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 ’ ‘ ‘
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).
FIGURE 4.23 One-dimensional heat flow.
Integration of Eq. (4.154) with constant heat conductivity gives
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.
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