An electronic device dissipating 18 W has a mass of 20 g, a specific heat of 850 J / kg ·K, a

step 1 Ok, so firstly we need to find the energy generated by the device. During the 5 minute operating

An electronic device dissipating 18 W has a mass of 20 g,...

An electronic device dissipating $18 \mathrm{~W}$ has a mass of $20 \mathrm{~g}$, a specific heat of $850 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}$, and a surface area of $4 \mathrm{~cm}^{2}$. The device is lightly used, and it is on for $5 \mathrm{~min}$ 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 $12 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$, determine the temperature of the device at the end of the 5-min operating period. What would your answer be if the device were attached to an aluminum heat sink having a mass of $200 \mathrm{~g}$ and a surface area of $80 \mathrm{~cm}^{2}$ ? Assume the device and the heat sink to be nearly isothermal.

Key Concepts

Surface Area in Heat Exchange

Surface area plays a critical role in heat transfer, particularly in convection, because it determines the amount of interface available for exchanging heat with the environment. A larger surface area generally enhances the rate of heat loss from a system, reducing the temperature rise during operation. This factor is essential when designing systems for efficient thermal management.

Heat Sink Integration

A heat sink is a device designed to absorb and dissipate heat more effectively, typically by providing additional thermal mass and increased surface area. When a heat sink is attached to a component, it helps to lower the overall temperature rise by spreading the generated heat over a larger area and increasing the rate of convective heat transfer. This strategy is commonly used in electronics to maintain safe operating temperatures under varying loads.

Thermal Transients

Thermal transients describe the time-dependent evolution of temperature in a system due to changes in energy input or removal. Instead of instantly reaching a steady state, most systems experience a transient period where temperatures gradually adjust to changes in energy balance. Understanding this concept is important for predicting how long it takes for a device to heat up or cool down and for determining the maximum operating temperature during transient operating conditions.

Convection Heat Transfer

Convection refers to the process of heat transfer between a surface and a fluid (such as air) surrounding it. The rate of convective heat loss is described by Newton’s law of cooling, which incorporates the convective heat transfer coefficient, the surface area available for heat exchange, and the temperature difference between the surface and the ambient environment. This principle is key to estimating how quickly a device or system cools down.

Energy Balance in Thermal Systems

This concept involves accounting for all energy inputs and outputs within a system. In thermal problems, it typically requires equating the energy supplied (such as through electrical power) to the energy absorbed by the material (as an increase in internal energy, which depends on mass and specific heat) as well as the energy lost (for example, through convective cooling). It is central to determining temperature changes over time in any system where heat is generated and dissipated.

Specific Heat Capacity

Specific heat capacity quantifies the amount of energy needed to raise the temperature of a unit mass of a material by one degree. It is an intrinsic property that links the energy absorbed to the resulting temperature increase, and is used extensively in calculating the temperature rise in materials when a known amount of heat is applied over time.

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