g below-grade h e a t l o s s . F o r v e r i f i c a t i o n , v a l u e s of f o u n d a t i o n h e a t l o s s o b t a i n e d by means of t h i s method were compared w i t h a c t u a l measured v a l u e s f o r d e e p basements ( M i t a l a s 1982). The comparison

-

s u g g e s t e d t h e f o l l o w i n g :

-

The e f f e c t of t h e a n n u a l v a r i a t i o n of ground s u r f a c e t e m p e r a t u r e on below-grade h e a t l o s s c a n be a c c o u n t e d f o r s a t i s f a c t o r i l y by a p e r i o d i c h e a t f l o w c a l c u l a t i o n a p p r o a c h , u s i n g a m p l i t u d e a t t e n u a t i o n ,

a,,

and t i m e - d e l a y f a c t o r s , A t n .

-

F o u n d a t i o n s w i t h s i m p l e r e c t a n g u l a r s h a p e s c a n b e t r e a t e d by u s i n g BHLFs d e t e r m i n e d f o r s t r a i g h t w a l l s e c t i o n s and c o r n e r a l l o w a n c e f a c t o r s t o a c c o u n t f o r t h r e e - d i m e n s i o n a l h e a t f l o w due t o c o r n e r s .

-

The BHLF method c a n p r e d i c t b o t h t h e t o t a l f o u n d a t i o n h e a t l o s s and t h e h e a t l o s s t h r o u g h s e c t i o n s of t h e f o u n d a t i o n w i t h i n + l o % of measured v a l u e s . NOMENCLATURE* An = a r e a of segment, n a n , b n , c n , a c o n s t a n t s s p e c i f i c t o t h e f o u n d a t i o n t h e r m a l i n s u l a t i o n system; t h e y a r e u s e d t o and d n c a l c u l a t e S and V n f a c t o r s RHLF

-

f o u n d a t i o n g e a t l o s s f a c t o r , namely, S , V , on, A t , o r Cn Cn = c o r n e r allowance f a c t o r D" = h e i g h t of f o u n d a t i o n w a l l a b o v e g r a d e G = f o u n d a t i o n p e r i m e t e r G~ = p e r i m e t e r f o r b o t h end s e c t i o n s G~ = p e r i m e t e r f o r t h e m i d d l e s e c t i o n H = t o t a l h e i g h t of f o u n d a t i o n w a l l k lower = s o i l t h e r m a l c o n d u c t i v i t y below f o u n d a t i o n f l o o r l e v e l k u p p e r = s o i l t h e r m a l c o n d u c t i v i t y above f o u n d a t i o n f l o o r l e v e l * A l l d i m e n s i o n s u s e d i n t h i s p a p e r a r e i n S I u n i t s e x c e p t a s n o t e d

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L = f o u n d a t i o n l e n g t h

M = h e i g h t of i n s u l a t i o n coverage o v e r w a l l m = month number ( 1 t o 12)

N = number of segments c o n s t i t u t i n g t h e i n t e r i o r s u r f a c e a r e a of below-grade p o r t i o n of t h e f o u n d a t i o n

QT = annual h e a t l o s s from below-grade p o r t i o n of f o u n d a t i o n Q ( t ) = h e a t l o s s from below-grade p o r t i o n of f o u n d a t i o n

Q W = below-grade f o u n d a t i o n h e a t l o s s f o r w i n t e r p e r i o d Q a n = annual mean v a l u e of q n ( t )

q n ( t ) = a v e r a g e h e a t f l u x through t h e segment a r e a , An, a t time t

qv,n = amplitude of a n n u a l harmonic of h e a t f l u x v a r i a t i o n

qV,,(t) = v a r i a b l e component of a v e r a g e h e a t f l u x t h r o u g h segment, An, a t time t R = thermal r e s i s t a n c e of f o u n d a t i o n i n s u l a t i o n RT o v e r a l l t h e r m a l r e s i s t a n c e of f o u n d a t i o n w a l l above g r a d e l e v e l S n = BHLF, t h e s teady-s t a t e h e a t l o s s component t = time U = o v e r a l l t h e r m a l conductance of f o u n d a t i o n w a l l above g r a d e l e v e l ,

l/RT

vn = BHLF f o r t h e p e r i o d i c h e a t l o s s component W = f o u n d a t i o n width Xn = c o r n e r allowance S u b s c r i p t s = s t e a d y - s t a t e component, e q u a l i n g a n n u a l mean v a l u e = i n t e r i o r s p a c e = end s e c t i o n = lower t e m p e r a t u r e boundary

= long-term time and s p a c e a v e r a g e

= month number ( 1 t o 12) = middle s e c t i o n = segment of t h e i n t e r i o r s u r f a c e of f o u n d a t i o n = ground s u r f a c e = v a r i a b l e component Greek Symbols = time l a g of h e a t f l u x harmonic r e l a t i v e t o s u r f a c e t e m p e r a t u r e v a r i a t i o n 8 = t e m p e r a t u r e @B = i n t e r i o r s p a c e a i r t e m p e r a t u r e

OG = ground s u r f a c e t e m p e r a t u r e averaged o v e r b o t h time and a r e a , e q u a l l i n g mean ground t e m p e r a t u r e

@o,m = monthly v a l u e of o u t d o o r a i r t e m ~ e r ~ a t u r e

Qv = amplitude of a n n u a l harmonic of ground s u r f a c e t e m p e r a t u r e On = amplitude a t t e n u a t i o n f a c t o r

w = a n g u l a r v e l o c i t y of a n n u a l harmonic

REFERENCES

Environment Canada. 1975. Canadian Normals Temperature 1941-1970, Vol. 1-SI. Environment Canada, Downsview, O n t a r i o (UDC 551-552[7]).

M i t a l a s , G.P. 1982. "Basement h e a t l o s s s t u d i e s a t DBR~NRC." N a t i o n a l Research Council of Canada, D i v i s i o n of B u i l d i n g Research, NRCC 20416.

M i t a l a s , G.P. 1983. " C a l c u l a t i o n of basement h e a t l o s s . " ASHRAE T r a n s a c t i o n s , V. 89, Pt. 1.

P h i l l i p s , D.W., and Aston, D. 1979. " S o i l t e m p e r a t u r e a v e r a g e s 1958-1978

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Environment Canada, Downsview, O n t a r i o . CL13-79.

The a u t h o r wishes t o acknowledge t h e a s s i s t a n c e of M.J. Lavoie and M.O. P e l l e t i e r i n t h e p r e p a r a t i o n of computer programs and r u n n i n g t h e t e s t . T h i s paper i s a c o n t r i b u t i o n of t h e I n s t i t u t e f o r Research i n C o n s t r u c t i o n , N a t i o n a l Research Council of Canada.

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APPENDIX A

C a l c u l a t i o n of House Foundation Heat Loss

The f o l l o w i n g summarizes t h e s t e p s t o be t a k e n i n c a l c u l a t i n g h e a t l o s s f o r a s p e c i f i c house f o u n d a t i o n system:

S t e p 1. Provide t h e r e q u i r e d i n p u t d a t a f o r ( A l l i n S I u n i t s ) : I n s i d e dimensions ( s e e F i g u r e s 1 , 2, 3, and 4 )

l e n g t h , L,

w i d t h , W , where W

<

L , o r w i d t h , W

,

and w i d t h , W 2 , of L-shaped f l o o r , where W1 and

W 2

a r e t h e widths of t h e two ends of t h e !loor;

t o t a l h e i g h t of w a l l , H , h e i g h t of w a l l above g r a d e , D. I n s u l a t i o n

-

o v e r a l l thermal r e s i s t a n c e of w a l l above g r a d e , RT,

o v e r a l l thermal conductance of w a l l above g r a d e , U (U = 1 / ~ ~ ) , r e s i s t a n c e v a l u e of i n s u l a t i o n , R,

h e i g h t of i n s u l a t i o n coverage of w a l l , M

-

i n c a s e of deep basement,

e x t e n t of i n s u l a t i o n coverage of f l o o r ( i . e . , none, 1 m wide s t r i p a d j a c e n t t o w a l l , o r f u l l coverage).

Temperature

-

i n t e r i o r space t e m p e r a t u r e , QB,

mean ground t e m p e r a t u r e , QG ( s e e T a b l e 2 o r P h i l l i p s and Aston 19791,

amplitude of t h e a n n u a l harmonic of t h e ground s u r f a c e t e m p e r a t u r e v a r i a t i o n , C$,, and t h e timing of t h e f i r s t s u r f a c e t e m p e r a t u r e harmonic ( s e e Table 2 ) ,

monthly average outdoor a i r t e m p e r a t u r e , Q0,,, where m i d e n t i f i e s t h e month (Environment Canada 197 5). S t e p 2. C a l c u l a t e t h e a r e a s of t h e segments c o n s t i t u t i n g t h e f o u n d a t i o n f l o o r and w a l l s where a p p l i c a b l e : A 1 = i n s i d e s u r f a c e a r e a of w a l l

-

above g r a d e , A 2 = upper i n s i d e s u r f a c e a r e a of w a l l

-

below g r a d e , A 3 = lower i n s i d e s u r f a c e a r e a of w a l l

-

below g r a d e , A 4 = i n s i d e s u r f a c e a r e a of f l o o r s t r i p 1 m wide a d j a c e n t t o w a l l , A5 = i n s i d e s u r f a c e a r e a of t h e remainder of t h e f l o o r .

I n some c a s e s t h e f o u n d a t i o n under c o n s i d e r a t i o n must be s u b d i v i d e d i n t o s e c t i o n s , depending on i t s shape and on t h e number of i n s u l a t i o n systems used, s i n c e s e c t i o n s t h a t a r e i n s u l a t e d d i f f e r e n t l y must be c o n s i d e r e d s e p a r a t e l y .

Square basements may be r e g a r d e d a s having two i d e n t i c a l end s e c t i o n s . R e c t a n g u l a r basements may be c o n s i d e r e d a s h a v i n g two i d e n t i c a l end s e c t i o n s w i t h three-dimensional h e a t flow o c c u r r i n g a t t h e c o r n e r s and a middle s e c t i o n w i t h two-dimensional h e a t f l o w ( F i g u r e

4).

The three-dimensional h e a t f l o w of i r r e g u l a r l y shaped basements (such a s an L-shaped basement) cannot be accommodated by t h i s s i m p l e method. Such a basement could be c o n s i d e r e d a s having f o u r c o r n e r s o n l y , s i n c e t h e three-dimensional h e a t flow e f f e c t a t an i n s i d e c o r n e r w a l l w i l l be t h e o p p o s i t e of t h a t a t a n o u t s i d e c o r n e r and s h o u l d t h e r e f o r e approximately

compensate. An L-shaped basement can b e t r e a t e d a s a r e c t a n g u l a r one, u s i n g t h e a c t u a l L-shaped c e n t e r f l o o r a r e a , As, and a c t u a l p e r i m e t e r l e n g t h f o r w a l l a r e a c a l c u l a t i o n s .

Rectangular f o u n d a t i o n s w i t h s i n g l e i n s u l a t i o n system

-

f o r both end s e c t i o n s , GE = 4 W ,

f o r t h e middle s e c t i o n , GM = 2L

-

2W, f o r t h e e n t i r e f o u n d a t i o n , G = 2(L+W),

where G = p e r i m e t e r , W = w i d t h , L = l e n g t h , and s u b s c r i p t s E , M, and no s u b s c r i p t r e f e r t o end s e c t i o n s , middle s e c t i o n , and e n t i r e f o u n d a t i o n , r e s p e c t i v e l y . T h e r e f o r e ,

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F u l l basement w i t h i n s u l a t i o n p a r t i a l l y c o v e r t n g t h e w a l l

-

F u l l basement w i t h i n s u l a t i o n c o v e r i n g t h e e n t i r e w a l l

-

Shallow basement

S l a b on g r a d e

S t e p 3. Determine BHLFs Sn and Vn:

For t h e p a r t i c u l a r t y p e of f o u n d a t i o n , t h e R-value of f o u n d a t i o n i n s u l a t i o n and s o i l t h e r m a l c o n d u c t i v i t i e s from T a b l e 1, o b t a i n t h e f a c t o r s Sn(R), Vn(R), Cn, an and At,. The h i g h v a l u e of s o i l t h e r m a l c o n d u c t i v i t y would p r o b a b l y be a p p r o p r i a t e f o r r o c k s and wet s a n d ; t h e lower v a l u e c o u l d be u s e d f o r w e l l - d r a i n e d c l a y .

S t e p 4. Using t h e s e l e c t e d c o r n e r a l l o w a n c e f a c t o r s , Cn, c a l c u l a t e t h e a c t u a l c o r n e r a l l o w a n c e , Xn:

1) For t h e two upper w a l l segments, A1 and A2, t h e i n c r e a s e d h e a t l o s s due t o c o r n e r s c a n b e n e g l e c t e d , i.e.,

X 1

=

X p

= 0.

2) For t h e bottom segment of t h e w a l l , A 3 ,

Xj

= 0 f o r s h a l l o w basement and s l a b on g r a d e and

X 3

= i C j f o r f u l l basement, where i = number of c o r n e r s b e i n g c o n s i d e r e d . 3) For t h e

1

m s t r i p of f l o o r , X4 = i C4.

4)

For t h e c e n t r a l a r e a of f l o o r ,

X5

= C5

V5.

S t e p 5. C a l c u l a t e t h e e f f e c t i v e a r e a s of t h e segments c o n s t i t u t i n g t h e f l o o r and w a l l s of t h e e n t i r e basement, i n c l u d i n g t h e c o r n e r a l l o w a n c e . (Because of t h e d i f f e r e n c e i n c o r n e r a l l o w a n c e f o r s t e a d y - s t a t e and v a r i a b l e f l o o r h e a t l o s s components and because t h e c o r n e r a l l o w a n c e i s i n terms of a r e a , t h e e f f e c t i v e f l o o r a r e a v a l u e s f o r t h e s t e a d y - s t a t e and v a r i a b l e component c a l c u l a t i o n s a r e d i f f e r e n t . )

(13)

where

---

s u b s c r i p t "s" i n d i c a t e s s u r f a c e a r e a t o b e u s e d i n c a l c u l a t i n g t h e s t e a d y - s t a t e component, s u b s c r i p t "v" i n d i c a t e s s u r f a c e a r e a v a l u e t o be u s e d i n c a l c u l a t i n g t h e v a r i a b l e basement h e a t - l o s s component. S t e p 6. C a l c u l a t e t h e monthly a v e r a g e h e a t - l o s s r a t e (power) t h r o u g h t h e i n t e r i o r s u r f a c e s of f o u n d a t i o n : For s l a b on g r a d e ,

and f o r s h a l l o w basement A2 = 0 .-.q2,, = 0. For o t h e r c a s e s ,

where "30" h a s u n i t s i n deglmonth. S t e p 7. C a l c u l a t e t h e a n n u a l below-grade f o u n d a t i o n h e a t l o s s ( e n e r g y ) , QT: where 2.63 x l o 6 = number of s e c o n d s p e r a v e r a g e month. S t e p 8. C a l c u l a t e t h e below-grade basement h e a t l o s s o v e r t h e w i n t e r p e r i o d , Qw:

-

w i n t e r months 5 Qw = (2.63)

C

qn,m

(MJ)

A l t e r n a t i v e l y , t h e above e q u a t i o n c a n b e r e a r r a n g e d a s f o l l o w s :

5

Qw = ( ( o B

-

QG)

C

An Sn (Number of w i n t e r months ) n= 2 w i n t e r

5

months

+

0,

C

An V n

an

C

s i n w ( 1 n + 8 + ~ t ~ ) ) (2.63) ( M J ) n= 2 S t e p 9. C a l c u l a t e t h e h e a t l o s s f r o m e n t i r e f o u n d a t i o n .

The whole basement h e a t l o s s i s s i m p l y t h e sum of t h e below-grade and above-grade f o u n d a t i o n h e a t l o s s e s . A sample c a l c u l a t i o n of basement h e a t l o s s i s g i v e n i n Appendix

B.

I n a p p l y i n g t h i s c a l c u l a t i n g p r o c e d u r e , t h e f i r s t problem e n c o u n t e r e d w i l l b e t h a t t h e f o u n d a t i o n u n d e r c o n s i d e r a t i o n d o e s n o t c o r r e s p o n d e x a c t l y t o any of t h e " s t a n d a r d "

f o u n d a t i o n s and i n s u l a t i o n s y s t e m s (e.g., t h e d e p t h of t h e f o u n d a t i o n f l o o r below g r a d e , t h e e x t e n t of i n s u l a t i o n c o v e r , o r s o i l t h e r m a l c o n d u c t i v i t y may b e d i f f e r e n t ) t h a n t h e o n e s l i s t e d i n T a b l e 1. To c o p e w i t h t h i s problem two a p p r o a c h e s c a n be used:

1. S e l e c t t h e " s t a n d a r d " f o u n d a t i o n c o n f i g u r a t i o n and i n s u l a t i o n s y s t e m t h a t b e s t match t h e f o u n d a t i o n u n d e r c o n s i d e r a t i o n , f r o m T a b l e 1. Using t h e

BHLF

s e t f o r t h i s f o u n d a t i o n and

(14)

a c t u a l dimensions of t h e basement under c o n s i d e r a t i o n , d e t e r m i n e below-grade h e a t l o s s of t h e f o u n d a t i o n i n q u e s t i o n .

2. Use an i n t e r p o l a t i o n ( o r e x t r a p o l a t i o n ) procedure t o e s t i m a t e below-grade h e a t l o s s of t h e f o u n d a t i o n i n q u e s t i o n : a ) S e l e c t a t l e a s t two " s t a n d a r d " f o u n d a t i o n c o n f i g u r a t i o n s t h a t b r a c k e t t h e f o u n d a t i o n under c o n s i d e r a t i o n . b ) C a l c u l a t e t h e below-grade h e a t l o s s f o r t h e s e " s t a n d a r d " c a s e s . c ) C a l c u l a t e t h e below-grade h e a t l o s s of t h e f o u n d a t i o n i n q u e s t i o n by i n t e r p o l a t i o n of t h e h e a t l o s s v a l u e s of t h e two " s t a n d a r d " c a s e s u s i n g a p p r o p r i a t e parameters f o r i n t e r p o l a t i o n , i . e . , d i f f e r e n c e i n d e p t h , i n s u l a t i o n c o v e r , e t c .

The e x t r a p o l a t i o n approach t o t h i s problem c a n be used i n a s i m i l a r way. It should be n o t e d , however, t h a t t h e e x t r a p o l a t i o n procedure s h o u l d be used only t o a l i m i t e d e x t e n t , s i n c e i t i s n o t p o s s i b l e t o e s t i m a t e a c c u r a t e l y t h e e r r o r of t h e h e a t l o s s determined by t h i s procedure.

APPENDIX B

Sample C a l c u l a t i o n of Deep Basement Heat Loss

The f o l l o w i n g sample c a l c u l a t i o n i s f o r t h e h e a t l o s s from one of t h e t e s t basements, which had i n s u l a t i o n o v e r t h e f u l l h e i g h t on t h e i n s i d e s u r f a c e of t h e basement w a l l and no i n s u l a t i o n on t h e f l o o r . S t e p 1. The g i v e n i n p u t d a t a a r e : Basement dimensions

-

l e n g t h , L = 9.2 m, w i d t h , W = 8.5 m, t o t a l w a l l h e i g h t , H = 2.13 m, h e i g h t of w a l l above g r a d e , D = 0.38 m. I n s u l a t i o n

-

above g r a d e , l / R T = U = 0.53 w/(m2

K),

i n s u l a t i o n r e s i s t a n c e , R = 1.55 m2 K / W , h e i g h t of i n s u l a t i o n c o v e r , M = 2.13 m ( f u l l h e i g h t ) , f l o o r i s u n i n s u l a t e d . Temperature

-

basement s p a c e t e m p e r a t u r e ,

BB

= 21°C,

ground s u r f a c e t e m p e r a t u r e (from Table 2 ) ,

OG

+

%,

= 8.9

+

11.4 s i n (30(m

+

8 ) )

o u t s i d e a i r t e m p e r a t u r e (Environment Canada 1975). (For Ottawa 0 = -11, -9, -3, 6 , 13, 18, 21, 19, 15, 9 , 2, - 7 ' ~ ; where m = J a n . t o Dec.) 0,"'

(15)

S t e p 3. Because t h e s o i l s u r r o u n d i n g t h e basement i s c l a y , t h e l o w e r v a l u e s of t h e r m a l c o n d u c t i v i t y were u s e d t o o b t a i n t h e f o l l o w i n g from T a b l e 1. Because t h e ground i s w e l l d r a i n e d and t h e w a t e r t a b l e i s l e v e l , t h e S, and S5 f a c t o r s a r e n o t augmented. For i n s u l a t i o n s y s t e m No. 3 t h e f a c t o r s a r e : Area Segment: n = 2 n = 3 n = 4 n = 5 S u b s t i t u t i n g R = 1.55 m 2 K/W and A t n , Area Segment: n = 2 n = 3 n = 4 n - 5 S 0.44 0.29 0.58 0.19 w/(m2 K) V 0.43 0.27 0.38 0.07 w/(m2

K)

u

0.9 0.7 0.4 0.3 D i m e n s i o n l e s s ( m + 8 + ~ t ) m + 8 m + 7 m + 6 m

+

4 Month C* 0 0.6 m2 2.4 m2 0.5 *C v a l u e h a s d i f f e r e n t u n i t , a s n o t e d . S t e p 4. Using t h e a l l o w a n c e f a c t o r s f r o m T a b l e 1 , t h e c o r n e r a l l o w a n c e s , X, are: S t e p 5. C a l c u l a t e t h e a r e a s of t h e s e g m e n t s t h a t i n c l u d e c o r n e r a l l o w a n c e f a c t o r s :

S t e p 6. The monthly h e a t l o s s (power) v a l u e s of t h e f i v e basement s e g m e n t s a r e :

q2,, =

A ~ [ s ~

(QB

-

OG)

-

V 2 u2 Ov s i n [30(m

+

8 ) ) ] = 21.2 [0.44(21

-

8.9)

-

0.43(0.9)(11.4) s i n (30(m

+

8 ) ) ] = 112

-

9 3 s i n (30(m

+

8 ) ) q 3 , m = A [ s 3 ( %

-

8

1 -

V

8 s i n (30(m

+

7 ) ) ] = 43.1 [0.29(2F

-

8.3) -%.27(8.7)(11.4) s i n (30(m t 7 ) ) ] = 151

-

9 3 s i n (30(m _, _-

+

7 ) ) _{- ,} Q 4 , m = A S ( 8

-

QG)

-

A4v V 4

a

$

s i n (30(m

+

6 ) ) = (47.7) 40.58 8 2 1

-

8.9)

-

( 4 1 . 0 ) ( 0 . 4 8 ) ( 0 . 4 ) ( l l . 4 ) s i n (30(m

+

6 ) ) = 265

-

71 s i n (30(m

+

6 ) ) 45,m = A S5

( $ -

8,)

- 6

v

o s i n (30(mt4) = (32.6) (0.1 ) ( 2 1

-

8.95"- [6?.9 ( 8 . 0 7 ) ~ 0 . 3 ) ( 1 1 . 4 ) s i n [30(m

+

4 ) ] = 126

-

16.3 s i n ( 3 0 ( m + 4 ) ) .

I n summary, t h e monthly h e a t l o s s e s of t h e f i v e basement s e g m e n t s a r e :

(16)

q3,m = 151

-

9 3 s i n

The a v e r a g e h e a t l o s s v a l u e s Eor t h e f i v e basement segments f o r e a c h month of t h e y e a r , t h e t o t a l basement a v e r a g e v a l u e s , and t h e a n n u a l a v e r a g e v a l u e s f o r e a c h segment a r e l i s t e d i n T a b l e A-1.

The a n n u a l a v e r a g e h e a t l o s s r a t e was 762 W. The a n n u a l h e a t l o s s ( e n e r g y ) from t h e whole basement would b e

(17)

-

a 9 - m u u u o m u u

..

-

- ' N U u u u 0 0 O m

.. .,

m N N m

-

r . OD

-

N N O O D -

-

m N

.,

d u

-

r.- N 4.0 a N O - 9 * a u m w m m m P - P - O D I l l w w w

.

rl 4 ¶ 3 V) ln C

.

C d 4 .4

2 m 4

c21 .+ d d m m u O C Y C d 0 a 4 - I > 4 .4 4 0 0 u m m 0 P ) P ) w z s

Z U U

O ' U W 0 0 0 U h h 0 u U C 4 .4 > > w d .rl u u u m u u 3 ¶ - 2 1 2 1 m c c

-

0 0 o u u Z 4 d E m m O E E U L L ,

: 2 ;

O U U i l d u u w w

> 2 g

I

e '+

(18)

h

TABLE

1

House Foundation Heat Loss

4 m 0% F a c t o r s , R , m 2 * K / w

a ,

d i m e n s i o n l e s s AT, month For d e e p basement: U n i t s :

a,

=

0.9

A t g = 0 a3 = 0.7 A t 3 = -1

a,

= 0.4 A t , =

-2

a,

= 0.3 A t 5 =

-4

S

,

W/

( m 2 * ~ ) V ,

W/

(m2*K) C , m* o r d i m e n s i o n l e s s

(At i s t h e t i m e d e l a y of h e a t f l u x s i n e wave r e l a t i v e t o t h e ground s u r f a c e t e m p e r a t u r e s i n e wave.) SECTION A: SOIL THERMAL CONDUCTIVITY: k u p p e r = 0.8 W/(m*K); k lower = 0.9 W/(m*K)

(Systems 1 t o 13, 21 t o 26)

*

Table

1

l i s t s numerical v a l u e s of Cn, 6, and ATn f a c t o r s . The Sn and Vn f a c t o r s a r e g i v e n a s numbers and a s e x p r e s s i o n s i n t h e form of Equations

5

and 6. These l a t t e r e x p r e s s i o n s a r e v a l i d f o r

1(R<5

and f o r uniform i n s u l a t i o n cover o v e r t h e i n s u l a t e d s e c t i o n of t h e basement I n s u l a t i o n System Insulation

--p,

Concrete (n

.:

_

. .

. ,

.

. . 1 F l o o r Segments S n , V n and Cn F a c t o r s 1 m s t r i p a d j a c e n t t o w a l l n= 4 0.42 0.24 2.6 Wall Segments S= . . . C e n t r e n= 5 0.17 0.05 0.5 T o p s t r i p j u s t below g r a d e n= 2 1.9 1.9 0 Bottom s t r i p n= 3 0.74 0.6

5

1 .O

(19)

(20)

SECTION A ( c o n t ' d )

I n s u l a t i o n System

I

Wall Segments

I

Floor Segments

Insulation Concrete 0 .. V 1 . S n * v n and Cn F a c t o r s Top s t r i p j u s t below grade n= 2 1 m s t r i p a d j a c e n t t o w a l l n=

4

Bottom s t r i p n= 3 Centre n=

5

(21)

SECTION A ( c o n t ' d )

I n s u l a t i o n S y s t e m Wall Segments

Insulation

T,

,

S n , V n Top s t r i p

Concrete and Cn j u s t below Bottom

$

;:

F a c t o r s g r a d e s t r i p . I . . . n=

2

n=

3

7

. . , . . S=

(0.67+1.12~)'~

( 1.30+1.47~)-I V=

(0.67+1.14~)'1

(1.42+1.58~)-1

C=

0

0.6 ._,..;:

6

.

I . ' . S=

(0.69+1.08~)'~

(1.28+1.23~)-1

V=

(0.69+1.11~)'~

(1.41+1.36~)-~

,

+

0

0.6 .

. .

.

. .; _.

7

S=

(0.73+1.04~)^1

(1.42+1.03~)-1

V=

(0.72+1.08~)'~

(1.53+1.2 1~)'~

C=

0

0.6

': ..:.:: F l o o r Segments

1

m s t r i p a d j a c e n t t o w a l l n=

4 (1.82+0.055~)-1

(2.79+0.11~)'1

2.4 (3.48+0.64~)'1

(5.43+0.988)'1

2.4 (2.60+0.92~)-1

(4.21+0.58~)-I

2.4

C e n t r e n=

5

0.19

0.07

0.5 (4.44-0.13~)~~

(1

1.13-0.58~)'l

0.5 (4.93+0.71~)'~

(12.9 1+1.25~)'~

0.5

(22)

(23)

SECTION

B:

SOIL THERMAL CONDUCTIVITY:

k

upper

=

1.2 W/(m*K);

k

lower

=

1.35 w/(m*K)

(Systems 14 to 20, 97 to 99)

Insulation

System

I

Wall Segments

Floor Segments

Insulation

S,, V,

Top strip

1

m

strip

.'...

T,

#

.-

Concrete

,

and Cn

just below

Bottom

adjacent

Centre

0 "

Factors

grade

strip

to wall

n=

5 "

.:

_{. .}

n=

2 n=

3 n=

4 .

. .

.: .

3 .

9

....

. .

S=

2.12

0.98

0.59

0.26 V

=

2.10

0.88

0.35

0.08 C=

0 1 .O

2.6

0.5 ...

_.

_...

7

14 S=

(0.48+1.37~)-1

(0.85-0.008~)-~

0.59

0.27 V=

(0.48+1.388)-1

(0.93-0.0094~)-~

0.35

0.09 C=

0

1 .O

2.6

0.5 -

_ ' , I . . . .

..

15

.'.'.,..

T,.,

S=

(0.51+1.09~)'~

(0.97+1.38~)'1

(1.36-0.03~)'~

0.29 V=

(0.52+1.11~)'1

(1.06+1.49~)'~

(2.11-0.062R)'l

0.11 C=

0

0.6

2.4

0.5 .

_..',

.

_.

_:

_.

_:

_{. . .}

1 ,

16 .'.':

:

S=

(0.52+1.06~)'~

(0.96+1.2~)'~

(2.76+0.54~)'~

(2.93-0.07~)'~

V=

(0.53+1.08~)-I

(1.

15+1.33R)-l

(4.39+0.88~)-1

(7.25-0.30~)'~

C=

0

0.6

2.4

0.5 .

. .

,.

.'

+ ' .' :

.-

..

-::

,

l7

s=

(0.56+1.02~)-I

(1.08+1.01~)-1

(1.90+0.89~)'~

(3.27+0.76~)'1

V=

(0.55+1.06~)-I

(1.15+1.18~)-I

(3.14+1.58~)-1

(8.46+1.55~)'1

C=

0

0.6

0.5 ..

.

.:.:.:-:'

I

(24)

SECTION B ( c o n t ' d )

I n s u l a t i o n System

I

Wall Segments

Inw!ation

T,

,

S n , V , _{and Cn} _{j u s t below}T o p s t r i p _Bottom

.-

_o

_:.

Concrete _{F a c t o r s} _{g r a d e} _{s t r i p} '".

_{. .}

, , n=

2

n=

3

. , . .

dl-J0.5

m

,

18

S=

(1.19+0.47~)-I

(

1.37+0.05~)-1

V =

(1.18+0.51~)-I

(1.60+0.077~)-I

C=

0

1 .O

1.1 m _.

_{. .}

_-

. .

..

1 ,

l 9

S=

(1.29+0.29~)-I

(

1.12+0.0027~)-I

V =

(1.31+0.30~)-I

(1.27+0.0033~)-1

C=

0

1 .O

. . .

. . . .

.

.:.

3 ,

2o

_V=S=

_{(0.61+1.09~)-I}

(0.62+1.06~)-1

(1 .58+0.26~)-I

_{(1 .79+0.35~)-I}

C=

0

0.6 .

, _ . . . I .

97 S=

(0.62+1.05~)-I

(1.55+0.23~)-I

V =

(0.62+1.08~)-I

(1.77+0.32~)-I

- .

C=

0

0.6

.I

.

..:.

' ..: - S=

(0.65+1.02~)-I

(1.55+0.13~)-1

V-

(0.63+1.07~)'~

(1.79+0.24~)-~

Cm

0

0.6

F l o o r

1

m s t r i p a d j a c e n t t o w a l l n=

4

0.59

0.35

2.6

0.55

0.30

2.6

0.59

0.35

2.6

0.60

0.36

2.4 (2.26+0.09~)-1

(3.72+0.13~)-1

2.4

Segments C e n t r e n=

5

0.26

0.08

0.5

0.26

0.08

0.5

0.27

0.09

0.5 (3

-45-0.04R)-l

(10.03-0.228)~~

0.5 (3.57+1.02~)-1

(10.67+2.71~)-1

0.5

(25)

SECTION C: SOIL THERMAL CONDUCTIVITY: k u p p e r = 1.8 W/(m*K); k l o w e r = 2.0 W/(m*K) ( S y s t e m s 67 t o 7 6 )

I n s u l a t i o n S y s t e m

I

Wall Segments

I

F l o o r Segments Insulation

- .

.-. Concrete

0 :

S n , V n T o p s t r i p 1 m s t r i p

and Cn j u s t below Bottom a d j a c e n t C e n t r e F a c t o r s g r a d e s t r i p t o w a l l n= 5

n=

2 n= 3 n= 4

.

..

:;:

-j

,

67

S= 2.36 1.28 0.82 0.39 V= 2.33 1 . 1 4 0.49 0 . 1 3 C= 0 1 .O 2.6 0.5

. .

.

,

. .

. I

(26)

SECTION

C ( c o n t ' d )

I n s u l a t i o n S y s t e m

1

Wall Segments F l o o r Segments

.-:,

-..

l nsulation

T,

-

,

Sn,

and C n V n Top s t r i p j u s t below Bottom a d j a c e n t

1

m s t r i p C e n t r e

._

..

Concrete F a c t o r s

Ln" .;.

g r a d e s t r i p t o w a l l n=

5

.

n=

2

n=

3

n=

4

. . d J I o - 5 m

,

"

S=

(1

.14+0.34R)-l

(1.06+0.03~)'~

(1 .29+0.006~)-1

(2.60+0.004~)-I

V =

(1.15+0.39~)-1

(1.26+0*05~)-1

(2.33+0.02~)'~

(8.31+0.04~)'~

i

...'..'.

C=

0 1 .O

2.6 0 5

1.1 m

_{. . .}

...,,.

I

..

.

3 ,

73

S=

(1.16+0.20~)-1

(0.84+0.002~)-1

0.84

0.39

V=

(1.19+0.21~)-1

(0.95+0.002~)-I

0.49

0.13

C=

0

1 .O

2.6

0.5 .

. . . , . . _.

_{. .}

.

_{. .}

. .

-

. I . : . .

--j

,

74

S=

(0.53+1.04~)-I

(

1.34+0.22~)-~

(1.23+0.001~)-I

(2.49-0.008~)-l

V=

(0.53+1.07~)-I

(1.52+0.3 lR)-l

(2.13-0.02~)'~

(7

-28-0.09R)-l

.

C=

0

0.6

2.4

0.5

I

..,.''

" ,

...

.-:.

S=

(0.53+1.03~)-1

(1.32+0.20~)-1

(1.76+0.08~)-I

(2.28-0.028)-1

V =

(0.53+1.07~)-1

(1.51+0.28~)'~

(2.9 1+0.12~)'~

3 i 7 5

c=

(6.35-0.1 lR)-l

0

0.6

2.4

0.5 .

_{. .}_{. .}

.

,..: .: ' _{. .}.'

s=

(0.56+1.0~)'~

(1.29+0.11~)'~

(1.60+0.07~)-I

(2.39+0.98~)-I

V =

(0.55+1.05~)-1

(1.53+0.19~)-1

(2.77+0.13~)-~

(6.83+2.56~)-I

C=

0 0*6

I

0.5 .

.

I

(27)

U m f m C U U U

;

a a a

CJ m m

d

m a 0

8 d d d

4 rl 11 II 11 G m z m m D d D

(28)

1 4 d d l I I M A nn b M 0

*

@A d a rn m & u r n

? 9 ?

0 0 0

9 : ;

c

II 0 0 0 a e a m I I I I m U N h U G

? ?

m

*

9 4

rn N

S

u 4 w 4 V w bO a cn

(29)

4 4 -4 d 4 4 1 I I I nn I I n n nn d d m 4 4 a d d In r.

"

d d m a, m 4 m

₉

_{9 2}

o ? m b u n

. . .

l4

. . .

. .

u m 0 0 0 0 0 0 0 0 0 0 4 0

c

I1 I I I I n PI

+

al c 0 u .-'a rn U m h .r a U

. .

? 4

c

m PI m ln m \o

I

V w w w w w w w CA rl L, 4 0

3

4 4 d 4 4 4 0 I I nn 1 , nn 1 I I .-I a n- d o l4 U d 4 m d In d d 4 d d 03 r- (U m u .Y r.mIn o q m m m m 'J) u 11

. . .

.

. . .

C

c

0 0 4 00-4 0 0 4 O d d

? 4 ?

E a I I

+

L, u u m a a m 4 Cd - I n m 4 m 4 "l

.

. .

w

A A m n 4 m m w w V W w w u 4 4 4 4 4 4 c I I nn nn I I I I

2

nn & d u a ai d d d W E m 0 m u 03 9 w o a 4 o A rn V) u - d m

.

9 :

U & l 1 hl N O A 4 0 ,+-'a

"

C. d 4 o

4 o u c 4 m V ) 9

+

03

+

corn

+

9

+

In

+

(d

_{2 4}

4 ₄

In m 3

. .

0 0 0 0 W V w w 0 w w 0

-

cn c el4

> U Z

II I! I1 n I1 I1 I1 I1 It I1 I1 II V) > U V) > U m > w m > u - a u c c m V) cab u m \O PI m m n m E w U m 5 C

. .

._.....

_{. . - .}

_...

_{. - .}

_. . . . .

_....

_{. . .}

. . . .

I

.

(30)

(31)

SECTION

C:

SOIL THERMAL CONDUCTIVITY: k u p p e r =

1.8 W/m*K);

k lower =

2.0 W/(m*K)

(Systems

77

t o

83)

I n s u l a t i o n System

I

Wall Segment F l o o r Segments

lnsulstion Sn* vn Bottom

1 m

s t r i p , . . , . Concrete

#

l

-

and F a c t o r s Cn S t r i p

n=3

a d j a c e n t n=4 t o

w a l l

C e n t r e n=

5

U)

.

. , . .. . ., .

4 ,

7 7

S =

2.42

1.04

0.42 V=

2.33

0.75

0.17 C=

0 1 5

0.3 . . .

_....

...

_.

7 8

S=

(0.42+1.16~)-1

( 0 . 9 0 - 0 . 0 0 7 ~ ) ' ~

(2.24-0.006R)'l

V=

( 0 . 4 3 + 1 . 2 0 ~ ) ' ~

(

1 . 2 5 - 0 . 0 1 ~ ) ' ~

( 5 . 1 5 - 0 . 0 3 ~ ) ' ~

-:.:.

ill(

.-.

. , . . . . ,

. . .

C=

0

1.5

0.3 ,

79

S=

(0.42+1.088)'1

(2.0 1 + 0 . 4 6 ~ ) ' ~

(1

- 8 8 - 0 . 0 3 ~ ) - 1

, .

.

V=

( 0 . 4 4 + 1 . 1 3 ~ ) ' ~

( 2 . 7 8 + 0 . 7 0 ~ ) ' ~

(3.91-0.09R)-l

I

C=

0

1.5

0.3 . .

_...

, .,..

.

. . . I .

4 *

8

0

S=

(0.49+0.97~)-1

(1.2 1 + 0 . 9 0 ~ ) - ~

( 2 . 0 8 + 0 . 8 1 ~ ) ' ~

.... .

V=

( 0 . 4 9 + 1 . 0 5 ~ ) ' ~

( 1 . 7 0 + 1 . 4 3 ~ ) ' ~

( 4 . 4 7 + 1 . 5 9 ~ ) ' ~

C=

0

1.5

0.3 .

_:...:.:.:

.

_.: