Fourier’s Law of Conduction
An empirical relationship between the conduction rate in a material and the temperature gradient in the direction of energy flow, first formulated by Fourier in 1822. Fourier’s law is phenomenological. it is developed from observed phenomena rather than being derived from principles. Hence, we can view the rate equation as a generalization based on experimental evidence. According to Fourier’s Law, “Heat flux in a particular direction is directly proportional to the temperature gradient in same direction.’’ or we can also be stated as, “the rate of flow of heat transfer is directly proportional to the area of the section to the direction of heat flow and to change of temperature with respect to the length of the path of the heat flow.’’ Following equation represents the Fourier’s law :
Let’s see, All the parameters which is given in the above equation shortly
Thermal conductivity (k) : The rate at which heat passes through a specified material, expressed as the amount of heat that flows per unit time through a unit area with a temperature gradient of one degree per unit distance.
Heat flux(q) : Heat flux is the rate of heat transferred per unit area (normal to the direction of transfer) per unit time. If the transport taking place in ‘x’ then area will be ‘yz’. The SI unit of heat flux is (KJ/m2s)
Rate of heat transfer (Q) : The amount of heat that is transferred per unit time.(KJ/s)
Gradient(dT/dz) : In Fourier’s law, gradient means the differentiation of temperature with respect to direction(thickness, distance). gradient is negative quantity. generally gradient is call is at slope.
Assumptions of the Fourier’s Law
It is steady state heat transfer law that means no accumulation term or no time derivative is needed. In addition, heat transfer must be unidirectional. It also assumes that the direction of heat flow will always be normal to a surface of constant temperature which is also called as isothermal surface.
Generally, thermal conductivity varies with direction as the solid body is non uniform and non homogeneous. But here in the Fourier’s law we have assumed thermal conductivity of the material to be same in all the direction. Such materials are known as homogeneous, uniform and isotropic in nature. Here, the temperature gradient is constant and the temperature profile is linear.
Heat flux is a vector quantity. Following Equation 1 represents the heat flux where:
Q : rate of heat transfer
A : Area
k : Thermal Conductivity
The same equation can be written as follows :
We can write a more general statement of Fourier’s law is as follows where:
Q’n is heat flux in a direction ’n’ which is normal to an isotherm.
Each of these expressions relates to the heat flux across a surface to the temperature gradient in a direction perpendicular to the surface. The medium in which conduction occurs is isotropic. For such a medium, the value of thermal conductivity is independent of the coordinate direction. It is a vector expression indicating that the heat flux is normal to an isotherm and in the direction of decreasing temperature. Fourier’s law is applicable for all matters regardless of it’s state(solid, liquid , gas).
So here we come to an end of overall discussion on Fourier’s Law. Hope you liked the content :)
