In a tempering process, glass plate, which is initially at a uniform temperature Ti, is cooled by suddenly reducing the temperat
ure of both surfaces to Ts. The plate is 10 mm thick, and the glass has a thermal diffusivity of 6 × 10−7 m2/s. (a) How long will it take for the midplane temperature to achieve 75% of its maximum possible temperature reduction? (b) If (Ti − Ts) = 300°C, what is the maximum temperature gradient in the glass at the time calculated in part (a)? (c) Plot the temperature distribution within the glass plate at t = 10s
1 answer:
Answer:
See attached document for complete answers and also follow the step by step explanation to get given parameters
Explanation:
Given that:
In a tempering process, glass plate, which is initially at a uniform temperature Ti, is cooled by suddenly reducing the temperature of both surfaces to Ts. The plate is 10 mm thick, and the glass has a thermal diffusivity of 6 × 10−7 m2/s. (a) How long will it take for the midplane temperature to achieve 75% of its maximum possible temperature reduction? (b) If (Ti − Ts) = 300°C, what is the maximum temperature gradient in the glass at the time calculated in part (a)? (c) Plot the temperature distribution within the glass plate at t = 10s
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Answer:
(b)False
Explanation:
Given:
Prandtl number(Pr) =1000.
We know that
Where is the molecular diffusivity of momentum
is the molecular diffusivity of heat.
Prandtl number(Pr) can also be defined as
Where is the hydrodynamic boundary layer thickness and
is the thermal boundary layer thickness.
So if Pr>1 then hydrodynamic boundary layer thickness will be greater than thermal boundary layer thickness.
In given question Pr>1 so hydrodynamic boundary layer thickness will be greater than thermal boundary layer thickness.
So hydrodynamic layer will be thicker than the thermal boundary layer.
Answer:
a) , b)
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, c)
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Explanation:
a) The total number of users that can be accomodated in the system is:
b) The length of the side of each cell is:
Minimum time for traversing a cell is:
The maximum time for traversing a cell is:
The approximate time is giving by the average of minimum and maximum times:
c) The total number of users that can be accomodated in the system is:
The length of each side of the cell is:
Minimum time for traversing a cell is:
The maximum time for traversing a cell is:
The approximate time is giving by the average of minimum and maximum times: