Question

Which number is defined as the ratio of momentum diffusivity to thermal diffusivity?

(a) Prandtl number

(b) Nusselt number

(c) Reynold’s number

(d) Sherwood number

I got this question in homework.

My doubt stems from Liquid- Solid Mass Transfer Correlations topic in chapter Heterogenous Reactions of Bioprocess Engineering

Answer 1

Right choice is (a) Prandtl number

The explanation: The Prandtl number (Pr) or Prandtl group is a dimensionless number, It is defined as the ratio of momentum diffusivity to thermal diffusivity. That is, the Prandtl number is given as:

where:

v : momentum diffusivity (kinematic viscosity), v = μ/ρ, (SI units: m^2/s)

α : thermal diffusivity, α = k/(cp ρ), (SI units: m^2/s)

μ : dynamic viscosity, (SI units: Pa s = N s/m^2)

k : thermal conductivity, (SI units: W/m-K)

cp : specific heat, (SI units: J/kg-K)

ρ : density, (SI units: kg/m^3).