Chapter 3, Problem 3.105P

Unique characteristics of biologically active materials such as fruits, vegetables, and other products require special care in handling. Following harvest and separation from producing plants, glucose is catabolized to produce carbon dioxide, water vapor, and heat. with attendant internal energy generation. Consider a carton of apples, each of 80-mm diameter, which is ventilated with air at 5°C and a velocity of 0.5 m/s. corresponding value of the heat transfer coefficient is $7.5{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$ Within each apple thermal energy is uniformly generated at a total rate of $4000\text{J/kg}\cdot \text{day}\text{.}$ The density and thermal conductivity of the apple are $840{\text{kg/m}}^{\text{3}}$ and $0.5\text{W/m}\cdot \text{K,}$ respectively.

1. Determine the apple center and surface temperatures.
2. For the stacked arrangement of apples within the crate, the convection coefficient depends on the velocity as $h=C_1{V}^{0.425},$ where $C_1=10.1{\text{W/m}}^{\text{2}}\cdot \text{K}\cdot {\left(\text{m/s}\right)}^{0.425}.$ Compute and plot the center and surface temperatures as a function of the air velocity for $0.1\le V\le 1\text{m/s}\text{.}$