Biot Number Given Heat Transfer Coefficient And Time Constant Calculator

Biot Number Formula:

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

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

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 surface convection resistance. It's 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:

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

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)
\( Fo \) — Fourier Number (-)

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

3. Importance of Biot Number Calculation

Details: The Biot Number is crucial in heat transfer analysis. When Bi < 0.1, the temperature gradient within the body is negligible, and the lumped capacitance method can be applied. For higher values, spatial temperature variations must be considered.

4. Using the Calculator

Tips: Enter all parameters in the specified units. Ensure all values are positive and valid for accurate calculation of the Biot Number.

5. Frequently Asked Questions (FAQ)

Q1: What does a Biot Number less than 0.1 indicate?
A: A Biot Number less than 0.1 suggests that the internal resistance to heat conduction is much smaller than the external convection resistance, allowing the use of lumped capacitance method.

Q2: How is the Fourier Number related to Biot Number?
A: The Fourier Number represents dimensionless time, while the Biot Number represents the ratio of internal to external heat transfer resistances. Both are important in transient heat conduction analysis.

Q3: What are typical applications of Biot Number analysis?
A: Biot Number analysis is used in cooling/heating of electronic components, food processing, metallurgical processes, and various engineering applications involving heat transfer.

Q4: Can Biot Number be applied to mass transfer problems?
A: Yes, an analogous Biot Number exists for mass transfer, where it represents the ratio of internal diffusion resistance to external mass transfer resistance.

Q5: What limitations should be considered when using this formula?
A: This formula assumes constant properties and uniform surface conditions. It may not be accurate for complex geometries or when property variations with temperature are significant.