An experimental nuclear core simulation apparatus consists of a long thin-walled metallic tube of diameter D and length L , which is electrically heated to produce the sinusoidal heat flux distribution q s " ( x ) = q o " sin ( π x L ) where x is the distance measured from the tube inlet. Fluid at an inlet temperature T m , i flows through the tube at a rate of m ˙ . Assuming the flow is turbulent and fully developed over the entire length of the tube, develop expressions for: (a) the total rate of heat transfer, q , from the tube to the fluid; (b) the fluid outlet temperature, T m , o ; (e) the axial distribution of the wall temperature, T s ( x ) : and (d) the magnitude and position of the highest wall temperature. (e) Consider a 40-mm-diameter tube of 4-m length with a sinusoidal heat flux distribution for which q o " = 10 , 000 W / m 2 . Fluid passing through the tube has a flow rate of 0 .025 kg/s , a specific heat of 4180 J/kg ⋅ K , an entrance temperature of 25 ° C , and a convection coefficient of 1000 W/m 2 ⋅ K . Plot the mean fluid and surface temperatures as a function of distance along the tube. Identify important features of the distributions. Explore the effect of ± 25 % changes in the convection coefficient and the heat flux on the distributions.
An experimental nuclear core simulation apparatus consists of a long thin-walled metallic tube of diameter D and length L , which is electrically heated to produce the sinusoidal heat flux distribution q s " ( x ) = q o " sin ( π x L ) where x is the distance measured from the tube inlet. Fluid at an inlet temperature T m , i flows through the tube at a rate of m ˙ . Assuming the flow is turbulent and fully developed over the entire length of the tube, develop expressions for: (a) the total rate of heat transfer, q , from the tube to the fluid; (b) the fluid outlet temperature, T m , o ; (e) the axial distribution of the wall temperature, T s ( x ) : and (d) the magnitude and position of the highest wall temperature. (e) Consider a 40-mm-diameter tube of 4-m length with a sinusoidal heat flux distribution for which q o " = 10 , 000 W / m 2 . Fluid passing through the tube has a flow rate of 0 .025 kg/s , a specific heat of 4180 J/kg ⋅ K , an entrance temperature of 25 ° C , and a convection coefficient of 1000 W/m 2 ⋅ K . Plot the mean fluid and surface temperatures as a function of distance along the tube. Identify important features of the distributions. Explore the effect of ± 25 % changes in the convection coefficient and the heat flux on the distributions.
Solution Summary: The author explains the expression for total rate of heat transfer from tube to fluid.
An experimental nuclear core simulation apparatus consists of a long thin-walled metallic tube of diameter D and length L, which is electrically heated to produce the sinusoidal heat flux distribution
q
s
"
(
x
)
=
q
o
"
sin
(
π
x
L
)
where x is the distance measured from the tube inlet. Fluid at an inlet temperature
T
m
,
i
flows through the tube at a rate of
m
˙
. Assuming the flow is turbulent and fully developed over the entire length of the tube, develop expressions for: (a) the total rate of heat transfer, q, from the tube to the fluid; (b) the fluid outlet temperature,
T
m
,
o
; (e) the axial distribution of the wall temperature,
T
s
(
x
)
: and (d) the magnitude and position of the highest wall temperature. (e) Consider a 40-mm-diameter tube of 4-m length with a sinusoidal heat flux distribution for which
q
o
"
=
10
,
000
W
/
m
2
. Fluid passing through the tube has a flow rate of
0
.025 kg/s
, a specific heat of
4180 J/kg
⋅
K
, an entrance temperature of
25
°
C
, and a convection coefficient of
1000 W/m
2
⋅
K
. Plot the mean fluid and surface temperatures as a function of distance along the tube. Identify important features of the distributions. Explore the effect of
±
25
%
changes in the convection coefficient and the heat flux on the distributions.
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