# Bioprocess Engineering Questions and Answers – Liquid- Solid Mass Transfer Correlations

This set of Bioprocess Engineering Multiple Choice Questions & Answers (MCQs) focuses on “Liquid- Solid Mass Transfer Correlations”.

1. The ratio of inertial forces to viscous forces is called as ________
a) Nusselt number
b) Schmidt number
c) Sherwood number
d) Reynolds number

Explanation: The Reynolds number is the ratio of inertial forces to viscous forces and is a convenient parameter for predicting if a flow condition will be laminar or turbulent. It can be interpreted that when the viscous forces are dominant (slow flow, low Re) they are sufficient enough to keep all the fluid particles in line, and then the flow is laminar. Even very low Re indicates viscous creeping motion, where inertia effects are negligible. When the inertial forces dominate over the viscous forces (when the fluid is flowing faster and Re is larger) then the flow is turbulent.

2. Which number is analogous to Reynold’s number?
a) Nusselt number
b) Schmidt number
c) Sherwood number
d) Grashof number

Explanation: The Grashof number (Gr) is a dimensionless number in fluid dynamics and heat transfer which approximates the ratio of the buoyancy to viscous force acting on a fluid. It frequently arises in the study of situations involving natural convection and is analogous to the Reynolds number.

3. 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

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: m2/s)
α : thermal diffusivity, α = k/(cp ρ), (SI units: m2/s)
μ : dynamic viscosity, (SI units: Pa s = N s/m2)
k : thermal conductivity, (SI units: W/m-K)
cp : specific heat, (SI units: J/kg-K)
ρ : density, (SI units: kg/m3).

4. Which number is analogous to Prandlt number in terms of mass transfer?
a) Sherwood number
b) Schmidt number
c) Reynolds number
d) Nusselt number

Explanation: Schmidt Number, Sc, is a dimensionless parameter representing the ratio of diffusion of momentum to the diffusion of mass in a fluid. It is defined as
Sc = v/δ
where ν is kinematic viscosity and &delta diffusivity.
Schmidt number is the mass transfer equivalent of Prandtl Number. For gases, Sc and Pr have similar values (≈0.7) and this is used as the basis for simple heat and mass transfer analogies.
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5. What is the unit of slip velocity?
a) m min
b) m2/ min
c) m/min
d) m/min2

Explanation: The rate, expressed in feet (meters) per minute, at which a given size and shape of rock particle will descend or settle in water; e.g., the slip velocity in water of a round, flat particle of rock, 1/2 in (1.27 cm) in diameter, is about 54 ft/min (16.5 m/min).

6. Overall heat transfer coefficient is associated with?
b) Conduction and convection

Explanation: The overall heat transfer coefficient U is a measure of the overall ability of a series of conductive and convective barriers to transfer heat. It is commonly applied to the calculation of heat transfer in heat exchangers.

7. Evaporation of n-propyl alcohol into carbon dioxide for the same geometrical arrangement of tube diameter (d) of 38 mm when the carbon dioxide flows at a maximum velocity (ug) of 10 m/s at 300 K and 1 atm. Properties of dilute mixtures of propyl alcohol in carbon dioxide at 300 K and 1 atm are: Molecular weight (M) = 44 gm/mole, density (ρ) = 1.8 kg/m3 , Viscosity (μ) = 1.49×10-5 kg/m.s, diffusivity (DAB) = 7.6×10-6 m2 /s and universal gas constant (R) = 8.314 J/mole.K. Estimate the Reynolds number.
Nu = 0.453Re0.568 Pr0.36, where 10 < Re (= ρug d/μ)<106 and 0.7 < Pr < 500
a) 45906.04
b) 40906.05
c) 45906.05
d) 40906.04

Explanation: Re = 1.8*10*0.038/1.49×10-5 = 45906.04.

8. Refer to Q7 and Calculate the value of Schmidt number (Sc).
a) 1.02
b) 1.04
c) 1.06
d) 1.08

Explanation: Sc = (1.49×10-5)/(1.8*7.6×10-6) = 1.08.

9. Refer to Q7 and Q8 and calculate the mass-transfer coefficient by using the mass and heat transfer analogy.
a) 1.661×10-05 mole/m2 .s.Pa
b) 1.663×10-05 mole/m2 .s.Pa
c) 1.665×10-05 mole/m2 .s.Pa
d) 1.669×10-05 mole/m2 .s.Pa

Explanation: Analogy to heat transfer
Sh = 0.453 Re0.568 Sc0.36 = 207.68
So, kG RTd/DAB = 207.68
Therefore, kG = (207.68*DAB) / RTd = 1.665×10-05 mole/m2 .s.Pa.

10. Advection is related to Convection.
a) True
b) False

Explanation: The term advection sometimes serves as a synonym for convection, but technically, convection covers the sum of transport both by diffusion and by advection. Advective transport describes the movement of some quantity via the bulk flow of a fluid (as in a river or pipeline).

11. Nusselt number is the mass transfer analog of which number?
a) Sherwood number
b) Schmidt number
c) Reynolds number
d) Nusselt number

Explanation: The Sherwood number (Sh) (also called the mass transfer Nusselt number) is a dimensionless number used in mass-transfer operation. It represents the ratio of the convective mass transfer to the rate of diffusive mass transport.

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