# Fourier Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Fourier number, abbreviated as Fo, is a dimensionless number that is the ratio of heat conduction rate to the rate of thermal energy storage in a solid.  This is mainly used in unsteady state heat transfer. The Fourier Number Formula & Calculation is below.

 $$\large{ Fo = \frac{\alpha \; t}{l^2 } }$$          Where: $$\large{ Fo }$$ = Fourier number $$\large{ l_c }$$ = characteristic length $$\large{ \alpha }$$  (Greel symbol alpha) = thermal diffusivity $$\large{ t }$$ = time Solve for: $$\large{ \alpha = \frac{ Fo \; l^2 }{ t } }$$ $$\large{ t = \frac{ Fo \; l_{c}{^2} }{ \alpha } }$$ $$\large{ l_c = \sqrt { \frac{ \alpha \; t }{ Fo } } }$$