Page 291 - Modelling in Transport Phenomena A Conceptual Approach

8.2. ENERGY TRANSPORT WITHOUT CONVECTION 271

the resulting heat transfer rate and the temperature distribution as a function of
position are given in Table 8.6.
Table 8.5 Heat transfer rate and temperature distribution for onedimensional
conduction in a hollow sphere for the boundary conditions given by Eq. (8.2-51).

Heat Transfer
Constants Temperature Distribution
Rate

1 1

Table 8.6 Heat transfer rate and temperature distribution for onedimensional
conduction in a hollow sphere for the boundary conditions given by Eq. (8.2-52).
Heat Transfer
Constants Temperature Distribution
Rate

None 47rR:ql (A) k(T) dT = qlRy (: - k) (C)

Example 8.9 A spherical metal ball of radius R is placed in an infinitely large
volume of motionless fluid. The ball is maintained at a temperature of TR whale
the temperature of the fluid far from the ball is T,.
a) Determine the rate of heat transferred to the fluid.
b) Determine the temperature distribution within the fluid.
c) Determine the Nusselt number.
Solution

Assumptions
1. Steady-state conditions prevail.