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Conduction Through Spheres Conduction Through Spheres Conduction Through Spheres Conduction Through Spheres
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HEAT CONDUCTION IN SPHERES
dtk4r
drQ
dr
dt)r4-k(Q
r4A
dr
dt-kAQ
Law sFourier' From
2
2
2
)tt(k4r
1Q
)tt(k41
rQ
dtk4drrQ
12
2
1
12
2
1
1
2
21
12
21
12
21
12
21
12
12
12
rkr4
rrR
R
t
rkr4
rr
)tt(Q
)tt(k4rr
rrQ
)tt(k4r
1
r
1Q
HEAT TRANSFER FROM FLUID TO FLUID IN SPHERES
2
2o
oo
3
21
122
2
1i
ii
1
321
r4 A; Ah
iR
rkr4
rrR
r4 A; Ah
iR
RRR
totiQ
total
ooii
t
R
1AUAUUA
)t(UAQ
R
tQ
A 3 m internal diameter spherical tank made of 2 cm thick
stainless steel (k = 15 W/m-K) is used to store iced water
at t+ = 0C. The tank is located in a room whose temperature is
to = 22C. The walls of the room are also 22C. The outer sur –
face of the tank is black ( = 1) and heat transfer between the
outer surface of the tank and the surroundings is by natural
convection and radiation. The convective coefficients at the
inner and the outer surfaces of the tank are hi = 80 W/m2-K
and ho = 10 W/m2-K, respectively. Determine
a. the rate of heat transfer to the iced water in the tank
if the outer surface temperature is 5C
b. the amount of ice at 0C that melts during a 24 hrs
period
r1 r2 k hi ho hice
1.5 1.52 15 80 10 333.7
ti to t2 Ai Ao T2
0 22 5 28.274 29.03 278
To Qc Qr Q mice
295 4936 2.6E+03 7.6E+03 1960
kg 1960m
)mice(333.7sec) hrs)(3600 7.6(24Q
KW 7.6 Watts7600Q
)TT(AQ
)t22(AhQ
QQQ
ice
4
2
4
oor
2ooc
rc
