mac of bones: August 2007

ESE5002 Mini Project (5% Mark)

Your name: Your matriculation No.:

Literature study to briefly explain the following terms

1. What is convection/advection and how it contributes to mass transfer?

Convection in the most general terms refers to the movement of currents within fluids (i.e. liquids, gases and rheids).

Convection is one of the major modes of Heat and mass transfer. In fluids, convective heat and mass transfer take place through both diffusion – the random Brownian motion of individual particles in the fluid – and by advection, in which matter or heat is transported by the larger-scale motion of currents in the fluid. In the context of heat and mass transfer, the term "convection" is used to refer to the sum of advective and diffusive transfer.^[1]

A common use of the term convection relates to the special case in which the advected (carried) substance is heat. In this case, the heat itself often causes the fluid motion, while also being transported by it. In this case, the problem of heat transport (and related transport of other substances in the fluid due to it) may be more complicated.

Advection is transport in a fluid. The fluid is described mathematically for such processes as a vector field, and the material transported is described as a scalar concentration of substance, which is present in the fluid. A good example of advection is the transport of pollutants or silt in a river: the motion of the water carries these impurities downstream (see pigpen problem). Another commonly advected substance is heat, and here the fluid may be water, air, or any other heat-containing fluid material. Any substance, or conserved property (such as heat) can be advected, in a similar way, in any fluid.

Advection is important for the formation of orographic cloud and the precipitation of water from clouds, as part of the hydrological cycle.

In meteorology and physical oceanography, advection often refers to the transport of some property of the atmosphere or ocean, such as heat, humidity (see moisture) or salinity. Meteorological or oceanographic advection follows isobaric surfaces and is therefore predominantly horizontal.

2. What is diffusion and how it contributes to mass transfer?

Diffusion is the phenomenon of random motion causing a system to decay towards uniform conditions. For example, diffusion of particles causes a net movement of particles from areas of higher concentration to areas of lower concentration until equilibrium is reached. This is simply the statistical outcome of random motion: diffusion is a spontaneous process (more familiarly known as a "passive" form of transport, rather than "active"). Diffusion can affect a variety of different quantities. Examples include diffusion of concentration, heat, or momentum. Diffusion increases entropy, decreasing Gibbs free energy, and therefore is thermodynamically favorable.

Diffusion can be described mathematically by the diffusion equation. This equation is derived from Fick's law, which states that the net movement of diffusing substance per unit area of section (the flux) is proportional to the concentration gradient (how steeply the concentration changes in space), and is toward lower concentration. (Thus if the concentration is uniform there will be no net motion.) The constant of proportionality is the diffusion coefficient, which depends on the diffusing species and the material through which diffusion occurs. Fick's law is an assumption that may not hold for a given diffusive system (e.g., the diffusion may depend on concentration in addition to concentration gradient), in which case the motion would not be described by the normal (simple, Fickian) diffusion equation. An analogous statement of Fick's law, for heat instead of concentration, is Fourier's law.

Diffusion can also be described using discrete quantities (the diffusion equation has derivatives and thus applies to continuous quantities). A common model of discrete diffusion is the random walk. A random walk model is connected to the diffusion equation by considering an infinite number of random walkers starting from a non-uniform configuration, where the evolution of the concentration is described by the diffusion equation.

The spreading of any quantity that can be described by the diffusion equation or a random walk model (e.g. momentum, ideas, price) can be called diffusion.

Diffusion is often important in systems experiencing an applied force. In a conducting material, the net motion of electrons in an electrical field quickly reaches a terminal velocity (resulting in a steady current described by Ohm's law) because of the thermal (diffusive) motions of atoms. The Einstein relation relates the diffusion coefficient to the mobility of particles.

3. What is dispersion and how it contributes to mass transfer?

Dispersive mass transfer is the spreading of mass from highly concentrated areas to less concentrated areas. It is one form of mass transfer.

Dispersive mass flux is analogous to diffusion, and is written:

J = - E (d c / d x)

where c is mass concentration of the species being dispersed, E is the dispersion coefficient, and x is the position in the direction of the concentration gradient.

4. What are a plug flow reactor and its concentration characteristic?

The plug flow reactor (PFR) model is used to describe chemical reactions in continuous, flowing systems. One application of the PFR model is the estimation of key reactor variables, such as the dimensions of the reactor. (See Chemical reactors.). PFRs are also sometimes called as Continuous Tubular Reactors (CTRs).

Schematic diagram of a Plug Flow Reactor (PFR)

Fluid going through a PFR may be modelled as flowing through the reactor as an infinitely thin coherent "plug", where the plug is of a uniform composition travelling in the axial direction of the reactor, but with differing composition to the leading and trailing plugs. The required assumption is that as a plug flows through a PFR, the fluid is perfectly mixed in the radial direction but not in the axial direction (forwards or backwards). Each plug of differential volume is considered as a separate entity, effectively an infinitesimally small batch reactor, limiting to zero volume. As it flows down the tubular PFR, the residence time ( $τ$ ) of the plug is a function of its position in the reactor. In the ideal PFR, the residence time distribution is therefore a Dirac delta function with a value equal to $τ$ .

5. What are a completely mixed flow reactor and its concentration characteristic?

The continuous stirred-tank reactor (CSTR) model is used to estimate the key unit operation variables when using a continuous agitated-tank reactor to reach a specified output. (See Chemical reactors.) The mathematical model works for all fluids: liquids, gases, and slurries.

In a CSTR, one or more fluid reagents are introduced into a tank reactor equipped with an impeller while the reactor effluent is removed. The impeller stirs the reagents to ensure proper mixing. Simply dividing the volume of the tank by the average volumetric flow rate through the tank gives the residence time, or the average amount of time a discrete quantity of reagent spends inside the tank. Using chemical kinetics, the reaction's expected percent completion can be calculated. Some important aspects of the CSTR:

At steady-state, the flow rate in must equal the mass flow rate out, otherwise the tank will overflow or go empty (transient state). While the reactor is in a transient state the model equation must be derived from the differential mass and energy balances.
All calculations performed with CSTRs assume perfect mixing.
The reaction proceeds at the reaction rate associated with the final (output) concentration.
Often, it is economically beneficial to operate several CSTRs in series or in parallel. This allows, for example, the first CSTR to operate at a higher reagent concentration and therefore a higher reaction rate. In these cases, the sizes of the reactors may be varied in order to minimize the total capital investment required to implement the process.
It can be seen that an infinite number of infinitely small CSTRs operating in series would be equivalent to a PFR.

For ESE5002, given your opinion, if any, on:

1. What might be the most difficult part to you?

2. What may be of concern to you?

(Control the length within 3-5 pages. To be submitted by 29 Aug. 2007)

Finally I have learned how to use LaTeXiT to form mathematical equations & most of all to ALIGN multi-line equations to the equal mark (that's something that looks easy but damn complex to practice!) It's so simple that even the menu and the intro book I have found don't give a shit of how-to. After several hours of trying...trying... eventually I find out just put two "&" tab alignment sign at both end of the "=", then suddenly all things sort it in a flash!

M &=& [\int^5_0 {c_{(x)}}\cdot {dx}]\times 24m^2\\
&=& [\int^5_0 {\frac {2}{1+6\cdot{x}}}\cdot {dx}]\times 24m^2\\
&=& \frac {1}{6} [\int^5_0 {\frac {2}{1+6x}}\cdot {d(1+6x)}]\times 24m^2\\
&=& \frac{1}{3}\ln[31]kg/m^2\times 24m^2\\
&=& 8\ln{31}kg\\
&=& 27.47kg

Look! It comes out perfect!

Some useful imformation about LaTeX

LaTeX is a document markup language and document preparation system for the TeX typesetting program. Within the typesetting system, its name is styled as $\mathrm{L\!\!^{{}_{\scriptstyle A}} \!\!\!\!\!\;\; T\!_{\displaystyle E} \! X}$ .

It is widely used by mathematicians, scientists, philosophers, engineers, scholars in academia and the commercial world, and other professionals. As a primary or intermediate format (e.g. translating DocBook and other XML-based formats to PDF) LaTeX is used because of the quality of typesetting achievable by TeX. The typesetting system offers programmable desktop publishing features and extensive facilities for automating most aspects of typesetting and desktop publishing, including numbering and cross-referencing, tables and figures, page layout and bibliographies.

LaTeX is intended to provide a high-level language that accesses the power of TeX. LaTeX essentially comprises a collection of TeX macros and a program to process LaTeX documents. Because the TeX formatting commands are very low-level, it is usually much simpler for end-users to use LaTeX.

LaTeX was originally written in the early 1980s by Leslie Lamport at SRI International ^[1]. It has become the dominant method for using TeX—few people write in plain TeX anymore. The current version is LaTeX2e (styled $\mathrm{L\!\!^{{}_{\scriptstyle A}} \!\!\!\!\!\;\; T\!_{\displaystyle E} \! X} \, 2_{\displaystyle \varepsilon}$ ).
LaTeX, like TeX, is free software