Conduction is the heat transfer from one part of a substance to another part of the same substance, or from one substance to another in physical contact with it, without appreciable displacement of the molecules forming the substance. On the elementary particle level, the conduction is visualized as the exchange of kinetic energy between the particles In high and low temperature regions. Therefore, the conduction is attributed to the elastic collisions of molecules in gases and liquids, to the motion of free electrons in metals and to the longitudinal oscillation of atoms in solid insulators of electricity. A distinguishing characteristic of conduction is that it takes place within the boundary of a medium, or across the boundary of a medium into another medium in contact with the first, without an appreciable displacement of the matter.
The law of heat transfer in conduction mode at a macroscopic level is based on experiments of Biot and formulated by J.B. Fourier in 1882. This law can be illustrated by considering a wall of thickness L, surface area A and whose faces are kept at temperatures t1 and t2, as shown in Figure 7.1. t1 is greater than t2. Under these conditions, heat flows from the face of high temperature to the face of low temperature. According to Fourier’s law of heat conduction, the rate of heat transfer in the x-direction through the wall element, dx, located at x is proportional to
Figure 7.1 Heat Transfer Through Wall of Thickness L
- the gradient of temperature in that direction, dt/dx, and
- to the surface area normal to the direction of heat transfer, A
Therefore, the heat transfer rate is given by,
where k is the constant of proportionality and it is called the ‘thermal conductivity’; it is a property of the material. The negative sign appearing in equation is due to the convention that the heat is taken to be positive in the direction of increasing x and also ensures that heat flows in the direction of decreasing temperature, thus satisfies the second law of thermodynamics. If Q is in W; A is in m2; and dt/dx is in °C/m, then the unit of k is W/m2 °C/m. This may be written as W/m °C.
Example 7.1: The inner surface of a plane brick wall is at 60°C and the outer surface is at 20°C. Calculate the rate of heat transfer per m2 of surface area of the wall, which is 260 mm thick. The thermal conductivity of the brick is 0.55 W/m K.
Solution:
Given: t1 = 60°C; t2 =20°C; x = 260 mm; k = 0.55 W/m K
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