Mass diffusion in this section the mass transfer process is described. We use steady state to refer to a system where there may be net transfer of mass or energy to designate that the rate of transfer does not change with time. The above equation is the barometric equation and is used to calculate the pressure at any level above ground. There are 2 mass transfer equations for 2 different mass transfer coefficients, one in the gas phase and another in the liquid phase. J d drc 1 be aware that this is a vectorial equation. Inspecting this equation shows that the dimensions of dis. Describes, in its basic form, the rate at which two gas species diffuse through each other. Fundamentals of momentum, heat, and mass transfer 5th edition fundamentals of momentum, heat, and mass transfer 5th edition james r. Depending on the conditions, the nature, and the forces responsible for mass transfer, four basic types are distinguished. Velocity and temperature profile for natural convection flow over a hot vertical plate. Dec 11, 2008 lecture series on heat and mass transfer by prof.
Selection of the most applicable model is dependent on the materials and the system, or environment, being studied. Note that there is a departure from the linear dependence of or c 1 c 0 at high rates of mass transfer see sherwood et al. If the mass transfer rate calculated to be positive, our assumption of the mass. Time delays appear in many systems, typical examples are delays in nerve propagation, communication and mass transport.
In fact, development in mass transfer theory closely follows that in heat transfer, with the pioneering works of lewis and whitman in 1924 already proposing a mass transfer coefficient. In many instances the heat transfer process is analogous to the rate of transfer which appears in other fields. At this point it is worth citing maxwells statement. Dec 26, 2017 page 4 introduction to mass transfer introduction n three fundamental transfer processes. Convection can be viewed as a macroscopic form of energy transfer through a. Page 4 introduction to mass transfer introduction n three fundamental transfer processes. Proper sampling modes were chosen to eliminate the effect of the sampling zone on the mass transfer characterization in capillary microreactor systems. The mass transfer rate for mass transfer from the gas to the liquid phase can be written as m. Requirements on mass transfer have to be considered in the design of electrochemical reactors, such as the composition, configuration, and control of electrolyte systems. For the specific example of oxygen transporting from air to water, these three steps are. Mass transfer a tables b exact solutions of laminarboundarylayer equations c analytical relations for the heisler charts d use of microsoft excel for solution of heattransfer problems d. Reactions typically occur in a series of multiple reaction steps.
At a point a x al, y ag, we can write the mass transfer equations for each of the phases. O2 is the flux of oxygen out of the system and a is the crosssectional area of the system. Heat transfer equation sheet heat conduction rate equations. Liquidliquid mass transfer performance in a capillary microreactor system was studied with an improved experimental method. Departmentofmathematics universityofcalifornia,berkeley september,2001version 1. Mass transfer and diffusion lecture notes lecture 2. Exact solutions of nonlinear heat and masstransfer equations 405 this equation admits exact solutions of form 7 but has no exact solutions of form 5. The total mass concentration is related to the species mass concentration by. Therefore, mass transfer conditions will also affect heat exchange, heat balance, and operating temperature.
In mass transfer operation, the concentration gradient is the driving force when other driving forces temperature, pressure gradients, etc. Pdf fundamentals of momentum, heat and mass transfer 5ed. Because of its mathematical form, the massspringdamper system will be used as the baseline for analysis of a one degreeoffreedom system. Mass transfer heterogeneous and homogeneous chemical reactions. It means the concentration of the diffusing species at the start t 0 expressed in mass or molar units. Note that when the prandtl number is equal to one, this equation reduces to the reynolds analogy. In gasliquid and liquidliquid separation processes, the mass transfer resistance in. Numerical methods in heat, mass, and momentum transfer. Derivation of the diffusion equation using ficks law. If the temperature t is a function of the height z, then before integration you have to get the relation between t and z then substitute into equation 2. Characterization of liquidliquid mass transfer performance. Bubble size, interfacial area, and liquidphase mass transfer. The equation governing the convective diffusion in a tube is.
Whitman 1924 principles of gas transfer absorption, industrial and engineering chemistry, vol. This course will focus almost exclusively on conduction heat transfer. The conservation equation is written in terms of a speci. Molar flux, n a mass transfer coefficient x driving force. The best solution is to experimentally measure coefficients on a bench scale using a wettedwall column, etc. To define flux, first there must be a quantity q which can flow or move, such as mass, energy, electric charge, momentum, number of molecules, etc. In engineering, the mass transfer coefficient is a diffusion rate constant that relates the mass transfer rate, mass transfer area, and concentration change as driving force. A continuity equation is useful when a flux can be defined. The total mass concentration is the density of the mixture which is the total mass of the mixture per unit volume. The transfer of oxygen from the bulk air to the surface of the water. Mass leaving volume in t the control mass entering interval t in a time control volume mass in the change of a j 1. The condensation or evaporation side of the heat exchanger is associated with.
Therefore instead of analysis of mass transfer using ficks law, it is more convenient to write the molar flux of a using mass transfer equation of the form below. The theory considers that the resistance to mass transfer in a given turbulent fluid phase is present in a thin layer adjacent to the interface that is called a film seader et al. If the total length of the plate is l, then the length. Gaitonde, department of mechanical engineering, iit bombay. The generic model for a one degreeoffreedom system is a mass connected to a linear spring and a linear viscous damper i. Furthermore, this equa tion has more complex solutions of the form. Both temperature and heat transfer can change with spatial locations, but not with time steady energy balance first law of thermodynamics means that heat in plus heat generated equals heat out 8 rectangular steady conduction figure 263 from cengel, heat and mass transfer figure 32 from cengel, heat and mass transfer the heat. Exact solutions of nonlinear heat and masstransfer equations. The transfer of oxygen from the surface of the air to the bulk water. Similarly, it can be shown that the rate of transfer of mass in. The conservation equation is written on a per unit volume per unit time basis. Ppt introduction to mass transfer and diffusion chemical. A species that does not deviate from the velocity of the mixture i. Mass transfer is due partly to the motion of translation and partly to that of agitation.
Wilson department of mechanical engineering gregory l. Determining mass transfer coefficients it isnt reasonable to expect mass transfer coefficients to be readily available for any and all systems. Mass transfer traditionally follows and builds upon that of and not upon fluid heat transfer. Note that the mass velocities of each species in the equation above are given using the mass average velocity for the mixture as reference. Mass transfer heterogeneous and homogeneous chemical. The heat transfer rate in natural convection is expressed by newtons law of cooling as. This page to condensed lecture notes and multimedia resources as it has been presented in class by prof. To describe a mass transfer process by the differential equations of mass transfer the initial and boundary conditions must be specified. When heat flows inside a solid, the continuity equation can be combined with fouriers law heat flux is proportional to temperature gradient to arrive at the heat equation. This form includes the ratio of the mean velocities in the sublayer and core as well as the prandtl number for heat transfer. If the temperature t is a function of the height z, then before integration you have to get the relation between t and z. The analogy between heat transfer and dc electrical current flow will be used to illustrate some of the simpler heat transfer processes.
Interphase mass transfer involves three transfer steps. Mass transfer coefficients can be estimated from many different theoretical equations, correlations, and analogies that are functions of material properties, intensive properties and flow regime laminar or turbulent flow. Heat transfer equation sheet heat conduction rate equations fouriers law heat flux. Welty department of mechanical engineering charles e. Mass transfer operations welcome to a new, useful, and. The general differential equation for mass transfer of component a, or the equation of continuity of a, written in rectangular coordinates is initial and boundary conditions. This page to condensed lecture notes and multimedia resources as it has been presented in. Mass transfer rates from oscillating bubbles in bubble columns operating with viscous fluids. For now, we consider mass transport in a medium at rest and with no chemical reaction. In other words we would say that any mass flux may include both convection and diffusion because in many cases convection may be generated by diffusion. The film theory has been extensively applied to describe the mass transfer in systems in which fluid phases are present. In fact, development in masstransfer theory closely follows that in heat transfer, with the pioneering works of lewis and whitman in 1924 already proposing a masstransfer coefficient. The mass balance for this case can be written in the following form. Mass diffusion page 2 as usual, the basic study first focuses on homogeneous nonreacting systems with welldefined.