Small spherical particles of diameter D = 50 μ m contain a fluorescent material that, when irradiated with white light, emits at a wavelength corresponding to the material’s temperature. Hence the color of the particle varies with its temperature. Because the small particles are neutrally buoyant in liquid water, a researcher wishes to use them to measure instantaneous local water temperatures in a turbulent how by observing their emitted color. If the particles arc characterized by a density, specific heat, and thermal conductivity of ρ = 999 k g / m 3 , k = 1.2 W / m ⋅ K , and c p = 1200 J / k g ⋅ K , respectively, determine the time constant of the particles. Hint: Since the particles travel with the flow, heat transfer between the particle and the fluid occurs by conduction. Assume lumped capacitance behavior.
Small spherical particles of diameter D = 50 μ m contain a fluorescent material that, when irradiated with white light, emits at a wavelength corresponding to the material’s temperature. Hence the color of the particle varies with its temperature. Because the small particles are neutrally buoyant in liquid water, a researcher wishes to use them to measure instantaneous local water temperatures in a turbulent how by observing their emitted color. If the particles arc characterized by a density, specific heat, and thermal conductivity of ρ = 999 k g / m 3 , k = 1.2 W / m ⋅ K , and c p = 1200 J / k g ⋅ K , respectively, determine the time constant of the particles. Hint: Since the particles travel with the flow, heat transfer between the particle and the fluid occurs by conduction. Assume lumped capacitance behavior.
Solution Summary: The author calculates the heat transfer rates at two surfaces for a wall section of an area A by using the equation Fourier’s law at X=-L.
Small spherical particles of diameter
D
=
50
μ
m
contain a fluorescent material that, when irradiated with white light, emits at a wavelength corresponding to the material’s temperature. Hence the color of the particle varies with its temperature. Because the small particles are neutrally buoyant in liquid water, a researcher wishes to use them to measure instantaneous local water temperatures in a turbulent how by observing their emitted color. If the particles arc characterized by a density, specific heat, and thermal conductivity of
ρ
=
999
k
g
/
m
3
,
k
=
1.2
W
/
m
⋅
K
,
and
c
p
=
1200
J
/
k
g
⋅
K
, respectively, determine the time constant of the particles. Hint: Since the particles travel with the flow, heat transfer between the particle and the fluid occurs by conduction. Assume lumped capacitance behavior.
Quiescent means that you will be using natural convection (so buoyancy type of convection) (not forced
convection)
show a detailed solution to the problem. the solution is correct (use to double check)
A horizontal cylindrical rod with a length of 2 m and a diameter of 0.2 m is used for the top of a swing set. On a
sunny summer day, the temperature of the rod is 40°C and the temperature of the quiescent air is 30°C. What
is the convective heat transfer rate from the rod? |
416 w
A long, horizontal, cylindrical steel reactor, 1 m in diameter, has a surface temperature of 300ºC. The emissivity of the steel is 0.6, and the heat transfer coefficient for natural convection is 5 W m−2 K−1 . Heat is lost by convection to the air at 15ºC, and also by radiation to the surroundings, which can be considered to be a black body at 15ºC.
a) Calculate the total heat loss per metre length of the reactor, and the proportions lost by convection and radiation
b) The reactor is then insulated with a thin layer of insulation material to reduce the total heat loss to one-tenth of its original value. This causes the surface temperature of the steel to rise to 400ºC. The thermal conductivity of the insulation is 0.01 W m−1 K−1 , and its surface emissivity is 0.2. Show that the resulting surface temperature of the insulation is about 89ºC, and calculate the thickness of insulation required, stating any assumptions made.
Specifically need help with part b
A long, horizontal, cylindrical steel reactor, 1 m in diameter, has a surface temperature of 300ºC. The emissivity of the steel is 0.6, and the heat transfer coefficient for natural convection is 5 W m−2 K−1 . Heat is lost by convection to the air at 15ºC, and also by radiation to the surroundings, which can be considered to be a black body at 15ºC. a) Calculate the total heat loss per metre length of the reactor, and the proportions lost by convection and radiation.
b) The reactor is then insulated with a thin layer of insulation material to reduce the total heat loss to one-tenth of its original value. This causes the surface temperature of the steel to rise to 400ºC. The thermal conductivity of the insulation is 0.01 W m−1 K−1 , and its surface emissivity is 0.2. Show that the resulting surface temperature of the insulation is about 89ºC, and calculate the thickness of insulation required, stating any assumptions made.
can you solve part b please?
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