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Grashof Number, Gr, is the ratio of buoyancy to viscous forces Gr gL3 T 2 in .NET Integrating Code39 in .NET Grashof Number, Gr, is the ratio of buoyancy to viscous forces Gr gL3 T 2

Appendix generate, create bar code 39 none on .net projects iPhone Marangoni flow, liquid brid visual .net barcode 3/9 ges, axial excitation of liquid bridges with and without rotation of their supports, and thermocapillary convection. The third group deals with the sloshing of superfluids.

The fourth group deals with hydroelastic oscillations in microgravity. This chapter did not address the capillary problem in conical containers. This problem was treated by Ambrazyavichus (1981a,b).

The stability of the configuration of liquid layers in containers describing rotational motion was studied by Capodano (2001). The modeling of low gravity liquid motion in spinning containers was discussed by Cutshall, et al. (1996) and Dodge (1996).

Other issues not addressed in this chapter include numerical simulation of the surface tension effect on interface instability (Daly, 1969a,b), the influence of liquid sloshing on the dynamics of satellites (Guibert, et al., 1978, Hung, Long, and Chi, 1996, and Monti, et al., 2001), and magnetic effects on nonlinear Marangoni flow (Viviani, et al.

, 1997).. Appendix A1 Common dimensio nless numbers Biot Number, Bi, is the ratio of internal thermal resistance of a solid to the convective boundary layer thermal resistance, and is defined by the expression Bi hL ks. Bond Number, Bo, is the rat VS .NET Code39 io of gravitational to surface tension forces, and is defined by the expression Bo gL2 . Froude Number, Fr, is the r atio of inertia to body (gravitational) forces, and is defined by the expression Fr V2 V p gL gL. Grashof Number, Gr, is the ratio of buoyancy to viscous forces Gr gL3 T 2 Marangoni Number, Ma, (also Thermal Marangoni Number) is the ratio of the imbalance in surface tension forces to liquid tangential forces, and is defined by the expression   @ L T Ma @T  Marangoni Concentration Number (also Solutal Marangoni Number), MaC, measures the ratio of the imposed concentration difference and the damping (the viscosity and solute diffusion),   @ C0 L MaC @C0 D. Microgravity sloshing dynamics Nusselt Number, Nu, is the ratio of the surface heat transfer into the fluid to the conduction heat transfer in the fluid, and is given by the expression Nu hL kf. Ohnesorge Number, Oh, or Ca .net vs 2010 USS Code 39 pillary Number, Ca provides a measure of the surface deflection in response to thermocapillary induced stresses, and is defined by the expression Oh Ca  L. Prandtl Number, Pr, is the ratio of the momentum transport to the thermal transport in the fluid (or the energy transferred by convection to the energy transferred by conduction), and is defined by the expression Pr cp  k. It is also defined as the r barcode 39 for .NET atio of the momentum to thermal diffusivities. Rayleigh Number, <, for a fluid-filled space between two parallel horizontal planes a distance apart, measures the balance between the buoyant force associated with thermal expanson and the dissipation energy due to viscosity and thermal diffusion < T1 T2 g 2 k.

Reynolds Number, Re, is the ratio of inertia to viscous forces, and is defined by the expression Re LV LV  . Weber Number, We, is the ratio of inertia to surface tension forces We LV2  where cp is the specific he at at constant pressure (in joules/kilogram kelvin), D is the mass (Solutal) diffusivity, g is the gravitational acceleration (in m/s2) h is the heat transfer coefficient from a surface to a fluid (in watts/meter2 kelvin) and is defined in terms of the heat flow rate Q hA T0 T1 , T0 is the imposed temperature of the surface (in K), T1 is the ambient temperature (in K), k is the thermal conductivity (in watts/meter kelvin), L is a reference length, ~ ~ ~ T is the absolute temperature (in K), T0 T y 1 T y 0 , a tilde denotes a dimensionless quantity, V is the velocity (in m/s), k/(cp) (in m2/s) is the thermal diffusivity, is the volumetric thermal expansion coefficient 1= @=@T p ,  is the dynamic viscosity (in Pa s N s/m2 kg/(m s), v is the kinematic viscosity (in m2/s),  is the surface tension (in N/m kg/s2),  is the density (in kg/m3), C0 is a dimensionless concentration of the denser component (S/, S is the concentration of the denser component in kg/m3, C0 is the concentration difference)..
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