Chapter - 4 Convective Mass Transfer Essays - Thermodynamics

Chapter - 4 Convective Mass Transfer 4.1 Introduction 4.2 Convective Mass Transfer coefficient 4.3 Significant parameters in convective mass transfer 4. The application of dimensional analysis to Mass Transfer 4.4.1 Transfer into a stream flowing under forced convection 4.4.2 Transfer into a phase whose motion is due to natural convection 5. Analogies among mass, heat, and momentum transfer 4.5.1 Reynolds analogy 4.5.2 Chilton - Colburn analogy 6. Convective mass transfer correlations 4.6.1 For flow around flat plat 4.6.2 For flow around single sphere 4.6.3 For flow around single cylinder 4.6.4 For flow through pipes 7. Mass transfer between phases 8. Simultaneous heat and mass transfer 4.8.1 Condensation of vapour on cold surface 4.8.2 Wet bulb thermometer 4.1 Introduction Our discussion of mass transfer in the previous chapter was limited to molecular diffusion, which is a process resulting from a concentration gradient. In system involving liquids or gases, however, it is very difficult to eliminate convection from the overall mass-transfer process. Mass transfer by convection involves the transport of material between a boundary surface (such as solid or liquid surface) and a moving fluid or between two relatively immiscible, moving fluids. There are two different cases of convective mass transfer: 1. Mass transfer takes place only in a single phase either to or from a phase boundary, as in sublimation of naphthalene (solid form) into the moving air. 2. Mass transfer takes place in the two contacting phases as in extraction and absorption. In the first few section we will see equation governing convective mass transfer in a single fluid phase. 4.2 Convective Mass Transfer Coefficient In the study of convective heat transfer, the heat flux is connected to heat transfer coefficient as [pic] -------------------- (4.1) The analogous situation in mass transfer is handled by an equation of the form [pic] -------------------- (4.2) The molar flux N A is measured relative to a set of axes fixed in space. The driving force is the difference between the concentration at the phase boundary, CAS (a solid surface or a fluid interface) and the concentration at some arbitrarily defined point in the fluid medium, C A . The convective mass transfer coefficient kC is a function of geometry of the system and the velocity and properties of the fluid similar to the heat transfer coefficient, h. 4.3 Significant Parameters in Convective Mass Transfer Dimensionless parameters are often used to correlate convective transfer data. In momentum transfer Reynolds number and friction factor play a major role. In the correlation of convective heat transfer data, Prandtl and Nusselt numbers are important. Some of the same parameters, along with some newly defined dimensionless numbers, will be useful in the correlation of convective mass-transfer data. The molecular diffusivities of the three transport process (momentum, heat and mass) have been defined as: [pic] ----------------------------- (4.3) [pic] --------------------------- (4.4) and [pic]--------------------------- (4.5) It can be shown that each of the diffusivities has the dimensions of L2 / t, hence, a ratio of any of the two of these must be dimensionless. The ratio of the molecular diffusivity of momentum to the molecular diffusivity of heat (thermal diffusivity) is designated as the Prandtl Number [pic] ------------------------ (4.6) The analogous number in mass transfer is Schmidt number given as [pic] -------------- (4.7) The ratio of the molecular diffusivity of heat to the molecular diffusivity of mass is designated the Lewis Number, and is given by [pic] ------------- (4.8) Figure Lewis number is encountered in processes involving simultaneous convective transfer of mass and energy. Let us consider the mass transfer of solute A from a solid to a fluid flowing past the surface of the solid. The concentration and velocity profile is depicted in figure ( ). For such a case, the mass transfer between the solid surface and the fluid may be written as [pic] ---------------------- (4.1 a) Since the mass transfer at the surface is by molecular diffusion, the mass transfer may also described by [pic] ------------------------- (4.9) When the boundary concentration, CAs is constant, equation (4.9) may be written as [pic] ---------------------- (4.10) Equation (4.1a) and (4.10) may be equated, since they define the same flux of component A leaving the surface and entering the fluid [pic] --------------- (4.11) This relation may be rearranged into the following form: [pic] -------------------- (4.12) Multiplying both sides of equation(4.12) by a characteristic length, L we obtain the following dimensionless expression: [pic] ----------------- (4.13) The right hand side of equation (4.13) is the ratio of the concentration gradient at the surface to an overall or reference concentration gradient; accordingly, it may be considered as