An air heater may be fabricated by coiling Nichrome wire and passing air in cross flow over the wire. Consider a heater fabricated from wire of diameter D = 1 mm, electrical resistivity ρ e = 10 − 6 Ω ⋅ m, thermal conductivity k = 25 W/m ⋅ K, and emissivity ε = 0.20. The heater is designed to deliver air at a temperature of T ∞ = 50 ° C under flow conditions that provide a convection coefficient of h = 250 W/m 2 ⋅ K for the wire. The temperature of the housing that encloses the wire and through which the air flows is T sur = 50 ° C . If the maximum allowable temperature of the wire is T max = 1200 ° C, what is the maximum allowable electric current 1? If the maximum available voltage is Δ E = 110 V, what is the corresponding length L of wire that may be used in the heater and the power rating of the heater? Hint: In your solution, assume negligible temperature variations within the wire, but after obtaining the desired results, assess the validity of this assumption.
An air heater may be fabricated by coiling Nichrome wire and passing air in cross flow over the wire. Consider a heater fabricated from wire of diameter D = 1 mm, electrical resistivity ρ e = 10 − 6 Ω ⋅ m, thermal conductivity k = 25 W/m ⋅ K, and emissivity ε = 0.20. The heater is designed to deliver air at a temperature of T ∞ = 50 ° C under flow conditions that provide a convection coefficient of h = 250 W/m 2 ⋅ K for the wire. The temperature of the housing that encloses the wire and through which the air flows is T sur = 50 ° C . If the maximum allowable temperature of the wire is T max = 1200 ° C, what is the maximum allowable electric current 1? If the maximum available voltage is Δ E = 110 V, what is the corresponding length L of wire that may be used in the heater and the power rating of the heater? Hint: In your solution, assume negligible temperature variations within the wire, but after obtaining the desired results, assess the validity of this assumption.
An air heater may be fabricated by coiling Nichrome wire and passing air in cross flow over the wire. Consider a heater fabricated from wire of diameter
D
=
1
mm,
electrical resistivity
ρ
e
=
10
−
6
Ω
⋅
m,
thermal conductivity
k
=
25
W/m
⋅
K,
and emissivity
ε
=
0.20.
The heater is designed to deliver air at a temperature of
T
∞
=
50
°
C
under flow conditions that provide a convection coefficient of
h
=
250
W/m
2
⋅
K
for the wire. The temperature of the housing that encloses the wire and through which the air flows is
T
sur
=
50
°
C
.
If the maximum allowable temperature of the wire is
T
max
=
1200
°
C,
what is the maximum allowable electric current 1? If the maximum available voltage is
Δ
E
=
110
V,
what is the corresponding length L of wire that may be used in the heater and the power rating of the heater? Hint: In your solution, assume negligible temperature variations within the wire, but after obtaining the desired results, assess the validity of this assumption.
An array of 190 electrical components, each dissipating P = 35 W, are attached to the bottom surface of a square copper
plate. The length of the edge of the square plate is L= 0.1 m. All of the energy dissipated in the electrical components is
transferred to water flowing over the top surface of the copper plate. The water flow over the plate in a direction that is
parallel to the edge of the plate. A proturbence at the leading edge of the plate acts to trip the bounary layer into turbulent
flow. The plate may be assumed to be isothermal since the thermal conductivity of copper is so high. The water velocity
and temperature far from the plate are u» = 2.3 m/s and To = 22 °C. The water's thermophysical properties (for application
in correlations for the Nusselt number) may be approximated as v = 0.96×10-6 m2/s, kf = 0.62 W/m-K, and Pr = 5.2. What is
the temperature of the copper plate in °C?
1. A lead pipe has 2 cm inside diameter, 3 cm outer diameter, length of 130 cm. Liquid water at
4°C flows through the pipe with a bulk velocity of 2.50 km/hr. Air is blown around the
outside of the pipe at 20 deg C. The inside wall of the said pipe has a temperature of 8 deg
Celsius.
Density of liquid water= 999.6509 kg/m³
Cp=4.218 kJ/kgK
Viscosity of liquid water= 1.6193x10-3 Pa.s
k (thermal conductivity of water) = 0.5742 W/mK
Find:
Overall heat coefficient (U) based on outside surface area
b. Prandtl (Pr) and Reynolds (Re) numbers based on classification of flow
а.
Conduction
1. A thermodynamic analysis of a proposed Brayton cycle gas turbine yields P=
5 MW of net power production. The compressor, at an average temperature
of T. = 400°C, is driven by the turbine at an average temperature of T₁ =
1000°C by way of an L = 1m-long, d= 70mm - diameter shaft of thermal
conductivity k = 40 W/m K.
Compressor
min
T
Combustion
chamber
Shaft
L
Turbine
Th
out
(a) Compare the steady-state conduction rate through the shaft connecting the hot
turbine to the warm compressor to the net power predicted by the thermodynamics-
based analysis.
(b) A research team proposes to scale down the gas turbine of part (a), keeping all
dimensions in the same proportions. The team assumes that the same hot and cold
temperatures exist as in part (a) and that the net power output of the gas turbine is
proportional to the overall volume of the device. Plot the ratio of the conduction through
the shaft to the net power output of the turbine over the range 0.005 m s Ls 1 m. Is a…
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