Engine oil flows through a 25 − mm -diameter tube at a rate of 0. 5 kg / s . The oil enters the tube at a temperature of 25 ° C , while the tube surface temperature is maintained at 1 00 ° C . (a) Determine the oil outlet temperature for a 5 − m and for a 1 00 − m bug tube. For each case, compare the log mean temperature difference w the arithmetic mean temperature difference. (b)For 5 ≤ L ≤ 100 m, compute and plot the average Nusselt number N u ¯ D and the oil outlet temperature as a function of L.
Engine oil flows through a 25 − mm -diameter tube at a rate of 0. 5 kg / s . The oil enters the tube at a temperature of 25 ° C , while the tube surface temperature is maintained at 1 00 ° C . (a) Determine the oil outlet temperature for a 5 − m and for a 1 00 − m bug tube. For each case, compare the log mean temperature difference w the arithmetic mean temperature difference. (b)For 5 ≤ L ≤ 100 m, compute and plot the average Nusselt number N u ¯ D and the oil outlet temperature as a function of L.
Solution Summary: The author compares the oil outlet temperature for given lengths of tube and the Reynolds number, LMTD, and nusselt formula.
Engine oil flows through a
25
−
mm
-diameter tube at a rate of
0.
5 kg
/
s
. The oil enters the tube at a temperature of
25
°
C
, while the tube surface temperature is maintained at
1
00
°
C
.
(a) Determine the oil outlet temperature for a
5
−
m
and for a
1
00
−
m
bug tube. For each case, compare the log mean temperature difference w the arithmetic mean temperature difference.
(b)For
5
≤
L
≤
100
m, compute and plot the average Nusselt number
N
u
¯
D
and the oil outlet temperature as a function of L.
48. Water is flowing in a smooth pipe of diameter D. A section of this pipe hav-
ing a length of L is heated. Water at the inlet to the heated section has a tempera-
ture of Tŋ. Water temperature at the exit of the heated section is Tp. The heated
section of the pipe wall is maintained at a constant heat flux so that a constant
temperature difference of AT, = T, – T, exists between the wall and the bulk wa-
ter temperature. Show that for turbulent flow in the pipe and a specified heated
length and pipe diameter, water temperature at the exit of the heated section is
given by:
402
0.6
Pr
T52 =Tf
+0.0876
L
AT
DO.8
0.2
m
A shell-and-tube heat exchanger is used to cool compressed liquid methanol
from 176 °F to 104 °F. The methanol flows on the shell side of the
exchanger. The coolant is water that rises in temperature from 50 °F to
86 °F and flows within the tubes at a rate of 68.9 kg s1. Finding the
appropriate thermophysical data and applying the proper equations, you are
required to do the following:
(a)
Calculate i) methanol mass flow rate in the exchanger, ii) methanol
volumetric flowrate at the inlet of the exchanger.
(b) i) For the counter-current flow of the fluids calculate the log
temperature difference, ii) explain the purpose of calculating this
difference, iii) explain, quantitatively, why is the counter-current flow in
heat exchangers preferred to co-current flow.
mean
Water (cp = 4197 J / kgC, k = 0.67W / mC, Pr = 2.2, dynamic viscosity = 352 * 10 ^ -6 Ns / m ^ 2) with a flow rate of 0.01 kg / s and an inner diameter of 0.1 m at 20C temperature It is requested to be heated to 80C. If the pipe inner wall is kept constant at 120C, what is the average logarithmic temperature difference with fully developed flow acceptance?
a. 65.48 C b. 43.3 C. c. 316.3 K D. 723.4 K e. 2300 K.
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