Review on Basic Concepts of Heat Transfer

Heat transfer is the transfer of thermal energy because of a temperature difference. It occurs by conduction, convection and radiation, and in most practical problems two or three modes act together.

Conduction

Energy moves from a hotter to a colder part of a body (or between bodies in contact) by molecular vibration, free-electron motion and collisions, without bulk movement of matter. It is the only mode in an opaque solid. The rate is given by Fourier's law:

$$Q = -kA\frac{dT}{dx}$$

where $k$ is thermal conductivity (W/m K), $A$ the area normal to heat flow and $dT/dx$ the temperature gradient. The minus sign shows that heat flows toward falling temperature. Example: heat flow through a furnace wall.

Convection

Energy is carried by the motion of a fluid over a surface. It is conduction plus bulk fluid motion. If the motion is caused by a fan or pump it is forced convection; if it is caused by density differences it is natural convection. Newton's law of cooling gives the rate:

$$Q = hA\,(T_s - T_\infty)$$

where $h$ is the convective heat transfer coefficient (W/m$^2$ K). Example: cooling of an engine radiator by air, or a hot cup of tea cooling in a room.

Radiation

Energy is emitted by every body above absolute zero as electromagnetic waves. It needs no medium and also works in vacuum. For a real surface:

$$Q = \varepsilon\sigma A\,(T_s^4 - T_{sur}^4)$$

with $\sigma = 5.67\times10^{-8}\ \text{W/m}^2\text{K}^4$, $\varepsilon$ the emissivity and temperatures in kelvin. Example: heat received from the sun, heat loss from a boiler furnace to its surroundings.

The rate of heat transfer depends on the temperature difference, the area available, the properties of the material or fluid, and the geometry of the flow path.

Factors affecting heat transfer

• Conduction: temperature difference, area normal to heat flow, thickness of the material and its thermal conductivity $k$. A larger $\Delta T$, larger $A$, larger $k$ and smaller thickness give a higher rate.
• Convection: temperature difference between surface and fluid, surface area, fluid velocity, fluid properties (density, viscosity, specific heat, conductivity), type of flow (laminar or turbulent), shape and roughness of the surface, and whether convection is natural or forced.
• Radiation: surface temperature (fourth-power effect), surface area, emissivity and absorptivity, the surface colour and finish, and the geometry and orientation of surfaces facing each other (shape factor).

Heat transfer can be increased by raising $\Delta T$, increasing area (fins) or the coefficient (higher velocity), and decreased by insulation, reflective shields or lower $k$.

Engineering applications

1. Boilers, condensers and other heat exchangers in power plants.
2. Cooling of IC engines (radiator, cooling fins on motorcycle cylinders).
3. Refrigeration and air conditioning (evaporator and condenser coils).
4. Cooling of electronic components with heat sinks, and thermal insulation of buildings, pipes and cold storages.