Page 220 - Modelling in Transport Phenomena A Conceptual Approach

200 CHAPTER 7. UNSTEADY-STATE MACROSCOPIC BALANCES

For air at 40 "C (313 K) : p = 19.11 x kg/ m. s
p = 8924 kg/ m3
For copper at 40 "C (313 K) : &p = 387 J/ kg. K
{ k=397W/m.K
Assumptions

1. No temperature gradients m'st within the sphere, i.e., Bi << 1.
2. The average heat transfer coeficient on the surface of the sphere is constant.

3. The physical properties of copper are independent of temperature.
4. Pseudo-steady-state behavior.

Analysis
System: Copper sphere
For the problem at hand, the terms in Eq. (7.5-8) are

min = m,,t = 0
ws = 0
Qint = - (rDg)(h)(T - Tm)

msys = (&/6) Pcu
fisys = (&P)c~(T Twf)
-
where T is the copper sphere temperature at any instant and T, is the air temper-
ature.
Therefore, Eq. (7.5-8) becomes

Integration of Eq. (1) with the initial condition that T = Ti at t = 0 gives

To determine the average heat transfer coeflcient, (h), first it is necessary to cal-
culate the Reynolds number:
Rep = -
DPV,
Y