A large 2.54-cm.-thick copper plate is placed between two air streams. The heat transfer coefficient on the one side is 28 W/(m2 K) and on the other side is 57 W/(m2 K). If the temperature of both streams is suddenly changed from 38°C to 93°C, determine how long it will take for the copper plate to reach a temperature of 82°C.
GIVEN
• A large copper plate between two air streams whose temperatures suddenly change
• Plate thickness (2L) = 2.54 cm = 0.0254 m
• The heat transfer coefficients are
? lch = 28 W/(m2 K)
? 2ch = 57 W/(m2 K)
• Air temperature changes from 38°C to 93°C
FIND
• How long it will take for the copper plate to reach a temperature of 82°C
ASSUMPTIONS
• The initial temperature of the plate is 38°C
• The plate can be treated as an infinite slab
SKETCH
The Biot number for this case, using the larger of the heat transfer coefficients is
Therefore, the internal resistance of the slab can be neglected (the temperature of the slab remains uniform)
and the temperature-time history can be calculated from an energy balance
Change in internal energy = heat flow from both sides
Integrating between a temperature of To at time = 0 to a temperature of T at time = t yields
Solving this for the time
You might also like to view...
When a load of wood is thrown overboard from a boat in a swimming pool, the pool level
A) rises. B) falls. C) remains unchanged.
An ac generator with peak voltage 100 volts is placed across a 10-? resistor. What is the average power dissipated?
a. 100 W b. 150 W c. 500 W d. 1000 W e. 2000 W
An ac generator consists of 100 loops of wire, each of area 0.090 m2, and has a total resistance 12 ?. The loops rotate about a diameter in a magnetic field of 0.50 T at a constant angular speed of 60 revolutions per second
Find the maximum induced emf in the generator. A) 1.7 kV B) 0.27 kV C) 0.54 kV D) 3.4 kV
Two bodies, A and B, collide as shown in Figures I and II below
Which statement is true?
a.
They exert equal and opposite forces on each other in I but not in II.
b.
They exert equal and opposite force on each other in II but not in I.
c.
They exert equal and opposite force on each other in both I and II.
d.
The forces are equal and opposite to each other in I, but only the components of the forces parallel to the velocities are equal in II.
e.
The forces are equal and opposite in I, but only the components of the forces perpendicular to the velocities are equal in II