An electronic device dissipating 20 W has a mass of 20 g , a...

An electronic device dissipating 20 W has a mass of 20 g , a specific heat of $850 \mathrm{~J} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}$, and a surface area of $4 \mathrm{~cm}^2$. The device is lightly used, and it is on for 5 min and then off for several hours, during which it cools to the ambient temperature of $25^{\circ} \mathrm{C}$. Taking the heat transfer coefficient to be $12 \mathrm{~W} / \mathrm{m}^2$, ${ }^{\circ} \mathrm{C}$, determine the temperature of the device at the end of the $5-\mathrm{min}$ operating period. What would your answer be if the device were attached to an aluminum heat sink having a mass of 200 g and a surface area of $80 \mathrm{~cm}^2$ ? Assume the device and the heat sink to be nearly isothermal.

Key Concepts

Lumped Capacitance Analysis

This concept assumes that an object can be treated as having a uniform temperature throughout its volume because the internal resistance to heat conduction is much lower than the resistance to heat transfer at the surface. It simplifies transient heat conduction problems into ordinary differential equations, making it easier to predict how temperature changes over time.

Thermal Energy Balance

Thermal energy balance involves equating the energy input into a system with the energy stored within it and the energy lost to the environment. In transient heating problems, the increase in the system’s internal energy, which depends on its mass and specific heat, is balanced by the net energy supplied minus the energy dissipated, allowing one to calculate the temperature rise.

Convective Heat Transfer

Convective heat transfer is the mechanism by which heat is exchanged between a surface and a moving fluid, typically characterized by the heat transfer coefficient. This coefficient, together with the surface area and the temperature difference between the surface and the ambient environment, determines the rate at which heat is lost or gained, which is crucial in transient thermal analyses.

Heat Sink Integration

Attaching a heat sink introduces additional thermal mass and increases the effective surface area available for convective heat loss. This reduces the overall temperature rise of the system for the same power dissipation, as the additional material absorbs more heat and facilitates more efficient cooling, which is a key strategy in managing thermal loads in electronics.

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