Biot Number Using Characteristic Length Calculator

Biot Number Formula:

\[ Bi = \frac{h_{transfer} \times L_{char}}{k_{fin}} \]

Heat Transfer Coefficient:

W/m²·K

Characteristic Length:

Thermal Conductivity of Fin:

W/m·K

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 temperature gradient is significant within a body.

2. How Does the Calculator Work?

The calculator uses the Biot Number formula:

\[ Bi = \frac{h_{transfer} \times L_{char}}{k_{fin}} \]

Where:

\( h_{transfer} \) — Heat Transfer Coefficient (W/m²·K)
\( L_{char} \) — Characteristic Length (m)
\( k_{fin} \) — Thermal Conductivity of Fin (W/m·K)

Explanation: The Biot Number compares the rate of heat transfer at the surface to the rate of heat conduction within the material.

3. Importance of Biot Number Calculation

Details: The Biot Number is crucial in heat transfer analysis. A small Biot Number (Bi < 0.1) indicates that conduction within the body is much faster than convection at the surface, meaning the temperature can be assumed uniform throughout the body.

4. Using the Calculator

Tips: Enter heat transfer coefficient in W/m²·K, characteristic length in meters, and thermal conductivity in W/m·K. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What does a high Biot Number indicate?
A: A high Biot Number (Bi > 0.1) indicates that conduction within the body is slower than convection at the surface, meaning significant temperature gradients exist within the body.

Q2: How is characteristic length determined?
A: Characteristic length is typically calculated as the ratio of volume to surface area (V/A) for the object being analyzed.

Q3: What are typical values for heat transfer coefficients?
A: Heat transfer coefficients vary widely depending on the fluid and flow conditions, ranging from 5-25 W/m²·K for natural convection to 50-20,000 W/m²·K for forced convection.

Q4: When is the lumped capacitance method applicable?
A: The lumped capacitance method is applicable when Bi < 0.1, indicating that temperature gradients within the body are negligible.

Q5: How does thermal conductivity affect the Biot Number?
A: Higher thermal conductivity results in a lower Biot Number, as heat conducts more easily through the material, reducing internal temperature gradients.