Mass transfer in laminar flow

Analytical Solution for Mass Transfer in Laminar Flow. 180... 

Particles enhance mass transfer in laminar flow for natural convection. Good fit with correlation of Ray et ak, Inti. J. Heat Mass Transfer, 41, 1693 (1998). = g A... 

Mass transfer in laminar flow in a tube. We consider the case of mass transfer from a tube wall to a fluid inside in laminar flow, where, for example, the wall is made of solid benzoic acid which is dissolving in water. This is similar to heat transfer from a wall to the flowing fluid where natural convection is negligible. For fully developed flow, the parabolic velocity derived as Eqs. (2.6-18) and (2.6-20) is... 

Loney, N.W., Analytical solution to mass transfer in laminar flow in hollow fiber with heterogeneous chemical reaction, Chem. Eng. Sci., 51, 3995, 1995. 

Jome, J., 1982. Mass transfer in laminar flow channel with porous wall. J. Electrochem. Soc. 129,1727-1733. 

Terrill, R.M., Walker, G., 1967. Heat and mass transfer in laminar flow between parallel porous plates. Appl. Sci. Res. 18, 193-220. 

In this book, we routinely assume that there is no slip at a solid fluid interface (i.e., that at a stationary solid interface, the fluid velocity is zero). This leads to expressions for mass transfer in laminar flow in short tubes like... 

Celata GP, Cumo M, Marcom V, McPhail SJ, Zummo Z (2006) Micro-tube liquid single phase heat transfer in laminar flow. Int. J. Heat Mass Transfer 49 3538-3546... 

In transverse flow along a flat plate the transition from laminar to turbulent flow occurs at Reynolds numbers waL/v between 3 105 and 5 10s wa is the initial flow velocity, L is the length of the plate over which the fluid is flowing. The heat and mass transfer in turbulent flows is more intensive than in laminar. In general, at the same time there is also an increase in the pressure drop. 

An exclusively analytical treatment of heat and mass transfer in turbulent flow in pipes fails because to date the turbulent shear stress Tl j = —Qw w p heat flux q = —Qcpw, T and also the turbulent diffusional flux j Ai = —gwcannot be investigated in a purely theoretical manner. Rather, we have to rely on experiments. In contrast to laminar flow, turbulent flow in pipes is both hydrodynamically and thermally fully developed after only a short distance x/d > 10 to 60, due to the intensive momentum exchange. This simplifies the representation of the heat and mass transfer coefficients by equations. Simple correlations, which are sufficiently accurate for the description of fully developed turbulent flow, can be found by... 

The focus of this review has been on mass transfer in laminar, single-phase flows. Significant work is necessary for the rigorous analysis of current distribution in turbulent flows. Progress is also required for the analysis of current distribution in multiphase flows, especially in porous media relevant to fuel cell or battery applications. 

Mizushina, T. and Kurivaki, Yu., Heat transfer in laminar flow of pseudoplastic fluids in a circular tube. In Heat and Mass Transfer, Vol. 3, Minsk, 1968 [in Russian]. 

Laminar Flow. The Graetz or Leveque solutions25 26 for convective heat transfer in laminar flow channels, suitably modified for mass transfer, may be used to evaluate the mass transfer coefficient where the laminar parabolic velocity profile is assumed to be established at the channel entrance but where the concentration profile is under development down the full length of the channel. For all thin-channel lengths of practical interest, this solution is valid. Leveque s solution26 gives ... 

There are more data for heat transfer in laminar flow than for mass transfer, and the correlations should be similar, with Pr and Nu replacing Sc and Sh. An empirical equation for heat transfer at Graetz numbers greater than 20 is [15]... 

Mass transfer in laminar boundary layer flow of power-law fluids... 

I. Mass transfer for laminar flow inside pipes. When a liquid or a gas is flowing inside a pipe and the Reynolds number Dvpjp is below 2100, laminar flow occurs. Experimental data obtained for mass transfer from the walls for gases (G2, Ll) are plotted in Fig. 7.3-2 for values of WID gpL less than about 70. The ordinate is(c — c o)/(c, - — where is the exit concentration, c o inlet concentration, and c, - concentration at the interface between the wall and the gas. The dimensionless abscissa is WjD pL or r= sc(D/E)(7i/4), where W is flow in kg/s and L is length of mass-transfer section in m. 

In the case of mass transfer involving laminar flow about simple geometries, no distinction is made between regions near the leading front of the particle and portions farther downstream. Instead, we report transfer coefficients averaged over tire entire particle. The results are expressed as correlations of the Sherwood or Stanton numbers as a function of Reynolds and Schmidt numbers. 

The rate of mass transfer in the liquid phase in wetted-waU columns is highly dependent on surface conditions. When laminar-flow conditions prevail without the presence of wave formation, the laminar-penetration theory prevails. When, however, ripples form at the surface, and they may occur at a Reynolds number exceeding 4, a significant rate of surface regeneration develops, resulting in an increase in mass-transfer rate. 

Davis EJ, Gill WN (1970) The effect of axial conduction in the waU on heat transfer with laminar flow. Int J Heat Mass Transfer 23 459 70... 

J. C., Irreversibility phenomena associated with heat transfer and fluid friction in laminar flows through singly connected ducts, Int. J. Heat Mass Transfer 40 (1997) 905-914. 

Fig. 5. Local mass transfer rate on the surface of a rotating hemisphere in laminar flow. Here the meridional angle, 9, is given in degrees.

The Chilton-Colburn analogy can be also used to estimate the local mass transfer rate in laminar flow where the wall shear stress is related to the azimuthal velocity gradient by... 

The basic theory of mass transfer to a RHSE is similar to that of a RDE. In laminar flow, the limiting current densities on both electrodes are proportional to the square-root of rotational speed they differ only in the numerical values of a proportional constant in the mass transfer equations. Thus, the methods of application of a RHSE for electrochemical studies are identical to those of the RDE. The basic procedure involves a potential sweep measurement to determine a series of current density vs. electrode potential curves at various rotational speeds. The portion of the curves in the limiting current regime where the current is independent of the potential, may be used to determine the diffusivity or concentration of a diffusing ion in the electrolyte. The current-potential curves below the limiting current potentials are used for evaluating kinetic information of the electrode reaction. 

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