Transferencia De Calor

4-25 An electronic device is on for 5 minutes, and off for several hours. The temperature of the device at the end of the 5-min operating period is to be determined for the cases of operation with and without a heat sink.

Assumptions 1 The device and the heat sink are isothermal. 2 The thermal properties of the device and of the sink are constant. 3 The heat transfer coefficient is constant and uniform over the entire surface.

Properties The specific heat of the device is given to be Cp = 850 J/kg.C. The specific heat of the aluminum sink is 903 J/kg.C (Table A-19), but can be taken to be 850 J/kg.C for simplicity in analysis.

Analysis (a) Approximate solution

This problem can be solved approximately by using an average temperature for the device when evaluating the heat loss. An energy balance on the device can be expressed as

or,

Substituting the given values,

which gives T = 527.8C

If the device were attached to an aluminum heat sink, the temperature of the device would be

which gives T = 69.5C

Note that the temperature of the electronic device drops considerably as a result of attaching it to a heat sink.

(b) Exact solution

This problem can be solved exactly by obtaining the differential equation from an energy balance on the device for a differential time interval dt. We will get

It can be solved to give

Substituting the known quantities and solving for t gives 527.3C for the first case and 69.4C for the second case, which are practically identical to the results obtained from the approximate analysis.

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