Total Heat Transfer During Time Interval Calculator

Heat Transfer Formula:

\[ Q = \rho \cdot c \cdot V_T \cdot (T_o - t_f) \cdot (1 - \exp(-(Bi \cdot Fo))) \]

Density (ρ):

kg/m³

Specific Heat (c):

J/kg·K

Total Volume (V_T):

m³

Initial Temperature (T_o):

Fluid Temperature (t_f):

Biot Number (Bi):

Fourier Number (Fo):

Heat Transfer (Q):

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1. What is Heat Transfer During Time Interval?

Heat Transfer during a time interval refers to the amount of thermal energy transferred between a system and its surroundings over a specific period. This calculation is essential in thermal engineering, HVAC systems, and materials processing.

2. How Does the Calculator Work?

The calculator uses the heat transfer formula:

\[ Q = \rho \cdot c \cdot V_T \cdot (T_o - t_f) \cdot (1 - \exp(-(Bi \cdot Fo))) \]

Where:

\( Q \) — Heat Transfer (J)
\( \rho \) — Density (kg/m³)
\( c \) — Specific Heat (J/kg·K)
\( V_T \) — Total Volume (m³)
\( T_o \) — Initial Temperature (K)
\( t_f \) — Fluid Temperature (K)
\( Bi \) — Biot Number
\( Fo \) — Fourier Number

Explanation: The formula calculates the total heat energy transferred based on material properties, temperature difference, and dimensionless numbers that characterize the heat transfer process.

3. Importance of Heat Transfer Calculation

Details: Accurate heat transfer calculation is crucial for designing thermal systems, optimizing energy efficiency, predicting temperature changes, and ensuring proper functioning of heat exchange equipment.

4. Using the Calculator

Tips: Enter all required parameters with appropriate units. Ensure temperature values are in Kelvin, density in kg/m³, specific heat in J/kg·K, and volume in m³. Biot and Fourier numbers are dimensionless.

5. Frequently Asked Questions (FAQ)

Q1: What is the Biot Number?
A: Biot Number is a dimensionless quantity that represents the ratio of internal conduction resistance to external convection resistance in heat transfer.

Q2: What does the Fourier Number represent?
A: Fourier Number is a dimensionless time parameter that characterizes transient heat conduction, representing the ratio of heat conduction rate to heat storage rate.

Q3: When is this formula applicable?
A: This formula is particularly useful for transient heat conduction problems where a solid body is suddenly exposed to a fluid at a different temperature.

Q4: What are typical values for Biot and Fourier numbers?
A: Biot numbers typically range from 0.01 to 100, while Fourier numbers depend on the time scale of the process being analyzed.

Q5: How does temperature difference affect heat transfer?
A: Heat transfer rate is directly proportional to the temperature difference between the object and the surrounding fluid, as shown in the formula.