Biot Number Given Characteristic Dimension And Fourier Number Calculator

Biot Number Formula:

\[ Bi = \frac{h \cdot \tau}{\rho_B \cdot c \cdot s \cdot Fo} \]

Heat Transfer Coefficient (h):

W/m²·K

Time Constant (τ):

Density of Body (ρB):

kg/m³

Specific Heat Capacity (c):

J/kg·K

Characteristic Dimension (s):

Fourier Number (Fo):

Biot Number (Bi):

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1. What is the Biot Number?

The Biot Number is a dimensionless quantity that represents the ratio of internal conduction resistance to the surface convection resistance. It is used in heat transfer analysis to determine if a body can be treated with the lumped capacitance method.

2. How Does the Calculator Work?

The calculator uses the Biot Number formula:

\[ Bi = \frac{h \cdot \tau}{\rho_B \cdot c \cdot s \cdot Fo} \]

Where:

\( h \) — Heat Transfer Coefficient (W/m²·K)
\( \tau \) — Time Constant (s)
\( \rho_B \) — Density of Body (kg/m³)
\( c \) — Specific Heat Capacity (J/kg·K)
\( s \) — Characteristic Dimension (m)
\( Fo \) — Fourier Number (-)

Explanation: The formula calculates the Biot Number by relating heat transfer coefficients, material properties, and dimensionless numbers.

3. Importance of Biot Number Calculation

Details: The Biot Number is crucial in heat transfer analysis to determine if temperature gradients within a body are significant. A Biot Number less than 0.1 indicates that the lumped capacitance method can be applied.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. All values must be positive numbers greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What does a high Biot Number indicate?
A: A high Biot Number (>0.1) indicates significant temperature gradients within the body, meaning the lumped capacitance method cannot be used.

Q2: What is the characteristic dimension?
A: Characteristic dimension is the ratio of volume to surface area (V/A) for the body being analyzed.

Q3: How is Fourier Number related to Biot Number?
A: Fourier Number represents the ratio of diffusive transport rate to storage rate, while Biot Number represents the ratio of internal to external resistance.

Q4: What are typical Biot Number values?
A: Biot Number values typically range from 0.001 to 100, with values below 0.1 indicating uniform temperature distribution.

Q5: Can this calculator be used for mass transfer?
A: While the Biot Number concept applies to both heat and mass transfer, this specific calculator is designed for heat transfer applications.