# Conduction

Conduction takes place at a solid, liquid, or vapor boundary through the col­lisions of molecules, without mass transfer taking place. The process of heat con­duction is analogous to that of electrical conduction, and similar concepts and calculation methods apply. The thermal conductivity of matter is a physical prop­erty and is its ability to conduct heat. Thermal conduction is a function of both the temperature and the properties of the material. The system is often considered as being homogeneous, and the thermal conductivity is considered constant. Thermal conductivity, A, W m-1 °C_1 , is defined using Fourier’s law,

A = — A— = — (4 1 S4i

4* Adx A ’ ‘ ‘

Where

Q = <P/A = 4>" is the heat flow (W m“-) is the heat flow in the x direction dT/dx is the temperature gradient

The minus sign in the equation denotes that the heat flow is positive in the di­rection of decreasing temperature.

Figure 4.23 represents a simple one-dimensional system with constant heat flow \$ through the plate. The plate thickness is Ax (m) and the area of the plate is A (m2).

 Ax ‘<— ^  FIGURE 4.23 One-dimensional heat flow. Integration of Eq. (4.154) with constant heat conductivity gives DT (4.155)

One-dimensional heat conduction means that the heat flow is in one di­rection only, and one coordinate is required to represent the case. For exam­ple, in the case of a cylinder it is parallel with the radius.