Parcel Temperature Calculator

Formula

The formula to calculate the final temperature of a parcel (T_final) is:

\[ T_{\text{final}} = T_{\text{initial}} + (T_{\text{ambient}} - T_{\text{initial}}) \left(1 - e^{\left(-\frac{h \cdot A \cdot t}{3600}\right)}\right) \]

Where:

\(T_{\text{final}}\) is the final temperature of the parcel (°C)
\(T_{\text{initial}}\) is the initial temperature of the parcel (°C)
\(T_{\text{ambient}}\) is the ambient temperature (°C)
\(h\) is the heat transfer coefficient (W/m²K)
\(A\) is the surface area of the parcel (m²)
\(t\) is the time (hours)

What is Parcel Temperature?

Parcel temperature refers to the temperature of a package or container, which can change over time due to heat transfer with its surroundings. This is particularly important in the context of shipping temperature-sensitive goods, where maintaining a specific temperature range is crucial. The heat transfer coefficient, surface area, and ambient temperature are key factors that influence how quickly a parcel’s temperature will converge to the ambient temperature.

Example Calculation

Let's assume the following values:

Initial Temperature (T_initial) = 20 °C
Ambient Temperature (T_ambient) = 25 °C
Heat Transfer Coefficient (h) = 10 W/m²K
Surface Area (A) = 2 m²
Time (t) = 3 hours

Using the formula to calculate the final temperature (T_final):

\[ T_{\text{final}} = T_{\text{initial}} + (T_{\text{ambient}} - T_{\text{initial}}) \left(1 - e^{\left(-\frac{h \cdot A \cdot t}{3600}\right)}\right) = 20 + (25 - 20) \left(1 - e^{\left(-\frac{10 \cdot 2 \cdot 3}{3600}\right)}\right) = 20 + 5 \left(1 - e^{-0.0167}\right) \approx 20.08 \text{ °C} \]

The final temperature (T_final) is approximately 20.08 °C.