Subtopic: Transient heat transfer in simple geometry
Question Statement:
Peas which have an average diameter of 6 mm are blanched to give a temperature of 85 °C at the centre. The initial temperature of the pea is 15 °C and temperature of the hot water blancher is 95 °C. The thermal conductivity, specific heat and density of peas are 0.35 W m⁻¹ K⁻¹, 3.3 kJ kg⁻¹ K⁻¹ and 980 kg m⁻³ respectively. The heat transfer coefficient is 1200 W m⁻² K⁻¹. If the value of Fourier number (Fo) is 0.32, the time of blanching will be
Options:
(A) 26.6 s
(B) 26.0 s
(C) 20.6 s
(D) 20.0 s
Official Answer Key:
A
Step-by-Step Solution & Explanation
Thermal diffusivity α = k/(ρCp) = 0.35/(980×3300) = 1.082×10⁻⁷ m²/s. Radius r = 0.003 m. Fo = αt/r² → t = Fo·r²/α = 0.32×(0.003)²/1.082×10⁻⁷ = 0.32×9×10⁻⁶/1.082×10⁻⁷ = 26.6 s.
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