(a) A vertical building external envelope of

5m\\\\times 5m

is made of opaque wall. The surface absorptance

\\\\alpha

of the wall is 0.473 . The wall thickness is

100mm

, and its thermal conductivity is

0.06(W)/(m*K)

. Indoor air temperature is maintained at

23\\\\deg C

. The indoor air convective heat transfer coefficient,

h_(i)

, is at

3.64(W)/(m^(2)*K)

and the outdoor air convective heat transfer coefficient is related to outdoor air velocity,

v

, as follows:\

h_(o)=10+3.272v,[(W)/(m^(2)*K)]

\ At

2pm

on

21July

, the outdoor air temperature is

33.3\\\\deg C

, the outdoor air velocity,

v

, is

2.5(m)/(s)

and the incoming total surface irradiance,

I_(t)

, is

436.7(W)/(m^(2))

.\ Determine the percentage reduction in total heat input at the external surface of the envelope, if an additional layer of

30mm

thick is added to the external side of the wall, at the above time and date. Assume that the surface absorptance of the wall after adding the layer is only

50%

of its original value of 0.473 , and that the thermal conductivity of the additional layer,

K^(')

, is 0.025

(W)/(m*K)

. All other parameters remain unchanged after adding the layer.\ (15 marks)

a) A vertical building external envelope of 5m5m is made of opaque wall. The surface absorptance of the wall is 0.473 . The wall thickness is 100mm, and its thermal conductivity is 0.06W/(mK). Indoor air temperature is maintained at 23C. The indoor air convective heat transfer coefficient, hi, is at 3.64W/(m2K) and the outdoor air convective heat transfer coefficient is related to outdoor air velocity, v, as follows: ho=10+3.272v[W/(m2K)] At 2pm on 21 July, the outdoor air temperature is 33.3C, the outdoor air velocity, v, is 2.5m/s and the incoming total surface irradiance, It, is 436.7W/m2. Determine the percentage reduction in total heat input at the external surface of the envelope, if an additional layer of 30mm thick is added to the external side of the wall, at the above time and date. Assume that the surface absorptance of the wall after adding the layer is only 50% of its original value of 0.473 , and that the thermal conductivity of the additional layer, K, is 0.025 W/(mK). All other parameters remain unchanged after adding the layer