Heat Conduction in a cooling fin

ADVANCED TRANSPORT PROCESSES /

TRANSPORT PHENOMENACCB/CBB 30335. Mass TransportLesson 24: Introduction to Mass TransportCourse Outcomes

Semester May 2013CLO1Explain the theoretical aspect of momentum, mass and energy transportCLO2Apply mathematical and numerical methodology in analyzing momentum transfer problemCLO3Apply mathematical and numerical methodology in analyzing heat transfer problemCLO4Apply mathematical and numerical methodology in analyzing mass transfer problemCLO5Analyze and solve transport phenomena using Computational Fluid Dynamics (CFD) tools.23At the end of the lesson the student should be able to Lesson 24. Introduction to Mass transportExplain the principle of mass transfer.Formulate the Concentration distribution for diffusion through stagnant gas film. Lesson outcomesMolecular transport/diffusion is the movement ofindividual molecules through fluid by means of random motion of the molecules. (random-walk process)Overview4First, to get a general idea, let me begin with the outline of my presentation.The background of the problem and a brief overview of ozone photochemistry will be introduced to gain familiarity with the subject.Then I will go over some of the previous works that are based on statistical methodologies.The environmental and meteorological data sets used in this work will be discussed next. Here the time series of ozone and its covariates are explored and the annual trends are illustrated.The gist of this work lies on the application of statistical analyses as an avenue to investigate O3 phenomena. In particular, the results of O3 predictions based on linear regression, kriging and stochastic simulation will be shown.Last but not least, I will conclude by presenting the main findings of this research and making some recommendations for future research works.Modes of mass transfer:1. Diffusiona. Molecular diffusionb. Knudsen diffusion. ( gas )2. Convection.Diffusion is more complicated than viscous flow or heat conduction because we deal with mixtures( more than one component)Overview5First, to get a general idea, let me begin with the outline of my presentation.The background of the problem and a brief overview of ozone photochemistry will be introduced to gain familiarity with the subject.Then I will go over some of the previous works that are based on statistical methodologies.The environmental and meteorological data sets used in this work will be discussed next. Here the time series of ozone and its covariates are explored and the annual trends are illustrated.The gist of this work lies on the application of statistical analyses as an avenue to investigate O3 phenomena. In particular, the results of O3 predictions based on linear regression, kriging and stochastic simulation will be shown.Last but not least, I will conclude by presenting the main findings of this research and making some recommendations for future research works.6 Mass Transport Equation Ficks Law

How a steady state concentration profile for the diffusion of helium (A) through fused silica (B) builds. The symbol A stands for the mass fraction of helium, and A0 is the solubility of helium in fused silica.Mass Transport Equation Ficks Law7

Divergence, divAt steady statewAy The mass flow of A in positive y directionA Mass fraction of helium, A0 Solubility of helium in fused silica, Mass concentration jAy The molecular mass flux of helium in positive y directionDAB The diffusivity of silica-helium systemFicks first law of diffusion Diffusivity, DAB

Gas Pairs8First, to get a general idea, let me begin with the outline of my presentation.The background of the problem and a brief overview of ozone photochemistry will be introduced to gain familiarity with the subject.Then I will go over some of the previous works that are based on statistical methodologies.The environmental and meteorological data sets used in this work will be discussed next. Here the time series of ozone and its covariates are explored and the annual trends are illustrated.The gist of this work lies on the application of statistical analyses as an avenue to investigate O3 phenomena. In particular, the results of O3 predictions based on linear regression, kriging and stochastic simulation will be shown.Last but not least, I will conclude by presenting the main findings of this research and making some recommendations for future research works.Diffusivity, DABLiquid Mixture

9First, to get a general idea, let me begin with the outline of my presentation.The background of the problem and a brief overview of ozone photochemistry will be introduced to gain familiarity with the subject.Then I will go over some of the previous works that are based on statistical methodologies.The environmental and meteorological data sets used in this work will be discussed next. Here the time series of ozone and its covariates are explored and the annual trends are illustrated.The gist of this work lies on the application of statistical analyses as an avenue to investigate O3 phenomena. In particular, the results of O3 predictions based on linear regression, kriging and stochastic simulation will be shown.Last but not least, I will conclude by presenting the main findings of this research and making some recommendations for future research works.Diffusivity, DABSolid

10First, to get a general idea, let me begin with the outline of my presentation.The background of the problem and a brief overview of ozone photochemistry will be introduced to gain familiarity with the subject.Then I will go over some of the previous works that are based on statistical methodologies.The environmental and meteorological data sets used in this work will be discussed next. Here the time series of ozone and its covariates are explored and the annual trends are illustrated.The gist of this work lies on the application of statistical analyses as an avenue to investigate O3 phenomena. In particular, the results of O3 predictions based on linear regression, kriging and stochastic simulation will be shown.Last but not least, I will conclude by presenting the main findings of this research and making some recommendations for future research works. Ficks law of diffusion for binary mixtures11

The basic equation for Ficks law for an isobaric and isothermal system is : A = the mass fraction of A jAy [=] kg/m2s Molecular (diffusive) mass flux in y direction DAB[=] m2/s.. Diffusivity Molar & Mass Flux The previously discussed Ficks Law of diffusion was given in terms of mass units, in general:when chemical reactions are involved, molar units are preferredWhen the diffusion equations are solved together with the equation of motion, mass units are usually preferred. Therefore it is necessary to be familiar with both12Molar & Mass Flux13The mass concentration is defined as the mass of species per unit volume of solution

The mass fraction is defined as the mass of species per unit volume of the solution divided by the total mass of all species per unit volume of solution.

The mass flux

Molar & Mass Flux14

The molar concentration c is defined as the number of moles of species per unit volume of solution.

The molar fraction x is defined as the number of moles of species per unit volume of solution divided by the total number of moles of all species per unit volume of solution.

The molar flux

Molar & Mass Flux15Comparison of mass flux and molar flux formula

The mass fluxThe molar flux The convective mass flux16

The convective molar flux17

Combined Mass Flux18Combined Mass Flux of species A in z-direction is given by :

Molecular fluxConvective fluxResulting from concentration gradientSimilarly for species B:Resulting from the bulk motion of the fluid

Combined Molar Flux19Combined Molar Flux of species A in z-direction is given by :

Molecular fluxConvective fluxResulting from concentration gradientSimilarly for species B:

Resulting from the bulk motion of the fluid20At the end of the lesson the student should be able to Lesson 24. Introduction to Mass transportExplain the principle of mass transfer.Formulate the Concentration distribution for diffusion through stagnant gas film. Lesson outcomes