Fourier number, abbreviated as Fo, also called Fourier modulus, a dimensionless number, 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.
In heat transfer analysis, the Fourier number is used to determine the relative importance of conduction within a material compared to the time and length scales involved. It helps in understanding the transient behavior of heat conduction and predicting how quickly temperature changes will propagate through a solid or fluid. A smaller Fourier number indicates that heat conduction is dominant compared to the time and length scales involved, meaning that temperature changes will propagate rapidly. A larger Fourier number suggests that the effects of conduction are less significant, and temperature changes will propagate more slowly.
The Fourier number is particularly useful in the analysis of unsteady state or transient heat conduction problems, where temperature changes occur over time. By considering the Fourier number, engineers and researchers can make predictions about the thermal behavior of materials and optimize the design of heat transfer systems.
Fourier Number Interpretation
- Small Fourier Number (Fo << 1) - Indicates that the time scale is short or the characteristic length is large. Heat or mass has not penetrated deeply into the material, and the process is dominated by the initial transient phase (temperature or concentration changes are limited to a thin layer near the surface).
- Large Fourier Number (Fo >> 1) - Suggests a long time scale or a small characteristic length. The system has had sufficient time for heat or mass to penetrate fully, approaching a steady-state or uniform condition throughout the material.
- Fourier Number (Fo ≈ 1) - Represents a balance where the diffusion process has progressed significantly but not yet reached equilibrium, often a critical point in engineering design or analysis.
Fourier number formula |
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\( Fo \;=\; \dfrac{ \alpha \cdot t_c }{ l_c^2 }\) (Fourier Number) \( \alpha \;=\; \dfrac{ Fo \cdot l_c^2 }{ t_c }\) \( t_c \;=\; \dfrac{ Fo \cdot l_c^2 }{ \alpha }\) \( l_c \;=\; \sqrt{ \dfrac{ \alpha \cdot t_c }{ Fo } }\) |
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| Symbol | English | Metric |
| \( Fo \) = Fourier Number | \( dimensionless \) | \( dimensionless \) |
| \( \alpha \) (Greel symbol alpha) = Thermal Diffusivity | \(ft^2\;/\;sec\) | \(m^2\;/\;s\) |
| \( t_c \) = Characteristic Time | \( sec \) | \( s \) |
| \( l_c \) = Characteristic Length | \( ft \) | \( m \) |
Fourier number formula |
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\( Fo \;=\; \dfrac{ D \cdot t_c }{ l_c^2 }\) (Fourier Number) \( D \;=\; \dfrac{ Fo \cdot l_c^2 }{ t_c }\) \( t_c \;=\; \dfrac{ Fo \cdot l_c^2 }{ D }\) \( l_c \;=\; \sqrt{ \dfrac{ D \cdot t_c }{ Fo } }\) |
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| Symbol | English | Metric |
| \( Fo \) = Fourier Number | \( dimensionless \) | \( dimensionless \) |
| \( D \) = Mass Diffusivity | \(ft^3\;/\;sec\) | \(m^3\;/\;s\) |
| \( t_c \) = Characteristic Time | \( sec \) | \( s \) |
| \( l_c \) = Characteristic Length | \( ft \) | \( m \) |
