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Effect of air velocity on thermal insulation systems
Technical N o t e
Effect of Air Velocity on Thermal Insulation S y s t e m s
SUMMARY
A thermal comfort model has been developed to relate skin surface temperature to ambient air temperature and w#tdspeed. Relatively loB, wind assaults on clothing appreciably reduce the air boundary layer effective thermal resistance, whereas further equal increases in wind speed have decreasingly less effect in reducing the thermal resistance. Conclusions reached are extended to other insulation systems. The analysis assumes that no wind penetration through the insulant occurs.
NOMENCLATURE
Cp D g h /; k L R t T u w
= = = = = = = = = = = = =
Specific h e a t o f air at c o n s t a n t p r e s s u r e , J k g - ~K Dubois equivalent body diameter, m A c c e l e r a t i o n d u e to g r a v i t y , m s e c - 2 S u r f a c e h e a t t r a n s f e r coefficient, W m - 2 K A v e r a g e v a l u e o f h o v e r the s u r f a c e o f the b o d y , W m - 2 K T h e r m a l c o n d u c t i v i t y o f air, W m - ~K - 1 Height of body, m M e t a b o l i c rate, W m - z Thermal resistance per unit surface area, m 2 K WT e m p e r a t u r e , °C Absolute temperature, K U n d i s t u r b e d w i n d v e l o c i t y , m sec 1 Effective t h i c k n e s s o f c l o t h i n g , m
Greek symbols fl A /1 p
= = = =
Coefficient of volumetric expansion, KD i f f e r e n c e b e t w e e n (used as a prefix) C o e f f i c i e n t o f d y n a m i c v i s c o s i t y o f air, k g m - 1 s e c D e n/ s i"t y , k g m - 3
Subscripts c
= By c o n v e c t i o n = of clothing c + r = By t h e c o m b i n e d p r o c e s s e s o f c o n v e c t i o n a n d r a d i a t i o n 311 Applied Energy 0306-2619/79/0005-0311/$02-25 © Applied Science Publishers Ltd, England, 1979
cl
Printed in Great Britain
312 D
f L n o r s
P.W.
= = = = = = =
O'CALLAGHAN,
S. D. P R O B E R T
Based u p o n the D u b o i s equivalent d i a m e t e r F o r forced c o n v e c t i o n W i t h respect to height o f the b o d y F o r free c o n v e c t i o n R e l a t i n g to the e n v i r o n m e n t a l air c o n d i t i o n s D u e to r a d i a t i o n O f surface
Dimensionless groups f o r the air flow pZgflL3A T Gr L = Grashof number -
fiL
N u L = A v e r a g e Nusselt n u m b e r = ~ Pr
= P r a n d t l n u m b e r - t~Cp k
Re o
= R e y n o l d s n u m b e r - puD
PHYSICAL COMFORT MODEL
A p r e v i o u s analysis I c o n s i d e r e d the h u m a n b o d y as a vertical cylinder, o f base a r e a 1 m 2 a n d height 1.8 m c o r r e s p o n d i n g to the D u b o i s b o d y surface a r e a o f 1.8 m2. 2 T h e surface o f this b o d y should be m a i n t a i n e d at a skin t e m p e r a t u r e o f 33 °C for t h e r m a l c o m f o r t . U n d e r these c o n d i t i o n s a p p r o x i m a t e l y 25 ~o o f the basal m e t a b o l i c rate ( ~ 58.2 W m - 2) is dissipated by r e s p i r a t i o n a n d diffusion o f w a t e r t h r o u g h the o u t e r layers o f the skin. T o arrive at this c o n c l u s i o n it was a s s u m e d : (1) t h a t the m e a n air t e m p e r a t u r e equalled the m e a n e n v i r o n m e n t a l r a d i a n t t e m p e r a t u r e , (2) that a n y c l o t h i n g a p p l i e d to the surface offered no resistance to the passage o f water v a p o u r (i.e. infinite p e r m e a b i l i t y ) and (3) t h a t for low a d j a c e n t u n d i s t u r b e d air speeds the surface r a d i a t i v e heat transfer coefficient was o f the o r d e r o f the convective heat transfer coefficient. U n d e r these c i r c u m s t a n c e s the t e m p e r a t u r e difference r e q u i r e d between the surface o f the skin a n d the e n v i r o n m e n t in o r d e r to dissipate a m e t a b o l i c rate o f heat g e n e r a t i o n , q, f r o m a c l o t h e d b o d y is given 1 to a first a p p r o x i m a t i o n by: 33 - t o = 0-75q(R d + Re+,)
(1)
T h e t h e r m a l resistance o f a layer o f u n c o m p r e s s e d c l o t h i n g m a t e r i a l (i.e. including a c o n t r i b u t i o n f r o m the resistance o f air t r a p p e d in the voids) o f effective thickness w, has been f o u n d 3 to be:
R,. l = 23. I w
(2)
EFFECT O F AIR V E L O C I T Y O N T H E R M A L I N S U L A T I O N SYSTEMS
313
According to the assumption that heat exchanges by radiation at normal ambient temperatures are approximately the same as those due to convection: 1
1
R,. + r
R,.
+
1
2
~ - - = 2h, R~ R,.
(3)
Substituting eqns. (2) and (3) into eqn. (1) and rearranging gives the environmental temperature required for physical comfort as: t o = 33 -
0.754
23.1w +
(4)
T H E FREE C O N V E C T I V E H E A T T R A N S F E R C O E F F I C I E N T
The value of the mean convective heat transfer coefficient, h c, to be used in eqn. (4) depends upon the nature of the air movements at the external surface of the body. These can be due to free convection over the height, L, of the upright body, or to forced convection when air flows transversely over its surface. If the Archimedes number, GrL/ReZo, for the ambient air is much greater than unity, free convection dominates, whereas if GrL/Re ~ ,~ 1, forced convection overwhelms free convection. 4 It can be shown that, for a mean environmental air temperature of 20°C, and also if 0 < (t S - t o) < IO°C and u < 1 msec -1, GrL/ReZo >> 1 and free convection predominates. Therefore, for free convective heat transfers from the surface of a vertical cylinder: 4 I f G r L P r < 109 (i.e. in the l a m i n a r - f l o w r e g i m e ) : Nu L = 0.677(0.952 + Pr)-°'25Pr°'SGr °25
(5)
and: If GrLPr
>
10 9
(i.e. in the t u r b u l e n t - f l o w
regime):
Nu L = 0.0246Gr°4Pr°'466(l + 0-494Pr °'66)- 0.4
(6)
Using representative values for the transport properties, eqns. (5) and (6) become, respectively: hcL = 2"212(tot -- to) °z5
(5a)
~cL = 2"290(tot
(6a)
and: -
t o ) 0"40
F o r the configuration considered and for the values of the transport properties adopted, the G r a s h o f number varies with body height and temperature difference according to: GrLPr = 1-14 x 109(t~ -- to)L 3
(7)
314
P. W . O ' C A L L A G H A N ,
S. D. P R O B E R T
In addition, the clothing surface temperature, T,.t, varies with the clothing effectiveness, but an iterative analysis shows that ( t = - t o ) ~ - 3 ° C for typical arrangements. Thus: GrLPr -~ 3-4 x 1 0 9 L 3 and so, with the transition to turbulence occurring at ~ 3 m height, it is reasonable to assume that laminar flow predominates. Brundrett 5 arrived at a similar conclusion by a d o p t i n g the expression: h,L = 2'285(tot -- to) ° 2 5
(8)
INSIDE E N V I R O N M E N T A L T E M P E R A T U R E R E Q U I R E D F O R C O M F O R T
Substituting (tot - t o) ~- 3°C and /Y,L from eqn. (8) into eqn. (4) yields: t o ~- 33 - 0.75q(23.1w + 0.166)
(9)
which the authors further amended previously ~ to: t o "-, 33 - 0.75q(23w ÷ 0.133)
(10)
to a c c o u n t for the radiant emission o f clothing fabrics. F r o m this it can be seen that, for a given constant environmental temperature, the thickness o f clothing required to maintain c o m f o r t is a linear function o f the reciprocal o f the metabolic rate.
EFFECT OF AIR V E L O C I T Y O N C O M F O R T
Figure 1 represents a correlation o f measured average Nusselt numbers in terms o f Reynolds n u m b e r for air flowing transversely over circular cylinders ranging from 0.02 m m to 150 m m diameter. 6 F o r u > 10 m sec- 1, it can be demonstrated that forced convective heat transfer coefficients ( > 40 W m - 2 K - 1) overwhelm free convective and radiative coefficients ( < 1 0 W m - 2 K -1) and so eqn. (10) then tends to: t,, ~- 33 -
17-33qw
(11)
This relationship is illustrated in Fig. 2 in which the environmental temperature required for c o m f o r t under forced convective conditions is shown as a function o f metabolic rate and clothing effective thickness. C o m p a r i n g eqn. (11) with eqn. (10) it is deduced that for the same environmental temperature and metabolic rate the clothing level should be increased according to: ws - w, _~ 6 m m
(12)
in order to maintain the same level o f thermal c o m f o r t in forced convective
EFFECT OF AIR VELOCITY ON THERMAL INSULATION SYSTEMS
/
315
/I
jJ LOG Re
Fig. 1.
Average Nu versus Re for a circular cylinder in cross flow with air.
o
o8~ z
g
u_
o
5 5 EFFECTIVE
Fig. 2.
THICKNESS
10 OF CLOTHING
15 w (I0 IrnJ
Environmental air temperature required for thermal comfort under forced convective conditions.
316
p.w.
O'CALLAGHAN, S. D. PROBERT
conditions, whereas, for the same clothing level and metabolic rate, the environmental temperature should be increased according to: (13)
tof - to. = O. lr~
RECOMMENDED CLOTHING THICKNESSES
It is of interest to consider in more detail the levels of clothing necessary to offset increased heat losses incurred by the presence of high winds or by the subject moving at speed. If it is assumed that forced convection dominates, eqn. (4) may be rewritten as:
w
(14)
\ 17-33qJ
where h c is the forced convection heat transfer coefficient. Now: NUD =
(15)
ficD
k
and, substituting for the thermal conductivity of the air, k, and a representative value for the mean diameter, D, of the human body, namely 0.318m, then: w = 0.058
( ~ )
0.287 Nu °
(16)
The Nusselt number, Nu o, depends upon adjacent air velocity in the manner shown in Fig. 1. Inspection of eqn. (16) and Fig. 1 indicates that the thickness of clothing required to maintain the skin surface temperature at the thermally comfortable temperature of 33 °C is, to a first approximation, a linear function of the amount by which the environmental temperature is lower than 33 °C, the reciprocal of the metabolic rate and the reciprocal of the undisturbed local wind or draught speed. For air speeds between 10 m sec-1 and 50 m sec-1, the relationship between the Nusselt number and the Reynolds number may be approximated by: Nu o = 0" 19 Re °'643
(17)
N u o = l 1 5 u 0"643
(18)
Substituting values:
Thus, from eqns. (16) and (17): W=
0"058 ( ~ )
-- 0'0025U - °'643
(19)
EFFECT OF AIR VELOCITY ON THERMAL INSULATION SYSTEMS
3 !7
This relationship demonstrates the relative insensitivity of w to changes in wind speed compared with temperature variations, i.e. for a basal metabolic rate of 58-2 W m - 2 , a decrease in environmental temperature from 30 °C to 20 °C requires an increased level of clothing of ,-~ 10 m m under constant wind speed, but an increase of adjacent air velocity from 10 m sec- ~ to 50 m sec- ~, for a constant environmental temperature, requires only 0.37 m m of clothing to be added in order to regain the thermal comfort state.
OTHER COMFORT CONSIDERATIONS
Apart from the parametric combinations implied by the equations derived, the human subject may not be in a thermally comfortable state and vasoregulation, active sweating or shivering would occur to maintain the correct deep body temperature. The simplified analysis presented also neglects the effects of asymmetry in the ambient thermal field. For example, the sensitivities of various parts of the body differ. Whereas, in general, air velocities > 0.15 m sec- ~ can be detected at ankle level, the face can only perceive velocities > 0-30 m sec- 1. For these deductions to apply, no wind penetration through the clothing must ensue.
OTHER INSULATION SYSTEMS
The main insulation provided by a sheet of glass in a window is due to the air boundary layers adjacent to its two faces and if either of these is disturbed the effective thermal resistance is thereby reduced. For example, as a result of wind assault on a single glass sheet vertical window, the overall heat transfer coefficient may rise from the sheltered value of 3.8 W m - 2 K - t to 6"6 W m - 2 K - 1 for the severe wind condition. Consequently, the cost effectiveness of double glazing is considerably better for windswept locations. Also, when predictions of building performance are being undertaken, it is wise to .realise that the appropriate overall heat transfer coefficients for external walls may rise by about 20 ?~, above the 'no wind' data which are usually presented in textbooks.
REFERENCES I. P.W. O'CALLAGHANand S. D. PROBERT, Thermal insulation properties of clothing fabrics, Buildhlg Sert'iees Engineer, 44, (1976), pp. 71 9. 2. A NON., Handbook t~fl/undamentals+American Society of Heating, Refrigerating and Air Conditioning Engineers, 1972. 3. P. W+ O'CALLAGHANand S. D. PROBERT, Thermal resistance behaviour of single and multiple layer clothing fabrics, Applied Energy, 3, (1977)+ pp. 3 12.
318
P. W. O'CALLAGHAN, S. D. PROBERT
4. F. KREITH,Pr&ciplesof heat trans/er, International Textbook Co., Scranton, Pennsylvania, USA, 1965. 5. G. W. BRUNDRET'r, An introduction to thermal comfort in buildings, Heating and Ventilating Engineer, 42, (1974), pp. 365-72. 6. R. HILBERT, W/irmeabgabe von geheizten Dr/ihten und Rohren, Forsch. Gebeite lngenieurwesen,4, (1933), p. 220. P. W . O'CALLAGHAN a n d S. D . PROBERT
Applied Energy Group, School of Mechanical Engineering, Cranfield Institute of Technology, Cranfield, Bedfordshire (Great Britain)
Effect of Air Velocity on Thermal Insulation S y s t e m s
SUMMARY
A thermal comfort model has been developed to relate skin surface temperature to ambient air temperature and w#tdspeed. Relatively loB, wind assaults on clothing appreciably reduce the air boundary layer effective thermal resistance, whereas further equal increases in wind speed have decreasingly less effect in reducing the thermal resistance. Conclusions reached are extended to other insulation systems. The analysis assumes that no wind penetration through the insulant occurs.
NOMENCLATURE
Cp D g h /; k L R t T u w
= = = = = = = = = = = = =
Specific h e a t o f air at c o n s t a n t p r e s s u r e , J k g - ~K Dubois equivalent body diameter, m A c c e l e r a t i o n d u e to g r a v i t y , m s e c - 2 S u r f a c e h e a t t r a n s f e r coefficient, W m - 2 K A v e r a g e v a l u e o f h o v e r the s u r f a c e o f the b o d y , W m - 2 K T h e r m a l c o n d u c t i v i t y o f air, W m - ~K - 1 Height of body, m M e t a b o l i c rate, W m - z Thermal resistance per unit surface area, m 2 K WT e m p e r a t u r e , °C Absolute temperature, K U n d i s t u r b e d w i n d v e l o c i t y , m sec 1 Effective t h i c k n e s s o f c l o t h i n g , m
Greek symbols fl A /1 p
= = = =
Coefficient of volumetric expansion, KD i f f e r e n c e b e t w e e n (used as a prefix) C o e f f i c i e n t o f d y n a m i c v i s c o s i t y o f air, k g m - 1 s e c D e n/ s i"t y , k g m - 3
Subscripts c
= By c o n v e c t i o n = of clothing c + r = By t h e c o m b i n e d p r o c e s s e s o f c o n v e c t i o n a n d r a d i a t i o n 311 Applied Energy 0306-2619/79/0005-0311/$02-25 © Applied Science Publishers Ltd, England, 1979
cl
Printed in Great Britain
312 D
f L n o r s
P.W.
= = = = = = =
O'CALLAGHAN,
S. D. P R O B E R T
Based u p o n the D u b o i s equivalent d i a m e t e r F o r forced c o n v e c t i o n W i t h respect to height o f the b o d y F o r free c o n v e c t i o n R e l a t i n g to the e n v i r o n m e n t a l air c o n d i t i o n s D u e to r a d i a t i o n O f surface
Dimensionless groups f o r the air flow pZgflL3A T Gr L = Grashof number -
fiL
N u L = A v e r a g e Nusselt n u m b e r = ~ Pr
= P r a n d t l n u m b e r - t~Cp k
Re o
= R e y n o l d s n u m b e r - puD
PHYSICAL COMFORT MODEL
A p r e v i o u s analysis I c o n s i d e r e d the h u m a n b o d y as a vertical cylinder, o f base a r e a 1 m 2 a n d height 1.8 m c o r r e s p o n d i n g to the D u b o i s b o d y surface a r e a o f 1.8 m2. 2 T h e surface o f this b o d y should be m a i n t a i n e d at a skin t e m p e r a t u r e o f 33 °C for t h e r m a l c o m f o r t . U n d e r these c o n d i t i o n s a p p r o x i m a t e l y 25 ~o o f the basal m e t a b o l i c rate ( ~ 58.2 W m - 2) is dissipated by r e s p i r a t i o n a n d diffusion o f w a t e r t h r o u g h the o u t e r layers o f the skin. T o arrive at this c o n c l u s i o n it was a s s u m e d : (1) t h a t the m e a n air t e m p e r a t u r e equalled the m e a n e n v i r o n m e n t a l r a d i a n t t e m p e r a t u r e , (2) that a n y c l o t h i n g a p p l i e d to the surface offered no resistance to the passage o f water v a p o u r (i.e. infinite p e r m e a b i l i t y ) and (3) t h a t for low a d j a c e n t u n d i s t u r b e d air speeds the surface r a d i a t i v e heat transfer coefficient was o f the o r d e r o f the convective heat transfer coefficient. U n d e r these c i r c u m s t a n c e s the t e m p e r a t u r e difference r e q u i r e d between the surface o f the skin a n d the e n v i r o n m e n t in o r d e r to dissipate a m e t a b o l i c rate o f heat g e n e r a t i o n , q, f r o m a c l o t h e d b o d y is given 1 to a first a p p r o x i m a t i o n by: 33 - t o = 0-75q(R d + Re+,)
(1)
T h e t h e r m a l resistance o f a layer o f u n c o m p r e s s e d c l o t h i n g m a t e r i a l (i.e. including a c o n t r i b u t i o n f r o m the resistance o f air t r a p p e d in the voids) o f effective thickness w, has been f o u n d 3 to be:
R,. l = 23. I w
(2)
EFFECT O F AIR V E L O C I T Y O N T H E R M A L I N S U L A T I O N SYSTEMS
313
According to the assumption that heat exchanges by radiation at normal ambient temperatures are approximately the same as those due to convection: 1
1
R,. + r
R,.
+
1
2
~ - - = 2h, R~ R,.
(3)
Substituting eqns. (2) and (3) into eqn. (1) and rearranging gives the environmental temperature required for physical comfort as: t o = 33 -
0.754
23.1w +
(4)
T H E FREE C O N V E C T I V E H E A T T R A N S F E R C O E F F I C I E N T
The value of the mean convective heat transfer coefficient, h c, to be used in eqn. (4) depends upon the nature of the air movements at the external surface of the body. These can be due to free convection over the height, L, of the upright body, or to forced convection when air flows transversely over its surface. If the Archimedes number, GrL/ReZo, for the ambient air is much greater than unity, free convection dominates, whereas if GrL/Re ~ ,~ 1, forced convection overwhelms free convection. 4 It can be shown that, for a mean environmental air temperature of 20°C, and also if 0 < (t S - t o) < IO°C and u < 1 msec -1, GrL/ReZo >> 1 and free convection predominates. Therefore, for free convective heat transfers from the surface of a vertical cylinder: 4 I f G r L P r < 109 (i.e. in the l a m i n a r - f l o w r e g i m e ) : Nu L = 0.677(0.952 + Pr)-°'25Pr°'SGr °25
(5)
and: If GrLPr
>
10 9
(i.e. in the t u r b u l e n t - f l o w
regime):
Nu L = 0.0246Gr°4Pr°'466(l + 0-494Pr °'66)- 0.4
(6)
Using representative values for the transport properties, eqns. (5) and (6) become, respectively: hcL = 2"212(tot -- to) °z5
(5a)
~cL = 2"290(tot
(6a)
and: -
t o ) 0"40
F o r the configuration considered and for the values of the transport properties adopted, the G r a s h o f number varies with body height and temperature difference according to: GrLPr = 1-14 x 109(t~ -- to)L 3
(7)
314
P. W . O ' C A L L A G H A N ,
S. D. P R O B E R T
In addition, the clothing surface temperature, T,.t, varies with the clothing effectiveness, but an iterative analysis shows that ( t = - t o ) ~ - 3 ° C for typical arrangements. Thus: GrLPr -~ 3-4 x 1 0 9 L 3 and so, with the transition to turbulence occurring at ~ 3 m height, it is reasonable to assume that laminar flow predominates. Brundrett 5 arrived at a similar conclusion by a d o p t i n g the expression: h,L = 2'285(tot -- to) ° 2 5
(8)
INSIDE E N V I R O N M E N T A L T E M P E R A T U R E R E Q U I R E D F O R C O M F O R T
Substituting (tot - t o) ~- 3°C and /Y,L from eqn. (8) into eqn. (4) yields: t o ~- 33 - 0.75q(23.1w + 0.166)
(9)
which the authors further amended previously ~ to: t o "-, 33 - 0.75q(23w ÷ 0.133)
(10)
to a c c o u n t for the radiant emission o f clothing fabrics. F r o m this it can be seen that, for a given constant environmental temperature, the thickness o f clothing required to maintain c o m f o r t is a linear function o f the reciprocal o f the metabolic rate.
EFFECT OF AIR V E L O C I T Y O N C O M F O R T
Figure 1 represents a correlation o f measured average Nusselt numbers in terms o f Reynolds n u m b e r for air flowing transversely over circular cylinders ranging from 0.02 m m to 150 m m diameter. 6 F o r u > 10 m sec- 1, it can be demonstrated that forced convective heat transfer coefficients ( > 40 W m - 2 K - 1) overwhelm free convective and radiative coefficients ( < 1 0 W m - 2 K -1) and so eqn. (10) then tends to: t,, ~- 33 -
17-33qw
(11)
This relationship is illustrated in Fig. 2 in which the environmental temperature required for c o m f o r t under forced convective conditions is shown as a function o f metabolic rate and clothing effective thickness. C o m p a r i n g eqn. (11) with eqn. (10) it is deduced that for the same environmental temperature and metabolic rate the clothing level should be increased according to: ws - w, _~ 6 m m
(12)
in order to maintain the same level o f thermal c o m f o r t in forced convective
EFFECT OF AIR VELOCITY ON THERMAL INSULATION SYSTEMS
/
315
/I
jJ LOG Re
Fig. 1.
Average Nu versus Re for a circular cylinder in cross flow with air.
o
o8~ z
g
u_
o
5 5 EFFECTIVE
Fig. 2.
THICKNESS
10 OF CLOTHING
15 w (I0 IrnJ
Environmental air temperature required for thermal comfort under forced convective conditions.
316
p.w.
O'CALLAGHAN, S. D. PROBERT
conditions, whereas, for the same clothing level and metabolic rate, the environmental temperature should be increased according to: (13)
tof - to. = O. lr~
RECOMMENDED CLOTHING THICKNESSES
It is of interest to consider in more detail the levels of clothing necessary to offset increased heat losses incurred by the presence of high winds or by the subject moving at speed. If it is assumed that forced convection dominates, eqn. (4) may be rewritten as:
w
(14)
\ 17-33qJ
where h c is the forced convection heat transfer coefficient. Now: NUD =
(15)
ficD
k
and, substituting for the thermal conductivity of the air, k, and a representative value for the mean diameter, D, of the human body, namely 0.318m, then: w = 0.058
( ~ )
0.287 Nu °
(16)
The Nusselt number, Nu o, depends upon adjacent air velocity in the manner shown in Fig. 1. Inspection of eqn. (16) and Fig. 1 indicates that the thickness of clothing required to maintain the skin surface temperature at the thermally comfortable temperature of 33 °C is, to a first approximation, a linear function of the amount by which the environmental temperature is lower than 33 °C, the reciprocal of the metabolic rate and the reciprocal of the undisturbed local wind or draught speed. For air speeds between 10 m sec-1 and 50 m sec-1, the relationship between the Nusselt number and the Reynolds number may be approximated by: Nu o = 0" 19 Re °'643
(17)
N u o = l 1 5 u 0"643
(18)
Substituting values:
Thus, from eqns. (16) and (17): W=
0"058 ( ~ )
-- 0'0025U - °'643
(19)
EFFECT OF AIR VELOCITY ON THERMAL INSULATION SYSTEMS
3 !7
This relationship demonstrates the relative insensitivity of w to changes in wind speed compared with temperature variations, i.e. for a basal metabolic rate of 58-2 W m - 2 , a decrease in environmental temperature from 30 °C to 20 °C requires an increased level of clothing of ,-~ 10 m m under constant wind speed, but an increase of adjacent air velocity from 10 m sec- ~ to 50 m sec- ~, for a constant environmental temperature, requires only 0.37 m m of clothing to be added in order to regain the thermal comfort state.
OTHER COMFORT CONSIDERATIONS
Apart from the parametric combinations implied by the equations derived, the human subject may not be in a thermally comfortable state and vasoregulation, active sweating or shivering would occur to maintain the correct deep body temperature. The simplified analysis presented also neglects the effects of asymmetry in the ambient thermal field. For example, the sensitivities of various parts of the body differ. Whereas, in general, air velocities > 0.15 m sec- ~ can be detected at ankle level, the face can only perceive velocities > 0-30 m sec- 1. For these deductions to apply, no wind penetration through the clothing must ensue.
OTHER INSULATION SYSTEMS
The main insulation provided by a sheet of glass in a window is due to the air boundary layers adjacent to its two faces and if either of these is disturbed the effective thermal resistance is thereby reduced. For example, as a result of wind assault on a single glass sheet vertical window, the overall heat transfer coefficient may rise from the sheltered value of 3.8 W m - 2 K - t to 6"6 W m - 2 K - 1 for the severe wind condition. Consequently, the cost effectiveness of double glazing is considerably better for windswept locations. Also, when predictions of building performance are being undertaken, it is wise to .realise that the appropriate overall heat transfer coefficients for external walls may rise by about 20 ?~, above the 'no wind' data which are usually presented in textbooks.
REFERENCES I. P.W. O'CALLAGHANand S. D. PROBERT, Thermal insulation properties of clothing fabrics, Buildhlg Sert'iees Engineer, 44, (1976), pp. 71 9. 2. A NON., Handbook t~fl/undamentals+American Society of Heating, Refrigerating and Air Conditioning Engineers, 1972. 3. P. W+ O'CALLAGHANand S. D. PROBERT, Thermal resistance behaviour of single and multiple layer clothing fabrics, Applied Energy, 3, (1977)+ pp. 3 12.
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P. W. O'CALLAGHAN, S. D. PROBERT
4. F. KREITH,Pr&ciplesof heat trans/er, International Textbook Co., Scranton, Pennsylvania, USA, 1965. 5. G. W. BRUNDRET'r, An introduction to thermal comfort in buildings, Heating and Ventilating Engineer, 42, (1974), pp. 365-72. 6. R. HILBERT, W/irmeabgabe von geheizten Dr/ihten und Rohren, Forsch. Gebeite lngenieurwesen,4, (1933), p. 220. P. W . O'CALLAGHAN a n d S. D . PROBERT
Applied Energy Group, School of Mechanical Engineering, Cranfield Institute of Technology, Cranfield, Bedfordshire (Great Britain)