Dimensionless numbers play an important role in correlating transfer coefficients during forced convection. In relation to the dimensionless numbers, the correct statement(s) is/are
Options:
(A) Prandtl number in heat transfer is analogous to Schmidt number in mass transfer
(B) Small value of Prandtl number signifies lower thermal diffusion as compared to momentum diffusion
(C) Prandtl number is the ratio of momentum diffusivity to the thermal diffusivity of the fluid
(D) Lewis number is the product of Schmidt number and Prandtl number
Official Answer Key:
A, C
Step-by-Step Solution & Explanation
Prandtl number, Pr = ν/α = momentum diffusivity/thermal diffusivity — this matches statement (C) exactly (TRUE). By direct analogy, Schmidt number Sc = ν/D_AB plays the identical role in mass transfer that Pr plays in heat transfer — so (A) is TRUE (Pr ↔ Sc analogy is a standard, well-established correspondence). Statement (B) is FALSE: a SMALL Pr means ν<<α, i.e., thermal diffusion is FASTER (not lower) relative to momentum diffusion — the opposite of what is stated. Statement (D) is FALSE: Lewis number is defined as Le = Sc/Pr = α/D_AB (a RATIO, not a product) — it compares thermal to mass diffusivity directly. Answer: (A) and (C).
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