Subtopic: Steady state heat transfer in conduction, convection and radiation
Question Statement:
Convective heat transfer coefficient outside an ice cream block is 10 W m⁻² K⁻¹. Thermal conductivity of frozen ice cream is 0.3 W m⁻¹ K⁻¹. Convection takes place across a layer of 10 mm of air for 5 minutes. If the density and the specific heat capacity of ice cream are respectively 600 kg m⁻³ and 2.5 kJ kg⁻¹ K⁻¹, then 0.33 is
Options:
(A) Biot Number
(B) Nusselt Number
(C) Fourier Number
(D) Prandtl Number
Official Answer Key:
A
Step-by-Step Solution & Explanation
Biot number Bi = h·Lc/k(solid), where Lc is the characteristic conduction length — here the 10 mm (0.010 m) air-side boundary layer thickness relevant to the surface resistance. Bi = (10 × 0.010)/0.3 = 0.333, which is the value quoted in the question stem. This is the Biot number by definition (ratio of internal conductive resistance to external convective resistance), matching option (A). (The density, specific heat and time data are extraneous to this particular sub-value — they would be needed for a Fourier-number calculation, which is a different quantity from the one being identified here.)
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