Consider flow over a flat plate for which it is desired to determine the average heat transfer coefficient over the short span x 1 to x 2 , h ¯ 1 − 2 , where ( x 2 − x 1 ) ≪ L . Provide three different expressions that can be used to evaluate h ¯ 1 − 2 in terms of (a) the local coefficient at x = ( x 1 + x 2 ) / 2 , (b) the local coefficients at x 1 and x 2 , and (c) the average coefficients at x 1 and x 2 . Indicate which of the expressions is approximate. Considering whether the flow is laminar, turbulent, or mixed, indicate when it is appropriate or inappropriate to use each of the equations.
Consider flow over a flat plate for which it is desired to determine the average heat transfer coefficient over the short span x 1 to x 2 , h ¯ 1 − 2 , where ( x 2 − x 1 ) ≪ L . Provide three different expressions that can be used to evaluate h ¯ 1 − 2 in terms of (a) the local coefficient at x = ( x 1 + x 2 ) / 2 , (b) the local coefficients at x 1 and x 2 , and (c) the average coefficients at x 1 and x 2 . Indicate which of the expressions is approximate. Considering whether the flow is laminar, turbulent, or mixed, indicate when it is appropriate or inappropriate to use each of the equations.
Solution Summary: The author calculates the heat rate per unit width for the shortest span from x_1 to
Consider flow over a flat plate for which it is desired to determine the average heat transfer coefficient over the short span
x
1
to
x
2
,
h
¯
1
−
2
,
where
(
x
2
−
x
1
)
≪
L
.
Provide three different expressions that can be used to evaluate
h
¯
1
−
2
in terms of (a) the local coefficient at
x
=
(
x
1
+
x
2
)
/
2
,
(b) the local coefficients at
x
1
and
x
2
,
and (c) the average coefficients at
x
1
and
x
2
.
Indicate which of the expressions is approximate. Considering whether the flow is laminar, turbulent, or mixed, indicate when it is appropriate or inappropriate to use each of the equations.
The correlation below is used to calculate the heat transfer coefficients for forced convection
owing to laminar flow outside flat plates.
k0.67 (vp)0.5 co.33
h = 0.644
D0.5µ0.17
Where h is in W/m²-K
v is in m/s
p is in kg/m³
Cp is in J/kg-K
D is in m
µ is in Pa-s
What units must the constant 0.644 have?
What should be the value of the constant when all units are
converted to English units (masses in lbm, lengths in ft, temperatures in oR,
times in h, energies in Btu)?
A thermocouple junction of spherical form is to be used to measure the temperature of a gas stream. h = 400w/m^2 deg C; k(thermocouple junction) = 20 w/m deg C; cp = 400 J/kg deg C; and density = 8500 kg/m^3;Calculate the following:i. Junction diameter needed for the thermocouple to have the thermal time constant of one second.ii. Time required for the thermocouple junction to reach 198 deg C if junction is initially at 25 deg C and is placed in gas stream which is at 200 deg C.
O A vertical cylinder 6 ft tall and 1 ft in diameter might be used to approximate a man
for heat-transfer purposes. Suppose the surface temperature of the cylinder is 78°F,
h=2 Btu/h - ft2 .°F, the surface emissivity is 0.9, and the cylinder is placed in a large
room where the air temperature is 68°F and the wall temperature is 45°F. Calculate
the heat lost from the cylinder. Repeat for a wall temperature of 80°F. What do you
conclude from these calculations?
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