What is fourier number?

The Fourier number (Fo) is a dimensionless number that is used in heat transfer analysis to characterize the importance of transient heat conduction as compared to convection. It is named after the French mathematician and physicist Jean Baptiste Joseph Fourier.

The Fourier number is defined as the ratio of the rate of heat conduction in a body to the rate of heat transfer by convection across the surface of the body. Mathematically, it is expressed as:

Fo = αt / L^2

Where:

• Fo is the Fourier number
• α is the thermal diffusivity of the material
• t is the characteristic time for heat transfer
• L is a characteristic length of the body

The Fourier number is often used in problems involving unsteady-state heat transfer, such as the cooling of a hot object in a cold fluid. It helps to determine the relative importance of conduction and convection in the overall heat transfer process.

A Fourier number less than 0.2 indicates that the heat transfer is dominated by conduction, while a Fourier number greater than 2 suggests that convection is the dominant mode of heat transfer. Values of the Fourier number between 0.2 and 2 indicate a transitional regime where both conduction and convection play significant roles in heat transfer.

Overall, the Fourier number is a useful parameter in heat transfer analysis for understanding the relative contributions of conduction and convection to the overall heat transfer process.