Biot Number Calculator Based On Volume To Area Ratio

Biot Number Equation:

\[ Bi = \frac{h V}{k A} \]

Heat Transfer Coefficient (h):

W/m²·K

Volume (V):

m³

Thermal Conductivity (k):

W/m·K

Surface Area (A):

m²

Biot Number (Bi):

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1. What is the Biot Number?

The Biot number (Bi) is a dimensionless quantity used in heat transfer calculations. It compares the resistance to heat transfer at the surface of a body to the resistance within the body. It's particularly important in transient heat conduction problems.

2. How Does the Calculator Work?

The calculator uses the Biot number equation:

\[ Bi = \frac{h V}{k A} \]

Where:

\( h \) — Heat transfer coefficient (W/m²·K)
\( V \) — Volume of the object (m³)
\( k \) — Thermal conductivity of the material (W/m·K)
\( A \) — Surface area through which heat transfer occurs (m²)

Explanation: The Biot number represents the ratio of internal thermal resistance to external thermal resistance. A small Biot number (Bi < 0.1) suggests that conduction inside the body is much faster than convection at its surface.

3. Importance of Biot Number

Details: The Biot number is crucial in heat transfer analysis as it determines whether a body can be treated as thermally thin (uniform temperature) or thermally thick (significant temperature gradients).

4. Using the Calculator

Tips: Enter all values in consistent SI units. The heat transfer coefficient, volume, thermal conductivity, and surface area must all be positive values for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What does a high Biot number indicate?
A: A high Biot number (Bi > 0.1) indicates significant temperature gradients within the object, meaning the internal conduction resistance is important.

Q2: What does a low Biot number indicate?
A: A low Biot number (Bi < 0.1) suggests the object can be treated as having uniform temperature (lumped capacitance method is valid).

Q3: How is Biot number different from Nusselt number?
A: While both relate convection to conduction, Biot number uses the object's conductivity (internal), while Nusselt number uses the fluid's conductivity (external).

Q4: What are typical values for heat transfer coefficients?
A: For air (natural convection) h ≈ 5-25 W/m²·K; for water (forced convection) h ≈ 50-10,000 W/m²·K; for boiling/condensation h can be much higher.

Q5: Can Biot number be applied to mass transfer?
A: Yes, an analogous Biot number exists for mass transfer where thermal conductivity is replaced by mass diffusivity.