Consider flow in a circular tube. Within the test section length (between 1 and 2) a constant heat flux q s n is maintained. (a) For the following two cases, sketch the surface temperature T s ( x ) and the fluid mean temperature T m ( x ) as a function of distance along the test section x . In case A. flow is hydrodynamically and thermally fully developed. In case B. flow is not developed. (b) Assuming that the surface flux q s n and the inlet mean temperature T m , 1 are identical for both cases, will the exit mean temperature T m , 2 for case A be greater than, equal to, or less than T m , 2 for case B? Briefly explain why.
Consider flow in a circular tube. Within the test section length (between 1 and 2) a constant heat flux q s n is maintained. (a) For the following two cases, sketch the surface temperature T s ( x ) and the fluid mean temperature T m ( x ) as a function of distance along the test section x . In case A. flow is hydrodynamically and thermally fully developed. In case B. flow is not developed. (b) Assuming that the surface flux q s n and the inlet mean temperature T m , 1 are identical for both cases, will the exit mean temperature T m , 2 for case A be greater than, equal to, or less than T m , 2 for case B? Briefly explain why.
Solution Summary: The author illustrates the surface temperature and fluid mean temperature as a function of distance along the test section for hydro-dynamically and thermally developed flow.
Consider flow in a circular tube. Within the test section length (between 1 and 2) a constant heat flux
q
s
n
is maintained.
(a) For the following two cases, sketch the surface temperature
T
s
(
x
)
and the fluid mean temperature
T
m
(
x
)
as a function of distance along the test section x. In case A. flow is hydrodynamically and thermally fully developed. In case B. flow is not developed.
(b) Assuming that the surface flux
q
s
n
and the inlet mean temperature
T
m
,
1
are identical for both cases, will the exit mean temperature
T
m
,
2
for case A be greater than, equal to, or less than
T
m
,
2
for case B? Briefly explain why.
2- To solve these problems, refer to notes on
Blackboard about convection inside pipes. Also,
assume that the inside wall temperature of the
cylinder is 100 °C
Steam condensing
circular tube of diameter D=50 mm and length L= 6 m
maintains a uniform outer surface temperature of 100 °C
Water flows through the tube at a rate m = 0.25 kg/s, and
its inlet bulk temperature is To 15 °C. Determine:
on the outer surface of a thin-walled
a If the flow is laminar or turbulent
b) The exit bulk temperature
c) T (C) h (W/m2.K)
d) Rate of heat transfer from steam to water
e) A plot of T vs x, where x is the distance in axial
direction along the pipe
= 57 °C. Only
State any assumptions made, and use
L, guess
one iteration is needed.
5. Consider Poiseuille flow through a tube. Use the more general bound-
ary condition for slip which includes a second term due to thermal creep,
3 µR dT
4 p dr
to derive an expression for the mass flow rate through the tube in terms of
the tube radius, temperature, Knudsen number, and temperature derivative
along the x-axis. Assume that the flow is incompressible.
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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