Page 219 - Modelling in Transport Phenomena A Conceptual Approach

7.5. CONSERVATION OF ENERGY 199

which is known as the general energy equation. Note that under steady conditions,
Eq. (7.54) reduces to Eq. (6.3-9). In terms of molar quantities, Eq. (7.5-4) is
written as

[(it + EK + EP)?i]. - [(it + l3K + EP)?i] + Qint - PSYS - +ws
dKYS
sn out dt

When the changes in the kinetic and potential energies between the inlet and
outlet of the system as well as within the system are negligible, Eq. (7.5-4) reduces
to
(fik)in - (fik)out + Qint - Psys 7 ws = z(om)sys (7.5-6)
.
d
dvsys
+
The accumulation term in Eq. (7.56) can be expressed in terms of enthalpy as

= -(Hm)sys - Psys - dPsy,
d*
dvsy,
vsys - (7.5-7)
-
dt dt dt
Substitution of Eq. (7.57) into Eq. (7.5-6) gives

On molar basis, Eq, (7.58) can be expressed as

Example 7.6 Air at atmospheric pressure and 25OC is flowing at a velocity
of 5 m/ s over a copper sphere, 1.5 cm in diameter. The sphere is initially at a
temperature of 50°C. How long will it take to cool the sphere to 30°C? How much
heat is transferred from the sphere to the air?

Solution
Physical properties

p = 18.41 x 10-6kg/m.s
air at 25 OC (298 K, ' v = 15.54 x m2/ s
= 25-96 10-3 W/ m. K
Pr = 0.712