Fourier's law of Heat Conduction

Fourier’s law of heat conduction or otherwise referred as the law of heat conduction denotes that the time rate of heat transfer through material is appropriate to the negative gradient in the temperature and to the region at correct angles to that gradient through which the heat if flowing. This law can be stated in couple of ways such as the integral form looking at the amount of energy flowing into or out of a body as a whole and the varied form in which looking at the flow rates or fluxes of energy locally.

Comparison with Newton and Ohm’s law

Newton’s law of cooling is a distinct analog of Fourier’s law of heat conduction when Ohm’s law is the electrical analogue of Fourier’s law. For instance

q = Q/A = -kdT/dx

The symbol q is the heat flux which is the heat per unit region and it is a vector. Q is the heat rate. The dT/dx is thermal gradient in the direction of the flow. The minus sign is to show that the flow of heat is from hotter to colder. If the temperature reduces with x, q will be positive and will flow in the direction of x. if the temperature raises with x, q will be negative and will flow opposite to the direction of x. according to the international system of units q is watts per meter squared.

Descriptions

The constant k is thermal conductivity and is employed to exhibit that not all materials heat up or retain heat equally well. In SI units, k is W/m*k, where W is watts. M is meters and K is Kelvin. It may also be J/m*s*k where J is joules and s is seconds. In the English system it is Btu/h*ft*°F or British thermal units horsepower*foot*Fahrenheit.

The thermal conductivity is bigger for conductors than insulators. Silver is an excellent conductor at 428W/m*k and so is copper with its value of 401 W/m*k. air and wool are insulators and are poor conductors. They are 0.026 and 0.043 W/m*k respectively. The heat transfer or conduction rate is a scalar and is

Q = -kA ΔT/L

Where L is the length of the slab, ΔT is the temperature variance between two different surfaces. Equations first and second state that heat can be considered to be a flow. The flow of heat relies upon the thickness of the material, the area, the conductivity and all of which combine to retard or resist this flow.

Questions:

• What is Fourier’s law of heat conduction?
• State the significance of Fourier’s law.