A processor chip dissipates $52$ W and is cooled by a fan at a

convection coefficient of $45$ W$/$m $2$ K$.$ The chip is attached to a

fin array with a total surface area of $30,000$ mm $2.$ The total

mass of the chip plus fins is $58$ g and the average specific heat

of the assembly is $808$ J$/$kgK$.$ The chip is switched on at $20$C

and air from the fan is at $20$C throughout. Conductivity of the

fins, the chip and the interface between them is high enough

that they can be treated as a single lumped capacitance.

Lumped capacitance

If the chip is running at $58$C$,$ and is then switched off, and the fan

keeps running, how long does it take to cool to $28$C$?$

What is the temperature $2$ minutes after the chip is switched off?