A grain dryer consists of a long semicircular duct of radius R = 1 m . One-half of the base surface consists of an electrically heated plate of emissivity ε p = 0.8 , while the other half supports the grain to be dried, which has an emissivity of ε g = 0.9 . In a batch drying process for which the temperature of the grain is T g = 330 K , 2.50 kg of Water are to be removed per meter of duct length over a 1-h period. (a) Neglecting convection heat transfer, determine the required temperature T p of the heater plate. (b) If the water vapor is swept from the duct by the flow of dry air, what convection mass transfer coefficient h m must be maintained by the flow? (c) If the air is at 300 K, is the assumption of negligible convection justified?
A grain dryer consists of a long semicircular duct of radius R = 1 m . One-half of the base surface consists of an electrically heated plate of emissivity ε p = 0.8 , while the other half supports the grain to be dried, which has an emissivity of ε g = 0.9 . In a batch drying process for which the temperature of the grain is T g = 330 K , 2.50 kg of Water are to be removed per meter of duct length over a 1-h period. (a) Neglecting convection heat transfer, determine the required temperature T p of the heater plate. (b) If the water vapor is swept from the duct by the flow of dry air, what convection mass transfer coefficient h m must be maintained by the flow? (c) If the air is at 300 K, is the assumption of negligible convection justified?
Solution Summary: The author explains the temperature of the heater required for specified drying rate.
A grain dryer consists of a long semicircular duct of radius
R
=
1
m
. One-half of the base surface consists of an electrically heated plate of emissivity
ε
p
=
0.8
, while the other half supports the grain to be dried, which has an emissivity of
ε
g
=
0.9
. In a batch drying process for which the temperature of the grain is
T
g
=
330
K
, 2.50 kg of Water are to be removed per meter of duct length over a 1-h period.
(a) Neglecting convection heat transfer, determine the required temperature Tpof the heater plate. (b) If the water vapor is swept from the duct by the flow of dry air, what convection mass transfer coefficient hmmust be maintained by the flow? (c) If the air is at 300 K, is the assumption of negligible convection justified?
Net movement of mass from one location, usually meaning stream, phase, fraction, or component, to another. Mass transfer occurs in many processes, such as absorption, evaporation, drying, precipitation, membrane filtration, and distillation.
You are working as an engineer in a bearing systems design company. The flow of
lubricant inside a hydrodynamic bearing (p = 0.001 kg m-1 s-1) can be approximated
as a parallel, steady, two-dimensional, incompressible flow between two parallel plates.
The top plate, representing the moving part of the bearing, travels at a constant speed,
U, while the bottom plate remains stationary (Figure Q1). The plates are separated by
a distance of 2h = 1 cm and are W = 20 cm wide. Their length is L = 10 cm. By
applying the above approximations to the Navier-Stokes equations and assuming that
end effects can be neglected, the horizontal velocity profile can be shown to be
y = +h
I
2h = 1 cm
x1
y = -h
u(y)
1 dP
2μ dx
-y² + Ay + B
moving plate
stationary plate
U
2
I2
L = 10 cm
Figure Q1: Flow in a hydrodynamic bearing. The plates extend a width, W = 20 cm,
into the page.
Question 1
You are working as an engineer in a bearing systems design company. The flow of
lubricant inside a hydrodynamic bearing (µ = 0.001 kg m¯¹ s¯¹) can be approximated
as a parallel, steady, two-dimensional, incompressible flow between two parallel plates.
The top plate, representing the moving part of the bearing, travels at a constant speed,
U, while the bottom plate remains stationary (Figure Q1). The plates are separated by
a distance of 2h = 1 cm and are W = 20 cm wide. Their length is L = 10 cm. By
applying the above approximations to the Navier-Stokes equations and assuming that
end effects can be neglected, the horizontal velocity profile can be shown to be
1 dP
u(y)
=
2μ dx
-y² + Ay + B
y= +h
Ꮖ
2h=1 cm
1
x1
y = −h
moving plate
stationary plate
2
X2
L = 10 cm
Figure Q1: Flow in a hydrodynamic bearing. The plates extend a width, W = 20 cm,
into the page.
(a) By considering the appropriate boundary conditions, show that the constants take
the following forms:
U
U
1 dP
A =…
Question 2
You are an engineer working in the propulsion team for a supersonic civil transport
aircraft driven by a turbojet engine, where you have oversight of the design for the
engine intake and the exhaust nozzle, indicated in Figure Q2a. The turbojet engine can
operate when provided with air flow in the Mach number range, 0.60 to 0.80. You are
asked to analyse a condition where the aircraft is flying at 472 m/s at an altitude of
14,000 m. For all parts of the question, you can assume that the flow path of air through
the engine has a circular cross section.
(a)
← intake
normal
shock
472 m/s
A B
(b)
50 m/s
H
472 m/s
B
engine
altitude: 14,000 m
exhaust nozzle
E
F
exit to
atmosphere
diameter: DE = 0.30 m
E
F
diameter: DF = 0.66 m
Figure Q2: Propulsion system for a supersonic aircraft.
a) When the aircraft is at an altitude of 14,000 m, use the International Standard
Atmosphere in the Module Data Book to state the local air pressure and tempera-
ture. Thus show that the aircraft speed…
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