Combined convection flow direction, effect

Oosthuizen, P.H. and Madan.S.. The Effect of Flow Direction on Combined Convective Heat Transfer from Cylinders to Air , J. Heat transfer. May. pp. 240-242. 1971. 

Equation (2.16) consists of two contributions the molecular momentum flow tensor, it, and the convective momentum flow tensor, pvv. The term p8 represents the pressure effect, while the contribution t, for a Newtonian fluid, is related to the velocity gradient linearly through the viscosity. The convective momentum flow tensor pw contains the density and the products of the velocity components. A component of the combined momentum flow tensor of x-momentum across a surface normal to the x-direction is... 

Safe and effective delivery of peptides has also been successfully demonstrated in human studies using iontophoresis, a technique that uses mild electric current to facilitate transport of molecules across the skin. ° Iontophoresis works primarily by a combination of two forces, electro-repulsion of charged drug molecule away from the electrode and into the skin, and electroosmosis, a convective solvent flow in the direction of the counter-ion transport. In general, cationic proteins and peptides are delivered more efficiently than anionic molecules because electro-osmosis works in the same direction as electro-migration for cationic species. 

The tube is packed with catalyst pellets. Flow may be either laminar or turbulent. The velocity profile is assumed to be flat. Transfer of heat and mass in the radial direction is modeled using empirical diffusion coefficients that combine the effects of convection and true diffusion in the radial direction. There is no axial diffusion. Details are given in Chapter 9. This model is important only for nonisothermai reactors. It reduces to piston flow if the reaction is isothermal. 

In more complicated models both equations have to be generalised by coupling surface and bulk convective diffusion and hydrodynamics. The situation is finely balanced since the motion of the surface has an effect on the formation of the dynamic adsorption layer, and vice versa. Adsorption increases in the direction of the liquid motion while the surface tension decreases. This results in the appearance of forces directed against the flow and retards the surface motion. Thus, the dynamic layer theory should be based on the common solution of the diffusion equation, which takes into account the effect of surface motion on adsorption-desorption processes and of hydrodynamics equations combined with the effect of adsorption layers on the liquid interfacial motion (Levich 1962). 

The two equations for the mass and heat balance, Eqs. (4.10.125) and (4.10.126) or the dimensionless forms represented by Eqs. (4.10.127), (4.10.128) and (4.10.130), consider that the flow in a packed bed deviates from the ideal pattern because of radial variations in velocity and mixing effects due to the presence of the packing. To avoid the difficulties involved in a rigorous and complicated hydrodynamic treatment, these mixing effects as well as the (in most cases negligible contributions of) molecular diffusion and heat conduction in the solid and fluid phase are combined by effective dispersion coefficients for mass and heat transport in the radial and axial direction (D x, Drad. rad. and X x)- Thus, the fluxes are expressed by formulas analogous to Pick s law for mass transfer by diffusion and Fourier s law for heat transfer by conduction, and Eqs. (4.10.125) and (4.10.126) superimpose these fluxes upon those resulting from convection. These different dispersion processes can be described as follows (see also the Sections 4.10.6.4 and 4.10.7.3) ... 

---