Derivation and usage Fourier number

-



given rod of length l being heated initial temperature, t0, application of higher temperature @ l, tl, , dimensionless temperature, u, defined



u
=




t
−

t

l





t

0


−

t

l








{\displaystyle u={\tfrac {t-t_{l}}{t_{0}-t_{l}}}}

, differential equation can reordered dimensionless form,





the dimensionless time defines fourier number, foh = αt/l.


this procedure may performed analogously on fick s second law of diffusion derive mass transfer fourier number, fom, , applied time depending mass transport problems.


for unsteady state conduction problems in solids, fourier number used nondimensional time parameter. biot number, fourier number can used determine heating or cooling of object. if biot number less 0.1, entire system can treated uniform in temperature. following equation, derived product of biot , fourier numbers, can used estimate time object reach specific temperature,





where t temperature of object @ time t, t0 initial temperature, t∞ temperature of bulk fluid, v volume of object, surface area, , h convective heat transfer coefficient surrounding fluid.







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