Dimensionless number

Dimensionless number in fluid dynamics and heat and mass transfer

1. DIMENSIONLESS NUMBER ANWESA KAR M.TECH(THERMAL ENGG.)

2. 1.REYNOLDS NUMBER It is the ratio of inertia force to the viscous force. Where, i s density is velocity is linear dimension is viscosity Significance-It is used to identify the nature of flow (Laminar or Turbulent) V

3. 2.FROUDE NUMBER It is the ratio of inertia force to the gravity force Where , V is the velocity g is the acceleration due to gravity L is the characteristics length Significance-It is used to analyze nature of flow where free surface is present. e.g. weirs ,channels ,spillways

4. 3.WEBERS NUMBER It is the ratio of inertia force to surface tension force. Where V is the velocity L is the characteristics length Significance-It is used in analyzing formation of droplet and in capillary studies. is the surface tension i s the density

5. 4.EULER NUMBER It is the ratio of inertia force to pressure force. Where P is the pressure V is the velocity Significance-It is used to characterize energy losses in a flow. is the density

6. 5.MACH NUMBER It is the ratio of inertia force to elastic force. Where V is the velocity of object C is the speed of sound Significance-It is used to analyze fluid flow where compressibility is a important factor.

7. 6.BIOT NUMBER It is the ratio of conductive resistance to convective resistance. Where h is the heat transfer coefficient K is the thermal conductivity Significance-It is used in the heat transfer calculation (lumped heat analysis). i s the characteristics length(volume of the body/surface area of contact)

8. 7.FOURIER NUMBER It is the ratio of heat conducted through a body to the heat stored. Where, t is the characteristics time Significance-It is used in transient heat analysis. is the thermal diffusivity i s the length

9. 8 .NUSSELT NUMBER It is the ratio of convective heat transfer to conductive heat transfer. Where h is the convective heat transfer coefficient L is the characteristics length K is the thermal conductivity Significance-It describe the enhancement of heat transfer because of convection in comparison to conduction

10. 9 .PRANDTL NUMBER It is the ratio of momentum diffusivity to heat diffusivity Where K is the thermal conductivity Significance-Prandtl number is used to describe thermal boundary layer. is the dynamic viscosity i s the specific heat

11. 10.GRASHOF NUMBER It is the ratio of buoyancy force to viscous force. Where g is acceleration due to gravity Significance-It is used in flow analysis in natural convection. is the coefficient of thermal expansion is the surface temperature is the fluid temperature far from the surface is the kinematic viscosity of fluid

12. 11.RAYLEIGH NUMBER Rayleigh number is the product of Grashof number and Prandtl number. Ra= Gr . Pr Significance-It is associated with buoyancy driven flow . Its value is used to characterize laminar to turbulent transition.

13. 12.STANTON NUMBER It is defined as the ratio of heat transferred by convection to the heat capacity of fluid. Where h is the heat transfer coefficient u is the speed of fluid Significance-It is used in heat transfer for forced convection flows. is the density of fluid is the Specific heat capacity of the fluid

14. 13.PECLET NUMBER It is defined as the product of Reynold number and Prandtl number. Where L is the characteristics length u is the velocity Significance-It is used in calculations including convective heat transfer rate. is the thermal diffusivity

15. 14.JAKOB NUMBER It is the ratio of sensible energy absorbed to latent energy absorbed during liquid- vapor phase change. Where Significance-It is used in analyzing flow pattern in process of boiling. is the specific heat capacity is the temperature difference Latent heat of vaporization

16. 15.BOND NUMBER It is the ratio of buoyancy force to the surface tension force. Where g is the acceleration due to gravity Significance-It is used in analyzing the behavior of bubbles. is the difference in density is the surface tension

17. 16.SCHIMDT NUMBER It is the ratio of momentum diffusivity to mass diffusivity. Where D is the mass diffusivity Significance-It is used in fluid flows where simultaneous mass and momentum diffusion occurs. is the kinematic viscosity

18. 17.LEWIS NUMBER It is the ratio of thermal diffusivity to the mass diffusivity. Where D is the mass diffusivity K is the thermal conductivity Significance-It is used to analyze fluid flow with simultaneous heat and mass transfer by convection. is the thermal diffusivity is the specific heat capacity

19. 18.SOMMERFELD NUMBER Sommerfeld number is defined by the following equation Where r is the radius of the journal c is the radial clearance P is the bearing pressure Significance-It is used in hydrodynamic lubrication analysis. is the dynamic viscosity is the journal speed in r.p.s

20. 19 .KNUDSEN NUMBER It is the ratio of molecular mean free path to the characteristics length. Where L is the characteristics length Significance-It is useful in determining whether continuum mechanics formulation can be applied or not in a system. is the mean free path

21. 20.SHERWOOD NUMBER It is the ratio of convection mass transfer to the diffusion mass transfer Where K is the mass transfer coefficient l is the characteristics length D is the mass diffusivity Significance-It is used in mass transfer problems.

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