Handbook of air conditioning and refrigeration / Shan K

Conduction heat from node i � 1 � conduction heat from node i � 1
� rate of change of internal energy of node i
where Ui � internal energy of node i, Btu/lb (J/kg)
� b, cb � density and specific heat of building material, lb/ft 3 (kg/m 3 �
) and Btu/lb�°F
(J/kg�°C)
�t � selected time interval, s or min
� qi�1:i � qi�1:i �
t��t t
bcb Ai�x (T i � T i) �t
�Ui �t
Substituting Eq. (6.50) into (6.52) and solving for T i t ��t , we have
(6.52)
In Eq. (6.53), Fo is the Fourier number and is defined as
(6.53)
Fo �
Subscript b indicates the building material.
(6.54)
The choice of spacing �x and the time interval �t must meet some criterion to ensure convergence
in the calculations. The criterion is the stability limit, or
k b �t
(�x) 2
t��t t T i � Fo(T i�1 � T t i�1) � (1 � 2Fo)T t i
Fo �
Similarly, for moisture transfer at the interior nodes,
1
2
and
where X � moisture content, dimensionless
D lv � mass diffusivity of liquid and vapor, ft 2 /s (m 2 /s)
Heat and Moisture Transfer at Surface Nodes
X i t��t � Fomass (X t i�1 � X t i�1) � (1 � 2 Fo mass) X t i
(6.55)
(6.56)
(6.57)
For a one-dimensional heat flow, the energy balance at surface node i of the partition wall as shown
in Fig. 6.8 is
Conductive heat from node i � 1 � convective heat transfer from space air
� latent heat of moisture transfer from space air � radiative heat from internal loads
� rate of change of internal energy of node i
t t kAi (T i�1 � T i)
�x
� bc b
Fomass � Dlv �t 1
� 2 2
(�x)
� h ci A i(T t r � T t i) � � ah mi A i X t i (w t r � w t is) h fg
� F1:iL r � Fp:iOr � Fm:i Mr � �bcb Ai �x
2 T i t��t t � T i
�t
LOAD CALCULATIONS 6.37