Time Taken To Reach Given Temperature Calculator

Formula Used:

\[ t = \ln\left(\frac{T_f - t_f}{T_o - t_f}\right) \times \left(\frac{\rho \times V_T \times c}{h \times A}\right) \]

Final Temperature (Tf):

Fluid Temperature (tf):

Initial Temperature (To):

Density (ρ):

kg/m³

Total Volume (VT):

m³

Specific Heat (c):

J/kg·K

Convection Heat Transfer Coefficient (h):

W/m²·K

Surface Area (A):

m²

Time Elapsed (t):

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1. What is the Time Taken To Reach Given Temperature Formula?

The Time Taken To Reach Given Temperature formula calculates the time required for an object to reach a specific temperature when exposed to a fluid environment with different temperature. It's based on Newton's law of cooling and heat transfer principles.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ t = \ln\left(\frac{T_f - t_f}{T_o - t_f}\right) \times \left(\frac{\rho \times V_T \times c}{h \times A}\right) \]

Where:

\( t \) — Time elapsed (seconds)
\( T_f \) — Final temperature (K)
\( t_f \) — Fluid temperature (K)
\( T_o \) — Initial temperature (K)
\( \rho \) — Density (kg/m³)
\( V_T \) — Total volume (m³)
\( c \) — Specific heat (J/kg·K)
\( h \) — Convection heat transfer coefficient (W/m²·K)
\( A \) — Surface area (m²)

Explanation: The formula calculates the time required for heat transfer through convection to change an object's temperature from initial to final value.

3. Importance of Time Calculation

Details: Accurate time calculation is crucial for thermal process design, heat treatment applications, food processing, and various industrial heating/cooling processes.

4. Using the Calculator

Tips: Enter all temperature values in Kelvin, ensure proper units for all parameters, and make sure initial and final temperatures are different from fluid temperature.

5. Frequently Asked Questions (FAQ)

Q1: What is the natural logarithm (ln) function?
A: The natural logarithm is the inverse function of the natural exponential function, used to solve exponential equations in heat transfer calculations.

Q2: Why are temperatures measured in Kelvin?
A: Kelvin is an absolute temperature scale required for thermodynamic calculations to avoid negative values in logarithmic functions.

Q3: What affects the convection heat transfer coefficient?
A: Fluid properties, flow velocity, surface roughness, and temperature difference influence the convection heat transfer coefficient.

Q4: When is this formula applicable?
A: This formula applies to objects with uniform temperature distribution and constant fluid temperature during the process.

Q5: What are typical values for specific heat?
A: Water has ~4184 J/kg·K, metals range from 385-900 J/kg·K, while air has ~1005 J/kg·K at room temperature.