Question

An aluminum sheet 0.4 m tall, 1m long, 2mm thick is to be cooled from initial temperature of 150C to 50C by immersing it suddenly at 20C.

Determine the initial and final rate of heat transfer from the plate.

Estimate the time required

Answer 1

Using Heat Conduction equation,

  

where, is rate of heat transfer

k = Thermal conductivity of the material. Here the material is Aluminium. So k= 205 W/m K

A = Area of the material = 0.4m x 1m = 0.4

= Hot object (Here, the Aluminium sheet) , = cold object (liquid where it is to be immersed)

d = Thickness of the material = 2mm = 0.002 m

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So, the Initial rate of heat transfer is :

Since, initial temperature ()= 150 and    = 20

  

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Also, final rate of heat transfer is :

Since, final temperature ()= 50 and    = 20

  

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Calculating time required for the Aluminum sheet to cool from 150 to 50 .

From the definition of heat capacity,

Here, Q = heat absorbed by the material

C = Heat capacity of the material. Here, C for Aluminium = 24.3 J/mol K

= Change in temperature

Since heat is being released from going from 150 to  50 , heat released from the plate is

Since, no information about the amount of aluminum in the form of mass or number of moles is given, we calculate the time taken for heat transfer per mole.

Finally, calculating the heat transfer rate when cooling from 150 to 50 ,

Hence, time taken will be

So that much seconds per mole is the time taken for the aluminum plate to cool from 150 to 50