Mass convection

The amount of mass convected into the volume AAx (where A is the area usually taken as unity) is... 

If the reactive gas produced at the burning surface of an energehc material reacts slowly in the gas phase and generates a luminous flame, the distance Lg between the burning surface and the luminous flame front is termed the flame stand-off distance. In the gas phase shown in Fig. 3.9, the temperature gradient appears to be small and the temperature increases relatively slowly. In this case, heat flux by conduction, the first term in Eq. (3.41), is neglected. Similarly, the rate of mass diffusion, the first term in Eq. (3.42), is assumed to be small compared with the rate of mass convection, the second term in Eq. (3.42). Thus, one gets... 

A more detailed picture of the 3D temperature and concentration distribution can be obtained by an appropriate numerical model. Besides the diffusion equations for heat and mass, convection caused by both thermal and solutal expansion needs to be taken into account. 

The transfer of mass from one point to the other may take place by two different modes, namely, diffusion and convection. The basic mechanisms for these modes of mass transfer are similar to those for heat transfer discussed in 4.2 and 4.3. Specifically, the mechanism for mass convection is analogous to heat convection and that for mass diffusion is analogous to heat conduction. 

Mass convection may be due to the bulk motion of the carrier gas or may be associated with the drift of the solute through the carrier gas as a result of net forces applied directly to the solute (e.g., centrifugation due to centrifugal force). Here, we discuss only the convection due to bulk motion of the carrier gas. 

Gr Grashof number for heat or mass convection he Heat convection coeflBcient, cal/cm -sec-K... 

Nn Positive roots of characteristic equation Nu Nusselt number for heat or mass convection P Pressure, atm... 

Gas-phase film thickness for heat or mass convection, cm, or delta... 

Limitation on the Heat-Mass Convection Analogy 816 Mass Convection Relations 816... 

Tire title of the book is changed to Heat and Mass Transfer A Practical Approach to attract attention to the coverage of mass transfer. All topics related to mass transfer, including mass convection and vapor migration through building materials, are introduced in one comprehensive chapter (Chapter 14). 

Various aspects of the analogy between heat and mass convection ate explored in Section 14—9. The analogy is valid for low mass transfer rate cases in which the flow rate of species undergoing mass flow is low (under 10 percent) relative to the total flow rate of the liquid or gas mixture. 

Like heal convection, mass convection is also complicated because of the complications associated with fluid flow such as the surface geomeiiy, flow regime, flow velocity, and the variation of the fluid properties and composition. Therefore, wc have to rely on experimental relations to determine mass transfer. Also, mass convection is usually analyzed on a mass basis rather than on a molar basis. Therefore, sve will present formulations in terms of mass concentration (density p or mass fraction iv) instead of molar concentration (molar density C or mole, fraction y). But the formulations on a molar basis can be obtained using the relation C piM where M is the molar mass. Also, for simplicity, wc will restrict our attention to convection in fluids that are (or can be treated as) binaiy mixtures. 

Consider the flow of air over the free surface of a water body such as a lake under isothermal conditions. If the air is not saturated, the concentration of water vapor will vtsry from a maximum at the water surface where the air is always saturated to the free steam value far from the surface. In heat convection, we defined the region in which temperature gradients exist as the thermal boundary layer. Similarly, in mass convection, we define the region of the fluid in which concentration gradients exist as the conceniration boundary layer, as shown in Figure 14 -38. In external flow, the thickness of the concentration boundary layer S,. for a. species A at a. specified location on the surface is defined as the normal distance y from the surface at which... 

The corresponding quantity in mass convection is the dimensionless Sclunidt number, defined as... 

Analogy between the quantities that appear in the formulation and solution of heat convection and mass convection... 

Finally, the heat-mass convection analogy is valid for low mass flux cases in which the flow rate of species undergoing mass flow is low relative to the total flow rate of the liquid or gas mixture so that the mass transfer between the fluid and the surface does not affect the flow velocity. (Note that convection relations are based on cero fluid velocity at the. surface, which is true only when there is no net mass transfer at the surface.) Therefore, the heat-mass convection analogy is not applicable when the rate of mass transfer of a species is high relative to the flow rate of that species. 

ShenvQod number relations in mass convection for specified concentration at the surface corresponding to the Nusselt number relations in heat convection for specified surface temperature ... 

I EXAMPLt 14-10 Mass Convection inside a Circular Pipe... 

The rale of mass convection of species A in a binary mixture is expressed in an analogous manner to Newton s law of cool-ifig as... 

I4-87C Heat convection is expressed by Newton s law of cooling as (2 = hA T, - T,). Express mass convection in an analogous manner on a mass basis, and identify all the quantities in the expression and state their units. 

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