In conduction heat is transferred without actual movement of molecules. The molecules that are in contact with the heat sources, take heat from the source directly and transfer it to the surrounding molecules by increasing the amplitude of their vibrations during collision between the adjacent atoms. So, region of increasing temperature extends it along the length.
Assume a slab of thickness x and cross-sectional
area A. Let the temperature of its two faces be T1 and T2, so that T1 > T2. The quantity of heat (∆Q) transmitted from hot face (with temp. T1) through cold face in time ∆t is directly proportional to time (∆t), the area of cross-section (A) and the difference in temperature (T1 - T2); and inversely proportional to thickness (x).
\(\Rightarrow \Delta Q\propto\frac{A(T_1 - T_2)}{x}\Delta t\)
or \(\Delta Q = \frac{K\ A(T_1 - T_2)\Delta t}{x}\)
where K is constant of propotionality and is called coefficient of thermal conductivity.
Thermal current: The flow of rate of heat is known as thermal current.
\(H = \frac{\Delta Q}{\Delta t}\)
\(H = \frac{kA(T_1-T_2)\ \Delta t}{\Delta tx}\)
\(H = \frac{KA\Delta T}{x}\)
The term \(\frac{T_1 -T_2}{x} = \frac{\Delta T}{x}\) is called temperature gradient. Eqn (1) is called Fourier's law and it defines as the coefficient of thermal conductivity K as:
Hence the coefficient of thermal conductivity is equal to the amount of heat when the temperature gradient, area of cross section and time are take as unity.
The unit of K is \(\frac{ Watt}{meter
×
kelvin
}\)
Thermal resistance: Thermal resistance is defined as the temperature difference per unit thermal current:
