Mechanisms of heat transfer

Heat as energy transfer

Heat is energy transferred because of a temperature difference. It flows spontaneously from higher temperature to lower temperature unless external work causes otherwise. There are three main mechanisms of heat transfer: conduction, convection, and radiation.

Real situations often involve all three. A hot cup of coffee cools by conduction through the cup, convection in the surrounding air, and radiation from its surface.

Conduction

Conduction is heat transfer through direct microscopic interactions within a material or between materials in contact. In solids, energy moves through molecular vibrations and, in metals, through mobile electrons.

For steady one-dimensional conduction through a slab, the heat transfer rate is

rac{Q}{t}=kArac{Delta T}{L}

Here $k$ is thermal conductivity, $A$ is cross-sectional area, $Delta T$ is temperature difference, and $L$ is thickness.

Materials with large $k$, such as metals, conduct heat well. Materials with small $k$, such as wood, foam, and air, are insulators.

Thermal resistance

The conduction equation resembles a flow law: larger temperature difference increases heat flow, while larger thickness reduces it. Insulation works by increasing resistance to heat transfer. Multiple layers can be combined conceptually like thermal resistances.

Good insulation often traps air because still air has low thermal conductivity.

Convection

Convection is heat transfer by the bulk motion of a fluid. When air or liquid moves, it carries internal energy with it. Natural convection occurs when temperature differences create density differences. Warm fluid expands, becomes less dense, and rises; cooler fluid sinks.

Forced convection occurs when a fan, pump, or wind moves the fluid. A fan cools your skin by replacing warm air near your body with cooler air.

A simplified convection model is Newton's law of cooling:

rac{Q}{t}=hA(T_s-T_f)

where $h$ is a convection coefficient, $T_s$ is surface temperature, and $T_f$ is fluid temperature far from the surface.

Radiation

Thermal radiation is energy transfer by electromagnetic waves. Unlike conduction and convection, radiation does not require matter. This is how the Sun transfers energy through space to Earth.

An ideal blackbody emits radiation according to the Stefan-Boltzmann law:

$P=sigma A T^4$

where $sigma$ is the Stefan-Boltzmann constant, $A$ is surface area, and $T$ is absolute temperature.

A real object emits approximately

$P=epsilonsigma A T^4$

where $epsilon$ is emissivity, between 0 and 1.

Net radiative exchange

An object also absorbs radiation from its surroundings. If an object at temperature $T$ is surrounded by an environment at temperature $T_{env}$, a useful model for net radiated power is

$P_{net}=epsilonsigma A(T^4-T_{env}^4)$

Temperature must be in kelvins.

Comparing mechanisms

Conduction dominates in solids with direct contact. Convection dominates in moving fluids. Radiation becomes especially important at high temperatures because of the $T^4$ dependence.

A vacuum thermos reduces conduction and convection by using a vacuum gap and reduces radiation with reflective surfaces.

The big idea

Heat transfer occurs by conduction, convection, and radiation. Conduction involves microscopic contact interactions, convection involves fluid motion, and radiation involves electromagnetic waves. Understanding these mechanisms allows us to analyze insulation, weather, engines, electronics cooling, climate, cooking, and thermal design.