Product of Biot and Fourier Number given System Properties Calculator

Formula Used:

\[ BiFo = \frac{h \times A \times t}{\rho \times V_T \times C_o} \]

Convection Heat Transfer Coefficient (h):

W/m²·K

Surface Area (A):

m²

Time Elapsed (t):

Density (ρ):

kg/m³

Total Volume (V_T):

m³

Specific Heat Capacity (C_o):

J/kg·K

Product of Biot and Fourier Numbers (BiFo):

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1. What is the Product of Biot and Fourier Number?

The product of Biot and Fourier numbers (BiFo) is a dimensionless quantity used in unsteady state heat transfer analysis. It combines the effects of convective heat transfer (Biot number) and transient heat conduction (Fourier number) to simplify temperature calculations in time-dependent heat transfer problems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ BiFo = \frac{h \times A \times t}{\rho \times V_T \times C_o} \]

Where:

\( h \) — Convection Heat Transfer Coefficient (W/m²·K)
\( A \) — Surface Area (m²)
\( t \) — Time Elapsed (s)
\( \rho \) — Density (kg/m³)
\( V_T \) — Total Volume (m³)
\( C_o \) — Specific Heat Capacity (J/kg·K)

Explanation: This formula calculates the combined effect of convective heat transfer and transient conduction by relating the convective heat transfer at the surface to the thermal energy storage capacity of the material.

3. Importance of BiFo Calculation

Details: The BiFo product is crucial for analyzing unsteady state heat transfer problems, determining temperature distributions over time, and designing thermal systems with time-dependent heating or cooling requirements.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Ensure all input values are positive and valid. The calculator will compute the dimensionless BiFo product.

5. Frequently Asked Questions (FAQ)

Q1: What does a high BiFo value indicate?
A: A high BiFo value indicates that convective heat transfer dominates over thermal energy storage, meaning the system responds quickly to temperature changes.

Q2: How is BiFo different from Biot number alone?
A: While Biot number compares convective to conductive resistance, BiFo incorporates time dependence by including the Fourier number component.

Q3: What are typical BiFo values in engineering applications?
A: BiFo values vary widely depending on the application, but typically range from 0.001 to 100 in most engineering heat transfer problems.

Q4: Can BiFo be used for all materials?
A: Yes, BiFo is applicable to all materials as long as the properties (density, specific heat) are known and the heat transfer is primarily convective at the surface.

Q5: How does time affect the BiFo value?
A: BiFo increases linearly with time, reflecting the cumulative effect of heat transfer over the elapsed period.