Fourier Number Given Heat Transfer Coefficient and Time Constant Calculator

Fourier Number Formula:

\[ Fo = \frac{h \times A_c \times \tau}{\rho_B \times c \times V \times Bi} \]

Heat Transfer Coefficient (h):

W/m²·K

Surface Area for Convection (A_c):

m²

Time Constant (τ):

Density of Body (ρ_B):

kg/m³

Specific Heat Capacity (c):

J/kg·K

Volume of Object (V):

m³

Biot Number (Bi):

Fourier Number (Fo):

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1. What is the Fourier Number?

The Fourier Number is a dimensionless quantity that represents the ratio of diffusive or conductive transport rate to the quantity storage rate, where the quantity may be either heat or matter. It's a crucial parameter in heat transfer analysis.

2. How Does the Calculator Work?

The calculator uses the Fourier Number formula:

\[ Fo = \frac{h \times A_c \times \tau}{\rho_B \times c \times V \times Bi} \]

Where:

\( h \) — Heat Transfer Coefficient (W/m²·K)
\( A_c \) — Surface Area for Convection (m²)
\( \tau \) — Time Constant (s)
\( \rho_B \) — Density of Body (kg/m³)
\( c \) — Specific Heat Capacity (J/kg·K)
\( V \) — Volume of Object (m³)
\( Bi \) — Biot Number (dimensionless)

Explanation: The Fourier Number characterizes the relative importance of heat conduction to heat storage in transient heat conduction problems.

3. Importance of Fourier Number Calculation

Details: Accurate Fourier Number calculation is essential for analyzing transient heat transfer processes, designing thermal systems, and predicting temperature distributions in materials over time.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure all values are positive and within reasonable physical ranges for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What does a high Fourier Number indicate?
A: A high Fourier Number indicates that heat conduction is dominant over heat storage, meaning the system reaches thermal equilibrium quickly.

Q2: How is Fourier Number related to Biot Number?
A: While Biot Number relates internal conduction resistance to surface convection resistance, Fourier Number relates conduction rate to storage rate. Both are important in transient heat transfer analysis.

Q3: What are typical Fourier Number values?
A: Fourier Number values vary widely depending on the system. Values greater than 0.2 often indicate that the lumped capacitance method may not be appropriate.

Q4: Can Fourier Number be used for mass transfer?
A: Yes, the concept can be extended to mass transfer where it represents the ratio of diffusive transport rate to storage rate of matter.

Q5: What are the limitations of this calculation?
A: The formula assumes constant properties and may not be accurate for systems with significant property variations or complex geometries.