Page 293 - Modelling in Transport Phenomena A Conceptual Approach

8.2. ENERGY TRANSPORT WTHOUT CONVECTION 273

so that Eq. (8.254) takes the form

Rz-R1 - Thickness 1
Resistance = - (8.2-56)
k&M ('Transport property) (Area)
The electrical circuit analog of the spherical wall can be represented as shown
in Figure 8.20.

R2-Rl
~AGM
0 0
TI T2
-Q
Figure 8.20 Electrical circuit analog of the spherical wall.

8.2.3.2 Transfer rate in terms of bulk fluid properties
The use of Eq. (8.2-53) in the calculation of the transfer rate requires surface values
TI and T2 to be known or measured. In common practice, the bulk temperatures
of the adjoining fluids to the surfaces at r = R1 and r = Rz, i.e., TA and TB, are
known. It is then necessary to relate TI and T2 to TA and TB.
The procedure for the spherical case is similar to that for the cylindrical case
and left as an exercise to the students. If the procedure given in Section 8.2.2.2 is
followed, the result is

(8.2-57)

Example 8.10 Consider a spherical tank with inner and outer radii of R1 and
R2, respectively, and investigate how the rate of heat loss varies as a function of
insulation thickness.
Solution

The solution procedure for this problem is similar to Example 8.7. For the geometry
shown in Figure 8.21, the de of heat loss is given by
~T(TA - TB)
Q= (1)
1 + Rz-Ri +R3-RZ +- 1
R? @A) RiRzk RzR3ki @i(h~)
-,
X
where k, and ki are the thermal conductivities of the wall and the insulating
material, respectively.