Thermal energy storage systems commonly involve a packed bed of solid spheres, through which a hot gas flows if the system is being charged, or a cold gas if it is being discharged. In a charging process, heat transfer from the hot gas increases thermal energy stored within the colder spheres; during discharge, the stored energy decreases as heat is transferred from the warmer spheres to the cooler gas. Consider a packed bed of 75-mm-diameter aluminum spheres ( ρ = 2700 kg/m 3 , c = 950 J/kg ⋅ K, k = 240 W/m ⋅ K ) and a charging process for which gas enters the storage unit at a temperature of T g , i = 300 ° C . . If the initial temperature of the spheres is T i = 25 ° C and the convection coefficient is h = 75 W/m 2 ⋅ K, how long does it take a sphere near the inlet of the system to accumulate 90 % of the maximum possible thermal energy? What is the corresponding temperature at the center of the sphere? Is there any advantage to using copper instead of aluminum?
Thermal energy storage systems commonly involve a packed bed of solid spheres, through which a hot gas flows if the system is being charged, or a cold gas if it is being discharged. In a charging process, heat transfer from the hot gas increases thermal energy stored within the colder spheres; during discharge, the stored energy decreases as heat is transferred from the warmer spheres to the cooler gas. Consider a packed bed of 75-mm-diameter aluminum spheres ( ρ = 2700 kg/m 3 , c = 950 J/kg ⋅ K, k = 240 W/m ⋅ K ) and a charging process for which gas enters the storage unit at a temperature of T g , i = 300 ° C . . If the initial temperature of the spheres is T i = 25 ° C and the convection coefficient is h = 75 W/m 2 ⋅ K, how long does it take a sphere near the inlet of the system to accumulate 90 % of the maximum possible thermal energy? What is the corresponding temperature at the center of the sphere? Is there any advantage to using copper instead of aluminum?
Solution Summary: The author explains the time required by the bed of aluminum spheres to accumulate 90% of the maximum possible thermal energy during charging with a hot gas and determine whether copper would provide an advantage over aluminum.
Thermal energy storage systems commonly involve a packed bed of solid spheres, through which a hot gas flows if the system is being charged, or a cold gas if it is being discharged. In a charging process, heat transfer from the hot gas increases thermal energy stored within the colder spheres; during discharge, the stored energy decreases as heat is transferred from the warmer spheres to the cooler gas.
Consider a packed bed of 75-mm-diameter aluminum spheres
(
ρ
=
2700
kg/m
3
,
c
=
950
J/kg
⋅
K,
k
=
240
W/m
⋅
K
)
and a charging process for which gas enters the storage unit at a temperature of
T
g
,
i
=
300
°
C
.
. If the initial temperature of the spheres is
T
i
=
25
°
C
and the convection coefficient is
h
=
75
W/m
2
⋅
K,
how long does it take a sphere near the inlet of the system to accumulate
90
%
of the maximum possible thermal energy? What is the corresponding temperature at the center of the sphere? Is there any advantage to using copper instead of aluminum?
A 1.2-in-outer-diameter pipe is to span across a river at a 115-ft-wide section while being completely immersed in water. The average flow velocity of the water is 8 ft/s, and its temperature is 70°F. Determine the drag force exerted on the pipe by the river.
Fins, or extended surfaces, commonly are used in a variety of engineering applications to enhance cooling. Common examples include a motorcycle engine head, a lawn mower engine head, extended surfaces used in electronic equipment, and finned tube heat exchangers in room heating and cooling applications. Consider aluminum fins of a rectangular profile, which are used to remove heat from a surface whose temperature is100° C . The temperature of the ambient air is 20° C. We are interested in determining how the temperature of the fin varies along its length and plotting this temperature variation. For long fins, the temperaturedistribution along the fin is given by
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