Heat Transfer · External and internal convection
An orange, modeled as a sphere of diameter 80 mm, is taken from storage at 4 °C and…
Problem
An orange, modeled as a sphere of diameter 80 mm, is taken from storage at 4 °C and placed in a kitchen at 22 °C with h = 12 W/m²·K. Effective fruit properties: ρ = 910 kg/m³, c = 3600 J/kg·K, k = 0.47 W/m·K. One-term spherical coefficients: λ_1 = 1.1656, C_1 = 1.2732, with center solution (T_c − T_∞)/(T_i − T_∞) = C_1 exp(−λ_1² Fo) and Fo = αt/r_o². Find the center temperature after 45 min.
Hint
A sphere’s center follows the one-term spherical Heisler solution for Fo > 0.2.
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