Prandtl number thermal diffusion rate

The Prandtl number is a dimensionless number named after Ludwig Prandtl. It is defined as the ratio of momentum diffusivity (kinematic viscosity) to the thermal diffusivity, as well as the ratio of viscous diffusion rate to thermal diffusion rate ... 

Thus at small Pol the growth rate of the oscillations is negative and the capillary flow is stable. The absolute value of sharply increases with a decrease of the capillary tube diameter. It also depends on the thermal diffusivity of the liquid and the vapor, as well as on the value of the Prandtl number. 

For sufficiently large values of the Prandtl or Schmidt number the rate of transfer is controlled by the region of thickness S near the wall. The terms of the convective-thermal diffusivity equation... 

The Prandtl number, Cu/k = (p/p)/(k/pC), compares the rate of momentum transfer through friction to the thermal diffusivity or the transport of heat by conduction. 

PRANDTL NUMBER. A dimensionless number equal to the ratio of llie kinematic viscosity to the tlienuoiiielric conductivity (or thermal diffusivity), For gases, it is rather under one and is nearly independent of pressure and temperature, but for liquids the variation is rapid, Its significance is as a measure of the relative rates of diffusion of momentum and heat m a flow and it is important m the study of compressible flow and heat convection. See also Heat Transfer. 

The Prandtl number via has been found to be the parameter which relates the relative thicknesses of the hydrodynamic and thermal boundary layers. The kinematic viscosity of a fluid conveys information about the rate at which momentum may diffuse through the fluid because of molecular motion. The thermal diffusivity tells us the same thing in regard to the diffusion of heat in the fluid. Thus the ratio of these two quantities should express the relative magnitudes of diffusion of momentum and heat in the fluid. But these diffusion rates are precisely the quantities that determine how thick the boundary layers will be for a given external flow field large diffusivities mean that the viscous or temperature influence is felt farther out in the flow field. The Prandtl number is thus the connecting link between the velocity field and the temperature field. 

The rate of developments of velocity and temperature profiles in the entrance region depends on the Prandtl number defined as the ratio of fluid momentum diffusivity v (kinetic viscosity) to fluid thermal diffusivity a ... 

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