An opaque, horizontal plate has a thickness of L = 21 m m and thermal conductivity k = 25 W / m ⋅ K . Water flows adjacent to the bottom of the plate and is at a temperature of T ∞ , w = 25 ∘ C . Air flows above the plateat T ∞ , α = 260 ∘ C withha h a = 40 W / m 2 . The top of the plate is diffuse and is irradiated with G = 1450 W / m 2 ,of which 435 W / m 2 is reflected. The steady-state top and bottom plate temperatures are T t = 43 ∘ C and T b = 35 ∘ C , respectively. Determine the transmissivity, reflectivity, absorptivity, and emissivity of the plate. Is the plate gray? What is the radiosity associated with the top of the plate? What is the convection heat transfer coefficient associated with the water flow?
An opaque, horizontal plate has a thickness of L = 21 m m and thermal conductivity k = 25 W / m ⋅ K . Water flows adjacent to the bottom of the plate and is at a temperature of T ∞ , w = 25 ∘ C . Air flows above the plateat T ∞ , α = 260 ∘ C withha h a = 40 W / m 2 . The top of the plate is diffuse and is irradiated with G = 1450 W / m 2 ,of which 435 W / m 2 is reflected. The steady-state top and bottom plate temperatures are T t = 43 ∘ C and T b = 35 ∘ C , respectively. Determine the transmissivity, reflectivity, absorptivity, and emissivity of the plate. Is the plate gray? What is the radiosity associated with the top of the plate? What is the convection heat transfer coefficient associated with the water flow?
An opaque, horizontal plate has a thickness of
L
=
21
m
m
and thermal conductivity
k
=
25
W
/
m
⋅
K
. Water flows adjacent to the bottom of the plate and is at a temperature of
T
∞
,
w
=
25
∘
C
. Air flows above the plateat
T
∞
,
α
=
260
∘
C
withha
h
a
=
40
W
/
m
2
. The top of the plate is diffuse and is irradiated with
G
=
1450
W
/
m
2
,of which
435
W
/
m
2
is reflected. The steady-state top and bottom plate temperatures are
T
t
=
43
∘
C
and T
b
=
35
∘
C
, respectively. Determine the transmissivity, reflectivity, absorptivity, and emissivity of the plate. Is the plate gray? What is the radiosity associated with the top of the plate? What is the convection heat transfer coefficient associated with the water flow?
A wood stove is used to heat a single room. The stove is cylindrical in shape, with a
diameter of D = 0.400 m and a length of L = 0.500 m, and operates at a temperature
of T, = 200 °C.
(a) If the temperature of the room is T, = 20°C, determine the amount of radiant
energy delivered to the room by the stove each second if the emissivity of the
stove is e = 0.920.
(b) By definition, the R-value of a conducting slab is given by
Atot(Th – To)
Poond
R =
where Atot is the total surface area, Pcond is the power loss by conduction through
the slab, Th and Te are the temperatures on the hotter and cooler sides of the
slab. If the room has a square shape with walls of height H = 2.40 m and width
W = 7.60 m, determine the R-value of the walls and ceiling required to maintain
the room temperature at T = 20°C if the outside temperature is T, = 0°C.
Note that we are ignoring any heat conveyed by the stove via convection and any
energy lost through the walls and windows via convection or radiation.
Two very large parallel metal plates are separated by a small
vacuum gap. Plate 1 is in contact with liquid nitrogen at T₁ = 77 K; plate 2 is at room
temperature, so T₂ = 300 K (see the figure). In order to reduce the heat loss by
radiation, a third plate is inserted in the middle. The absorptivity of the middle plate is
a=0.10 (i.e., it absorbs 10% of radiation). Both plates 1 and 2 are considered to be
blackbody, and the absorptivity equals 1.0. (The Stefan-Boltzmann
constant is o-5.67×10 W/(m²K))
T₁ Tm T₂
(a) Find the equilibrium temperature of middle plate Tm.
(b) Find energy flux between T₁ and T2 plates if the middle plate is
not inserted.
(c) Find energy flux between T₁ and T2 plates at the presence of
the middle plate.
A small sphere (emissivity = 0.745, radius = r1) is located at the center of a spherical asbestos shell (thickness = 1.72 cm, outer radius = r2; thermal conductivity of asbestos is 0.090 J/(s m Co)). The thickness of the shell is small compared to the inner and outer radii of the shell. The temperature of the small sphere is 727 °C, while the temperature of the inner surface of the shell is 406 °C, both temperatures remaining constant. Assuming that r2/r1 = 6.54 and ignoring any air inside the shell, find the temperature in degrees Celsius of the outer surface of the shell.
Fox and McDonald's Introduction to Fluid Mechanics
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