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The following quote (in italics) at the end of the book by BSL is an appropriate closing remark for this book.
No engineering project can be conceived, let alone completed, purely through the use of descriptive disciplines, such as transport phenomena. Transport phenomena can, however, prove immensely helpful by providing useful approximations, starting with order-of-magnitude estimates and going on to successively more accurate approximations.
I have tried to provide the knowledge base for this with scaling concepts, dimensionless arguments, and modeling at three scales, together with some computational snippets.
Much remains to be done, but the utility of transport phenomena can be expected to increase rather than diminish. Many challenges remain to be met. The quantitative undertones provided by transport phenomena will prove to be an immense help. I hope that you, the students and the readers, will able to participate in this exciting field.
• Orthogonal functions; the Sturm–Liouville equation.
• Fourier expansion of a function and evaluation of the Fourier coefficients.
• The Laplace transform and inverse Laplace transforms.
• Complex representation of a sine or cosine function; manipulations of complex variables.
In Chapters 8 and 10 we examined a number of steady-state problems in heat and mass transfer. In this chapter we examine unsteady-state problems. Owing to the similar mathematical structure heat and mass transfer problems can be treated in a similar manner. The concentration or temperature is now a function of both time and the spatial coordinates, and therefore the governing equations are now partial differential equations. This adds additional mathematical complexity to the solution. The most general problem in 3D and time and with time-varying boundary conditions needs a numerical solution. However, there are many simpler but nevertheless important problems where analytic solutions are possible and useful. This chapter introduces and solves such problems and illustrates a number of important techniques to obtain the solutions.
For linear partial differential equations, analytic solutions based on the method of separation of variables are commonly used. It can be applied to problems where the differential equations and the boundary conditions are homogeneous (as will be explained in the text) and applies to problems posed in a finite spatial domain.
No new mathematical perquisites are needed for the study of this chapter. The student may wish to revise the Green–Gauss theorem for converting volume integrals to surface integrals for the derivation of macroscopic models. The notion of the substantial derivative must also be revisited.
Problems involving mass transport are important in many contexts and find applications in chemical, biological, and environmental processes. Some examples were discussed in Chapter 1, and more will follow as we progress further through the study of mass transport processes. We have already solved some illustrative problems involving mass transfer in Chapter 2. The approach demonstrated there employed a problem-to-problem basis. For a specified problem, we studied how the mass conservation principle followed by the constitutive equation can be used for setting up models for problems involving diffusion and in some cases diffusion with reaction. Simple Fick's law was used as the constitutive model for diffusion. The goal of this chapter is to provide a more formal setting and derive general differential equations for mass transfer. The chapter is organized as follows.
As a preliminary, the concentration and other necessary variables needed to characterize mass transfer are introduced. This is followed by a brief discussion on the conditions prevailing at a phase interface (a gas–liquid boundary, for example).
No additional mathematical tools are needed for the study of this chapter. You may wish to review the vector calculus, plus your knowledge of tensors and the various operations on tensor quantities.
This chapter starts with the development of the differential equation of motion, which is nothing but the statement of the momentum conservation principle. Thus we combine the fluid acceleration calculations derived in Chapter 3 and the representation of forces derived in Chapter 4. This leads to a general equation of motion that is based on the conservation principle alone. This is the basic model for the transport of momentum, which is also called the equation of (fluid) motion. As you may have guessed already, the divergence of the stress tensor will appear as a term, and the model is not in terms of the velocity alone. The model needs to be closed with appropriate constitutive relations between the stress and the strain rate. This requires knowledge of the rheological properties or the flow behavior of the fluid. Hence a discussion of common fluid behaviour is presented, and a classification of the rheological behaviors of fluids is presented next. Fluids obeying a linear relation are referred to as Newtonian fluids.
This chapter continues the theme of convective transfer from Chapter 12, which discussed mainly problems with internal laminar flow. This chapter extends the study to other flow problems (e.g., external flow) and parallels Chapter 18 on convective heat transfer. The main goal is to examine how mass transfer rates and transfer coefficients can be calculated for illustrative problems for a prescribed or computed velocity profile. First we start with a well-defined flow problem, viz., laminar external flow over a flat plate with a low-flux model for mass transport taking place from (or to) the plate surface. This problem of mass transfer in boundary-layer flow is analyzed by four techniques, namely (i) dimensionless analysis, (ii) scaling analysis, (iii) integral analysis, and (iv) the similarity-transformation method. As discussed earlier, these are some of the widely used tools for solution of transport problems. Applying them to the same problem will give the student a good understanding of these tools. The similarity to heat transfer is also pointed out. One important difference is that mass transfer is often accompanied by chemical reaction. Hence we also examine how the chemical reaction modifies the rate of mass transfer.
The next problem examined in this chapter is the high-flux case where convection induced by mass transfer cannot be neglected. Various engineering models useful for such systems are presented.
No additional prerequisites are needed. Some idea of the Fourier transform is, however, useful to understand the last section of this chapter.
Turbulence is the result of flow instability. Any small disturbance could lead to a chaotic type of flow with velocity fluctuating on a small time scale around a mean value. This happens (usually) when the viscous forces are much smaller than the inertial forces. The viscosity effect stabilizes the flow and dampens any disturbance. In the absence of significant viscous forces, any disturbance persists and leads to a continuous fluctuation of velocity, leading to turbulent flow. Thus turbulent flows are characterized by small random fluctuations around a mean value and essentially are chaotic unsteady-state phenomena.
The goal of this chapter is to provide an introductory treatment of turbulent flow. The first goal is look at the time averaging of the Navier–Stokes (N–S) equations. The main idea is that, although the velocity field may be random in nature, the statistical (average) properties of flow are quite reproducible. This suggests that some time-averaged form of equation of motion can be used for practical applications. The problem associated with time averaging is the closure problem. As we have mentioned many times before, the averaging leads to a loss of information.
With the ubiquitous presence of technology, generating meaning in contemporary times harnesses influential technological capacities which have not only created a changed textual landscape ... but ... shifted the nature of interactions between people in their interpersonal, virtual, digital and textual spaces.
Christine Edwards-Groves (2012, p. 110)
Can you recall the technologies that were available to you when you were growing up? What kind of technologies do you remember your own school teachers using? Do you recall feeling excited when your teachers brought new technologies into the class? Did it make any difference to your learning or make you feel differently about school? How do those technologies compare with the technologies that are currently available to educators? How confident are you about using digital technologies in your teaching? Do you think it is important to use new technologies? How do you learn about the ways in which new technologies might enhance your classroom practice?
Over the past two or three decades increasing attention has been given to new technologies in education generally and in literacy education in particular. This attention has focused on multimodal technologies and social media that children and young people use in their everyday lives outside of school. James Gee argues that the practices of digital gaming reflect powerful learning, showing the complex cognitive operations in which teenagers engage when they play computer games (Gee 2003, 2007). Given the role that digital technologies play in young people’s lives, some educators have questioned whether schools provide sufficient opportunities for them to use and learn from such activities (Lankshear, Green & Snyder 2000; Lankshear & Knobel 2003).While some students are highly engaged in social media in out of school contexts, they are not necessarily able to use such media in schools and classroom settings and to reflect upon that use. How can schools possibly claim to be educating young people for the 21st century if they systematically exclude from the curriculum the digital literacy practices that are part of the modern world?
If we want to progress education reform and change, then the importance of value positions that are grounded by social and cultural beliefs about education, learning and difference need to be acknowledged.
Suzanne Carrington, Joanne Deppeler and Julianne Moss (2012, p. 1)
The literacy classroom: working to each child’s potential
In Australia, all young people have a right to attend their local school and to receive a good education. These rights are strongly protected in law.
The Melbourne Declaration on Educational Goals for Young Australians, ratified by the State, Territory and Commonwealth Ministers of Education meeting at the Ministerial Council on Education, Employment, Training and Youth Affairs (MCEETYA) in 2008, has two goals. First, that Australian schooling should promote equity and excellence.
You would find it useful to read the whole of The Melbourne Declaration on Education Goals for Young Australians. This document emerged out of negotiations between the Federal Government and the Australian states and territories, and provides a blueprint for educational reform in all sectors.
Second, that all young Australians should become successful learners, confident and creative individuals, and active and informed citizens (Commonwealth of Australia 2005, p. 7). This includes young Australians who have a disability.
In this chapter, we survey important workplace communication research, with the aim of showing how a combination of methods and theoretical concepts may contribute to intercultural understanding and smoother working relationships. The 1990s saw a series of key workplace communication studies, with many of these originating from the Australian context. Michael Clyne (1994), in particular, building on the seminal work of John Gumperz, played a major role in spearheading studies of intercultural communication in the workplace. In recent years, there have been growing numbers of workplace studies in the United Kingdom, the United States and beyond. We review some of these studies here to demonstrate how workplace research has evolved in recent years. In any case, a survey of intercultural communication in the workplace shows how research may highlight the causes of miscommunication and how such miscommunication may be resolved.
This book has noted a few times by now that within the intercultural communication field there has been an increased focus on ethnography, naturally occurring conversations and constructivist approaches in the past few decades. Thus, in this chapter we begin each section with a review of some of the seminal 1990s studies of workplaces. We use these as a foundation for discussing more recent and more ethnographically and constructivist-driven approaches. In doing so, we introduce a few more useful theoretical concepts for understanding workplace culture. Of particular note, monolithic, homogenous and nationalistic accounts of workplace cultures have been shown to be reductive. Thus, we show how the Community of Practice, devised in the field of education and used extensively by sociolinguists, provides a useful frame for understanding workplace culture(s).
Mis communications emerge in conversations between Korean shopkeepers and African American customers in Los Angeles, as we observed at the start of Chapter 2. We linked this miscommunication to the two groups speaking at cross-purposes: financial transactions and social exchanges respectively (Bailey 2001). Yet, even when these groups speak with the same purpose, miscommunication can result from differing conversational styles. In the following social exchange, an African American customer (‘cust’) describes a recent trip to Chicago to a Korean shop owner (‘own’), who has been in the United States for 20 years and has a degree from the University of California, Los Angeles:
1 Own: Is Chicago cold?
2 Cust: Uh:::h! ((lateral headshakes)) ((1.4-second pause)) man I got off the plane and walked out the airport and I said ‘oh shit.’
3 heh heh heh
4 Own: I thought it’s gonna be a nice spring over there
5 Cust: Well not now this is about a month – I been there – I was there
6 but you know (.) damn ((lateral headshakes))
7 ((1.4-second pause)) Too co:l’
8 I mean this was really cold.
(adapted from Bailey 2001, p. 131)
The African American customer’s style is emotional, performed and involved. This includes the use of falsetto voice, engaged body language (e.g. lateral headshakes) and profanity. The Korean shopkeeper’s style is less involved. He is looking at the floor and unsmiling as the customer recounts his trip.
Unlike humans, cephalopods don’t have blind spots, that is they don’t have an absence of photoreceptor cells in the retina. Humans usually don’t notice their blind spot because the other eye helps the brain fill in the missing information.
Chris Bigum & Leonnie Rowan (2012, p. 1)
Chris Bigum and Leonnie Rowan speculate about coming back as cephalopods. That way they wouldn’t have any blind spots with respect to their professional practice as educators. This metaphor is a good way to begin thinking about the complexities of your professional practice as a literacy educator in a primary classroom. Teachers often feel that there is something they could do better or that there is a ‘blind spot’ in their professional knowledge and practice they need to address.
This is not just something that applies to early career teachers. Experienced teachers also feel the need to engage in ongoing professional learning. They might have become aware of a new understanding about the relationship between print and visual media, or perhaps a new program that is being implemented in a neighbouring school that uses popular social media to engage children in their learning. Or, it could be a moment when they have gained insight into the values of the school community in which they are teaching, which helps to explain the children’s attitude towards schooling. Good teachers are always trying to fill the gaps in their knowledge in the process of interacting with their students, other teachers and the school administration. This is in order to develop their professional practice in a way that supports the literacy learning of all the students in their class and the school as a whole.
Staff at a British airport once complained that newly hired Indian and Pakistani cafeteria workers were uncooperative and surly. This was in spite of few words being exchanged between the staff and new workers. Gumperz (2004 [1982]) studied communication between the groups and found the miscommunication could be linked to the intonation and manner of speaking of the cafeteria workers in the British context. For instance, the cafeteria workers would offer gravy (gravy?) to the ground staff using a falling intonation rather than the rising intonation typical of Anglo-English questions. Consequently, this utterance was interpreted by staff as a statement (this is gravy) or imperative (have gravy!) rather than the cafeteria worker’s intended interrogative meaning (gravy?).
Preferred ways of speaking and the ways in which politeness and speech acts are accomplished are subtly different across cultures. An English speaker who wishes another to close a window will often say can you close the window? whereas a German speaker would be more likely to say you should close the window. We outline why this is the case through a synthesised discussion of the concepts of speech acts and politeness, introduced in the previous chapters. This discussion emerges from the influential Cross-Cultural Speech Act Realization Patterns (CCSARP) project (Blum-Kulka, House & Kasper 1989). The work of the CCSARP project is also extended through discussions of the studies that have been conducted in the wake of this project as well as more ethnographic and conversational approaches. As noted in Chapter 2, these latter approaches have sought to provide a more nuanced understanding of direct and indirect messages, speech acts and politeness.