Page 273 - Modelling in Transport Phenomena A Conceptual Approach

8.2. ENERGY TRANSPORT WITHOUT CONVECTION 253

Using Eq. (8.2-13) the resistances are calculated as follows:

LA
RA=-= 0.1 = 0.032 K/ W
kAA (35)(0.09 X 1)

LE 0.2
RB=-- = 0.278 K/ W
kBA - (12)(0.06 x 1)

LC 0.2
Rc=-- = 0.290 K/ W
kcA - (23)(0.03 x 1)

RD=-- LD - Omo8 = 0.178 K/ W
koA (5)(0.09 x 1)

('.') -1 = (-+-)
R,= 1 1 -* =0.142K/W
RB Re 0278 0.290

The total resistance of the entire circuit is

R = RA -I- R, + RD = 0.032 + 0.142 + 0.178 = 0.352 K/ W

Hence, the heat transfer rate is

TI -T2 300- 22 = 790w
&=-- -
*
CR 0.352
b) Note that

Therefore, the effective thermal conductivity is
0.1 + 0.2 + 0.08 = 12 w/
m.
keff = (0.09 x 1)(0.352)

8.2.1.2 Transfer rate in terms of bulk fluid properties
Consider the transfer of thermal energy from fluid A, at a temperature TA with
an average heat transfer coefficient (h~), through a solid plane wall with thermal
conductivity k, to Auid B, at a temperature TB with an average heat transfer
coefficient (hB), as shown in Figure 8.11.