Important dimensionless numbers commonly used in Food Engineering

Hello Everyone!

Just after one day, you are going to appear for your NET Exams. Wish you all best of luck for your exams.

Meanwhile, I've  compiled a list of some of the important dimensionless numbers which are commonly used in Food Engineering. They have a fair chance of coming in the exams. So have a look!

Reynold’s number : Ratio of inertial forces to viscous forces

N_RE <2100 : Laminar flow

2100<N_RE <4000: Transient flow

N_RE >4000: Turbulent flow

For agitated tanks, a Reynolds number less than 10 indicates laminar flow, greater than 100,000 is turbulent flow, and between 10 and 100,000 the flow field is considered to be transitional.

Nusselt number, N_Nu : Ratio of rate of heat transfer due to convection to that of due to conduction.

Prandtl number, N_Pr: Ratio of Molecular diffusivity of momentum to that of molecular diffusivity of heat. Or  Ratio of Kinematic Viscosity to that of Thermal diffusivity.

Grashof number, N_Gr: Ratio between the buoyancy forces and viscous forces. 

Similar to the Reynolds number, the Grashof number is useful for determining whether a flow over an object is laminar or turbulent.
For example, a Grashof number greater than 10⁹ for fluid flow over vertical plates signifies a turbulent flow.

Rayleigh number, N_Ra: Product of two dimensionless numbers, Grashof number and Prandtl number.

Biot number, N_Bi: Ratio of the internal resistance to heat transfer in the solid to the external resistance to heat transfer in the fluid is defined as the Biot number, N_Bi.

If the convective resistance at the surface of a body is much smaller than the internal conductive resistance, then the Biot number will be high. For Biot numbers greater than 40, there is negligible surface resistance to heat transfer. On the other hand, if internal conductive resistance to heat transfer is small, then the Biot number will be low. For Biot numbers less than 0.1, there is negligible internal resistance to heat transfer. Between a Biot number of 0.1 and 40, there is a fi nite internal and external resistance to heat transfer.

Fourier Number, N_Fo: For a given volume element, the Fourier number is a measure of the rate of heat conduction per unit rate of heat storage. Thus, a larger value of Fourier number indicates deep penetration of heat into the solid in a given period of time.

Stefan Number: Ratio of Sensible heat to latent heat.

Sherwood number, N_Sh : Ratio of Total mass transferred to total mass transferred by molecular diffusion.

Schmidt number, N_Sc: Ratio of Molecular diffusion of momentum to molecular diffusion of mass.

Note: Nusselt and Prandtl numbers for heat transfer are analogous to the Sherwood and Schmidt numbers, respectively, in mass transfer.

Lewis number: The ratio of thermal diffusivity to mass diffusivity. Or Ratio of Schmidt number to Prandtl number.

Froude number, N_Fr : Ratio of the inertial forces to gravitational forces. (Analogous to Reynolds number)

Power number, N_P : Important for impeller design

Screw power number: Important for viscous dissipation of energy

Update (17.09.2020): 

Me and my friend Arun Kumar Gupta, have started an initiative to put 5 #FoodTech questions on twitter daily. The questions are relevant to Entrance/NET/JRF/FSO/FSSAI/ICAR Exams. Please do have a look and share among your friends too! 

Abhinay Shashank 🇮🇳 (@AbhinayFoodTech): https://lnkd.in/epnMkck
ARUN KUMAR GUPTA (@guptaarunkumar7): https://lnkd.in/e2Rx85E

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-Abhinay Shashank