In this section a short overview of the definitions for characteristic numbers used in CrysMAS is given. In addition a short explanation of the physical meaning is added. For a more detailed description pleas refer to the literature. The units of the physical quantities used are given in the Appendix.
Characteristic number | Definition | Description |
---|---|---|
Prandtl number Pr | Pr = v_{d}*c_{p}/l v_{d} = dynamic viscosity, c_{p} = heat capacity, l = thermal conductivity | Material related characteristic number: Describes the ratio of sensitivity to convective or diffusive heat transfer in a material. High Pr means that in such a material it is expected that fluid flow will lead to significant changes even if the flow velocities are not to high. |
Grashof number Gr | Gr = (g*dT*b*L^{3}*rho^{2})/(v_{d}^{2}) L= characteristic length, g = gravity b = thermal expansion coefficient rho = density dT = thermal gradient | Ratio between thermal buoyancy forces and viscous forces. |
Rayleigh number Ra | Ra = (g*dT*b*L^{3})/(v_{k}*diff_{T}) v_{k} = kinematic viscosity diff_{T} = thermal diffusivity (l/(c_{p}*rho)) | Ratio between thermal buoyancy forces and viscous forces; Please note: Ra = Gr*Pr |
Reynolds number Re | Re = v*L*rho/v_{d} v = characteristic velocity | Ratio between dynamic and viscous forces. In the case of tube flow, if Re > 2000 the flow is considered to be turbulent. The Reynolds number for forced convection is computed here. Its value will depend on the prescribed fluid velocity at the inlet point. For the buoyancy driven convection the Reynolds number is computed as square root from the Grashof number. . |
Schmidt number Sc | Sc = v_{d}/(rho*D) D = diffusion coefficient | Material related characteristic number: Characterizes the ratio of convective and diffusive species transport for different materials with given flow field. |
Lewis number Le | Le = l/(c_{p}*rho*D) | Material related characteristic number: Characterizes the ratio of energy to species transport for different materials with given flow field. Le = Sc/Pr; |
Solutal Peclet number Pe_{C} | Pe_{C} =v*L/D | Ratio between diffusive and convective species transport in a flow field. |
Thermal Peclet number Pe_{T} | Pe_{T} = v*L/ diff_{T} | Ratio between diffusive and convective energy transport in a flow field. |
Magnetic Taylor number Ta_{m} | Ta_{m} = B_{0}^{2}* R^{4}*s*f/(2*rho*v_{k}*p) B_{0} = Magnetic induction at the wall R = sample radius s = electrical conductivity of the sample f = rotation frequency p = Number of pole pairs | Magnetic Taylor number for rotating magnetic fields. Give the ratio of the Lorentz-force to the viscous forces. High Ta indicates a time-dependent or turbulent flow. The actual critical Ta for the transition to time dependent flows depends on the aspect ratio of the sample. |
Hartmann number | Ha = B*L*sqrt(s/(v_{k}*rho)) | Describes the effective strength of the magnetic induction not depending on the material used as sample. Used for static magnetic fields. |