Thursday, December 22, 2011

Dimensionless Numbers & their Significance


Nomenclature:


D = diameter of pipe
DH = Hydraulic diameter
L = Length of the pipe
Lch = characteristic length
R = Length through which conduction occurs.
u = mean characteristic velocity of the object relative to the fluid.
Vch = Characteristic velocity
Cp = specific heat capacity at constant pressure.
k = thermal conductivity
μ = dynamic viscosity of the fluid
{\rho}\, = density of fluid.
DAB = mass diffusivity
h = heat transfer coefficient.
g = acceleration due to earths gravity.
t = characteristic time
ν = Kinematic viscosity of fluid.
α = Thermal diffusivity
β = volumetric thermal expansion coefficient ( = 1/T for ideal fluids, T = absolute temperature)
Ts = surface temperature
T∞ = Bulk Temperature










Significance:

  • Ratio of Inertial forces to viscous forces.
  • Primarily used to analyse different flow regimes namely Laminar, Turbulent, or both.
  • When Viscous forces are dominant its a laminar flow & when Inertial forces are dominant it is a Turbulent flow.
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Significance:
  • Depends only on fluid & its properties. It is also ratio of velocity boundary layer to thermal boundary layer
  • Pr = small, implies that rate of thermal diffusion (heat) is more than the rate of momentum diffusion (velocity). 
  • Also the thickness of thermal boundary layer is much larger than the velocity boundary layer.
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Significance:
  • Analogous of Prandtl number in Heat Transfer.
  • Used in fluid flows in which there is simultaneous momentum & mass diffusion
  • It is also ratio of fluid boundary layer to mass transfer boundary layer thickness.
  • To find mass transfer coefficient using Sherwood number, we need Schmidt number. 
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Significance:
  • Ratio of thermal diffusivity to mass diffusivity.
  • Fluid flow with simultaneous Heat & mass transfer by convection.
  • It is also ratio of Schmidt number to Prandtl number
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Significance:
  • Heat transported by convection to Heat transported by conduction.
  • Product of Re & Pr for Pe(HT) & product of Re & SC for Pe(MT)
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Significance:
  • It is the ratio of  heat transferred to the fluid to the heat transported by the fluid (ratio of Nusselt number to Peclet number)
  • Used to find heat transfer in forced convection flows.
  • St(HT) = Nu/(Re.Pr) & St(MT) = Sh/(Re.Sc)
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Significance:
A) Sherwood Number:
  • Ratio of Convective to diffusive mass transport. Used in mass transfer operations.
  • Analogous of Nusselt number in Heat transfer OR Sherwood number is Nusselt number for mass transfer.
B) Nusselt Number
  • Ratio of convective to conductive heat transfer coefficient across the boundary layer.
  • Low Nu => conduction is more => Laminar flow 
  • High Nu => convection is more=> Turbulent flow.
  • It can also be viewed as conduction resistance to convection resistance of the material.
  • Free convection: Nu = f(Ra, Pr)
  • Forced Convection: Nu = f(Re, Pr)
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Significance:
  • Ratio of Buoyancy force to viscous force in natural convection.
  • Reynolds number is used in forced convection of  fluid flow, whereas Grashof number is used in natural convection.
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Significance:
    • used in unsteady state (transient) heat  transfer conditions.
    • ratio of  heat  transfer resistance inside the body to  heat  transfer resistance at the surface of the body. OR ratio of  internal thermal resistance to external thermal resistance .
    • Shows the variation of temperature inside the body w.r.t to time.
    • Bi < 0.1 => heat transfer resistance inside the body is very low => inside the body conduction takes place faster compared to convection at the surface. => no temperature gradient inside the body (uniformity in temperature) vice versa implies that Temperature is not uniform throughout hte material volume.
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    Significance:
    • It shows the presence & strength of convection in a fluid body.
    • Heat transfer by Conduction within fluid < Critical value for that fluid < Heat transfer by convection. (consequences of Ra values)
    • Product of Gr.Pr
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    Significance:

    • Characterizes laminar flow in a conduit OR transfer of heat by streamline fluid flow in a pipe
    • In case of  mass transfer, Pr is replaced by Sc.
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    Significance:

    • Ratio of rate of heat conduction to the rate of heat storage.
    • Used along with Biot number to solve transient state heat transfer problems.
    • For mass transfer by diffusion, Fourier number for MT is used.
    • It can also be understood as current time to the time taken to reach steady state.
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    28 comments:

    1. good work dear....

      ReplyDelete
    2. liked the work..good assembly

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    3. Thanks dear.Excellent work.Keep it up

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    4. Excellent job. Helped a lot~

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    5. goood !!so specific

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    6. Awesome work, dude..!! (y)

      ReplyDelete
    7. really very useful thanx..
      PAVAN

      ReplyDelete
    8. Thank you.....



      ReplyDelete
    9. thanks for providing such a valuable information

      ReplyDelete
    10. thanks for providing such a valuable information!!!!!!!

      ReplyDelete
    11. Excellent compilation. Keep it up.

      ReplyDelete
    12. good job
      keep it up.

      ReplyDelete
    13. Really helpful..as works as a snapshot of Chem Engg..

      ReplyDelete
    14. Thank you for your feedback. I would appreciate if you could share some suggestions for improvement. You can also mail me at chemicalfiles@gmail.com
      Looking forward to it.

      ReplyDelete
    15. thanks for sharing such types of information.

      mass transfer

      ReplyDelete
    16. awesome work man.. keep it up

      ReplyDelete
    17. Thanx for this post, This is a very useful link below for everyone else:
      http://www.ywfyouthvoice.com/2016/06/dimensionless-numbers-with-significance.html
      List Of All Important Dimensionless Numbers And Their Significance.

      ReplyDelete
    18. nice work..very useful and good classification..

      ReplyDelete

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