PDT377 QUIZ

1. PDT377 QUIZ • Differentiate a cross-flow and counter-flow heat exchanger. • Explain the role of the baffles in a shell-and-tube heat exchanger. How does the presence of baffles affect the heat transfer? Explain. • Sketch the following • 1 shell pass 1 tube pass • 2 shell pass 4 tube pass • 1 shell pass 3 tube pass

2. Mass Transfer

3. Introduction • Three fundamental transfer processes: • Momentum transfer • Heat transfer • Mass transfer

4. Mass transfer may occur in a gas mixture, a liquid solution or solid. • Mass transfer occurs whenever there is a gradient in the concentration of a species. • The basic mechanisms are the same whether the phase is a gas, liquid, or solid.

5. Definition of Concentration i) Number of molecules of each species present per unit volume (molecules/m3) ii) Molar concentration of species i = Number of moles of i per unit volume (kmol/m3) iii) Mass concentration = Mass of i per unit volume (kg/m3)

6. Diffusion phenomena • Fick’s law: linear relation between the rate of diffusion of chemical species and the concentration gradient of that species. • Thermal diffusion: Diffusion due to a temperature gradient. Usually negligible unless the temperature gradient is very large. • Pressure diffusion: Diffusion due to a pressure gradient. Usually negligible unless the pressure gradient is very large.

7. Forced diffusion: Diffusion due to external force field acting on a molecule. Forced diffusion occurs when an electrical field is imposed on an electrolyte ( for example, in charging an automobile battery) • Knudsen diffusion: Diffusion phenomena occur in porous solids.

8. Diffusion process • If we define the amount of a commodity per unit volume as the concentration of that commodity, we can say that the flow of a commodity is always in the direction of decreasing concentration; that is, from the region of high concentration to the region of low concentration • The commodity simply creeps away during redistribution, and thus the flow is a diffusion process.

9. The rate of flow of the commodity is proportional to the concentration gradient dC/dx, which is the change in the concentration C per unit length in the flow direction x, and the area A normal to flow direction and is expressed as kdiff is the diffusion coefficient of the medium Flow rate ∝ (Normal area)(Concentration gradient) or

10. Before After • Whenever there is concentration difference in a medium, nature tends to equalize things by forcing a flow from the high to the low concentration region. • The molecular transport process of mass is characterized by the general equation: Rate of transfer process = driving force resistance

11. Example of Mass Transfer Processes • Consider a tank that is divided into two equal parts by a partition. • Initially, the left half of the tank contains nitrogen N2 gas while the right half contains O2 at the same temperature and pressure. • When the partition is removed the N2 molecules will start diffusing into the air while the O2 molecules diffuse into the N2. • If we wait long enough, we will have a homogeneous mixture of N2 and O2 in the tank.

13. Liquid in open pail of water evaporates into air because of the difference in concentration of water vapor at the water surface and the surrounding air. • A drop of blue liquid dye is added to a cup of water. The dye molecules will diffuse slowly by molecular diffusion to all parts of the water.

15. Factors influencing diffusion process • Temperature • The diffusion coefficients and thus diffusion rates of gases depend strongly on temperature since the temperature is a measure of the average velocity of gas molecules. • Therefore, the diffusion rates will be higher at higher temperatures.

16. Factors influencing diffusion process • Molecular spacing • The larger the spacing, in general, the higher the diffusion rate. • Therefore, the diffusion rates are typically much higher in gases than they are in liquids and much higher in liquids than in solids.

17. Factors influencing diffusion process • Molecular spacing • The larger the spacing, in general, the higher the diffusion rate. • Therefore, the diffusion rates are typically much higher in gases than they are in liquids and much higher in liquids than in solids.

18. Factors influencing diffusion process • Molecular spacing • The larger the spacing, in general, the higher the diffusion rate. • Therefore, the diffusion rates are typically much higher in gases than they are in liquids and much higher in liquids than in solids.

19. ANALOGY BETWEENHEAT AND MASS TRANSFER • The mechanisms of heat and mass transfer are analogous to each other, and thus we can develop an understanding of mass transfer in a short time with little effort by simply drawing parallels between heat and mass transfer

20. ANALOGY BETWEENHEAT AND MASS TRANSFER

21. ANALOGY BETWEENHEAT AND MASS TRANSFER • Temperature • The driving force for heat transfer is the temperature difference. In contrast, the driving force for mass transfer is the concentration difference. • We can view temperature as a measure of “heat concentration,” and thus a high temperature region as one that has a high heat concentration (Fig. 14–4). Therefore, both heat and mass are transferred from the more concentrated regions to the less concentrated ones.

22. ANALOGY BETWEENHEAT AND MASS TRANSFER • Heat Generation • Heat generation refers to the conversion of some form of energy such as electrical, chemical, or nuclear energy into sensible heat energy in the medium.

23. ANALOGY BETWEENHEAT AND MASS TRANSFER Convection • You will recall that heat convection is the heat transfer mechanism that involves both heat conduction (molecular diffusion) and bulk fluid motion. • Fluid motion enhances heat transfer considerably by removing the heated fluid near the surface and replacing it by the cooler fluid further away. • Likewise, mass convection (or convective mass transfer) is the mass transfer mechanism between a surface and a moving fluid that involves both mass diffusion and bulk fluid motion.

24. Convection Mass Transfer • In mass convection, we define a concentration boundary layer in an analogous manner to the thermal boundary layer and define new dimensionless numbers that are counterparts of the Nusselt and Prandtl numbers.

25. ANALOGY BETWEENHEAT AND MASS TRANSFER Convection

26. ANALOGY BETWEENHEAT AND MASS TRANSFER Where hmassis the mass transfer coefficient As is the surface area, is a suitable concentration difference across the concentration boundary layer.

27. ANALOGY BETWEENHEAT AND MASS TRANSFER Conduction • Heat transfer • Heat  conduction, convection, radiation. • Mass transfer • Mass is transferred by conduction (called diffusion) and convection only, and there is no such thing as “mass radiation”. the rate of mass diffusion of a chemical species A in a stationary medium in the direction x is proportional to the concentration gradient dC/dx in that direction and is expressed by Fick’s law of diffusion where DAB is the diffusion coefficient (or mass diffusivity) of the species in the mixture CA is the concentration of the species in the mixture at that location.

29. Molecular Diffusion Equation • Fick’s Law • is the diffusion coefficient or molecular or mass diffusivity of the molecule A in B in m2/s • CA is the concentration of A in kg mol/m3.

30. Fick’s Law of Diffusion • Molecular diffusion or molecular transport can be defined as the transfer or movement of individual molecules through a fluid by mean of the random, individual movements of the molecules. • If there are greater number of A molecules near point (1) than at (2), then since molecules diffuse randomly in both direction, more A molecules will diffuse from (1) to (2) than from (2) to (1). • The net diffusion of A is from high to low concentration regions. (2) A B B B B B B B B B B B (1) A Figure 3: Schematic diagram of molecular diffusion process

31. The two modes of mass transfer: • Molecular diffusion • Convective mass transfer

32. Molecular diffusion The diffusion of molecules when the whole bulk fluid is not moving but stationary. Diffusion of molecules is due to a concentration gradient.

33. Mass diffusion • Fick’s law of diffusion, proposed in 1855, states that the rate of diffusion of a chemical species at a location in a gas mixture (or liquid or solid solution) is proportional to the concentration gradient of that species at that location. • Although a higher concentration for a species means more molecules of that species per unit volume, the concentration of a species can be expressed in several ways. Next we describe two common ways.

38. True or False • Doubling the mass fraction of the diffusing species at the high concentration side will double the rate of mass transfer. • The higher the density of the wall, the higher the rate of mass transfer.

39. True or False • Doubling the mass fraction of the diffusing species at the high concentration side will double the rate of mass transfer.  False • The higher the density of the wall, the higher the rate of mass transfer.  True

42. Fick’s Law of Diffusion: Stationary Medium Consisting of Two Species • We mentioned earlier that the rate of mass diffusion of a chemical species in a stagnant medium in a specified direction is proportional to the local concentration gradient in that direction. • This linear relationship between the rate of diffusion and the concentration gradient proposed by Fick in 1855 is known as Fick’s law of diffusion and can be expressed as

43. Fick’s Law of Diffusion: Stationary Medium Consisting of Two Species • But the concentration of a species in a gas mixture or liquid or solid solution can be defined in several ways such as density, mass fraction, molar concentration, and mole fraction, as already discussed, and thus Fick’s law can be expressed mathematically in many ways. • It turns out that it is best to express the concentration gradient in terms of the mass or mole fraction, and the most appropriate formulation of Fick’s law for the diffusion of a species A in a stationary binary mixture of species A and B in a specified direction x is given by

46. Remember that the constant of proportionality in Fourier’s law was defined as the transport property thermal conductivity. • Similarly, the constant of proportionality in Fick’s law is defined as another transport property called the binary diffusion coefficient or mass diffusivity, DAB. • The unit of mass diffusivity is m2/s, which is the same as the units of thermal diffusivity or momentum • diffusivity (also called kinematic viscosity) (Fig. 14–11).

47. The diffusion coefficients of solids and liquids also tend to increase with temperature while exhibiting a strong dependence on the composition. • The diffusion process in solids and liquids is a great deal more complicated than that in gases, and the diffusion coefficients in this case are almost exclusively determined experimentally.

48. The binary diffusion coefficient for several binary gas mixtures and solid and liquid solutions are given in Tables 14–2 and 14–3. We make these two observations from these tables: • 1. The diffusion coefficients, in general, are highest in gases and lowest in solids. The diffusion coefficients of gases are several orders of magnitude greater than those of liquids. • 2. Diffusion coefficients increase with temperature. The diffusion coefficient (and thus the mass diffusion rate) of carbon through iron during a hardening process, for example, increases by 6000 times as the temperature is raised from 500°C to 1000°C.