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7.5. CONSERVATION OF ENERGY 203
where Dp is the diameter of the sphere, subscripts s and f stand for the sphere
and the fluid, respectively. Therefore, Eq. (7.5-8) becomes
where
System: Fluid in the tank
The terms in Eq. (7.5-8) are
Hence, Eq. (7.5-8) reduces to
where
From Eq. (1), the fluid temperature, Tf , is given in terms of the sphere temperature,
Substitution of Eq. (5) into Eq. (3) gives
&T, dT,
-+d==O
dt2
where
d=df +d, (7)
Two initial conditions are necessary to solve this second-order ordinary diflerential
equation. One of the initial conditions is
at t = 0 T, =TI (8)
