 I welcome all of you for the introduction of the next course which we are planning. Myself Akul Sharma will be taking this course. So, let us first start with brief introduction on what is CFA. It is a methodology for simulation of fluid dynamics and heat transfer problem. It is as is that if you learn this course, you there are two things which you can do. You can create a movie which has a fluid dynamic or heat transfer representation. So, if you take a video camera, you can capture a movie for when airplane is moving, but that movie will be pictorial information. With this subject, you create a movie which has a fluid dynamic information in terms of flow properties like velocities, pressures and temperature. You can also not only create movies, but you also calculate the parameters which are of final interest to the engineers like drag force, lift force, pressure drop and so on. So, this course results in developing CFD software by which you can create movies for fluid dynamics. So, it basically gives you the flow field information in time and it gives you the engineering parameter. And it is very useful in designing and analyzing engineering systems and processes. It is an open-ended application of fluid mechanics and heat transfer problem. In fluid mechanics heat transfer, we use normally calculators, but in here what you can do is that you can do lot of parametric investigation which is an open-ended application of the two course. CFD reduces the cost and time of designing and analyzing engineering system and it is slowly becoming part and parcel of a bigger pool which is called as computer aided engineering which involves solid modeling CAD, finite element methods and CFD as well. In academics, this course is taught in various branches of engineering from civil, chemical, metallurgy, mechanical and so on. In industry, it is applied in diverse areas such as aerospace, automobile, turbomachinery, biomedical, electronic cooling and so on. There is an increased importance of CFD software development, application and analysis. As well as this need is from the Indian let us say industry and research organization. As well as there is a lack of trained manpower in this subject. So, this gives us an importance of this course. However, there is a lack of trained teachers for this course. We have carefully thought about the outline of the course, taking into consideration the background of the most of the colleges who will be taking up this course. This course is not exactly the way we teach in our CFD course here in IIT. So, we have tried, we are starting with some essentials of CFD which we think are partly prerequisite for this course. So, we will talk, this will be taken by Professor Puranik. This includes fluid dynamics and heat transfer, numerical methods, essentials of those. Then discretization method, finite difference method will be taken by Professor Puranik and I will take finite volume method. There are two major objectives of this course. First to develop an appreciation of theory behind the screen because whenever you use a CFD software, you do not have an understanding of what is happening behind the screen. And the second is to, so first objective is regarding development, second objective is regarding application. Whenever you are using a software, you need to appreciate the application of CFD because in a CFD, it is not like a simple software. You have to very cleverly use it. So, you have to design your problems in a very careful manner, the domain size, the boundary conditions. So, what we are planning is that we will have some exercise problem which we will expose you to. And with this two pronged approach of theory and application, you will be firmly set to become a CFD expert in the academic as well as industrial field. So, the prerequisite of this course is undergraduate course on fluid mechanics and heat transfer and some introduction of numerical methods in computer programming. Now, Professor Puranik will discuss the first part of this course which he will be taking. So, we will begin by deriving the governing partial differential equations for fluid mechanics as well as heat transfer. I think you have already gone through some of those derivations, possibly all of them through this course. But nonetheless, for completeness what we will do is we will do the derivations anyways. Maybe we can do it from a different point of view than how it has been done here. I will find out from Professor Prabhu and Sridhar and how they are doing the derivations here. And accordingly, we will decide whether to follow exactly the same approach or a different approach to finally arrive at the same set of equations. If we do it differently, hopefully you will get a different perspective also. You can think about how this was done, how that was done and so on. In any case, this is very important step because in order to make sure that everyone is at the same base, before we in fact start talking about how to employ numerical methods to solve these, we thought of making sure that everyone should go through a formal exercise of deriving these governing equations for fluid dynamics and heat transfer. After that, we will begin with some basic discussion on application of numerical methods. And it is a good assumption here from my point that many of you will know this, the second point here, essentials of numerical methods that we have written. Where we will try to understand the basic ideas related to how you numerically find derivatives and integrals as well as if you have a linear system of equations. How do you solve that linear system of equations using certain very standard techniques called the Gauss-Seidel type algorithms or the Thomas algorithm or the Tridigonal matrix algorithm. So, these are minimally required, I will say, in order to go on and analyze a fluid dynamics and heat transfer problem from the so called CFD point of view. Then there are two different approaches, very popular approaches for solving these governing equations using a computer. So, one is what we normally call a finite difference method or a finite difference approach. What we plan to do here is with respect to this finite difference approach, we will not solve the entire set of governing equations for fluid mechanics and heat transfer. What we will do is to illustrate how a finite difference technique works, we will come up with what we call model equations, which are simplified forms of the governing equations of fluid mechanics and heat transfer. So, we will pick typically three types of model equations, they are what we call elliptic parabolic and hyperbolic equations and these will be solved using these finite difference methods as first part of your formal CFD introduction. And then there is some small affiliated topic of stability analysis, which is not only useful for this finite difference methods, but will also be useful later for the finite volume approach which Professor Sharma will teach. So, my part in this course would be to cover whatever is projected on this slide. So, we will start with the derivation of the governing equations, introduce the absolute essentials of the numerical methods, which are required to do a CFD analysis and then I will introduce the first approach of discretization, which we call finite difference. Next one, to go back to the history of development of computational fluid dynamics started with finite difference method, but slowly in the middle of the 80s it felt when people tried to solve more challenging problems like complex geometry problem, they came up with a finite volume method, which is nowadays commonly used in most of the CFD softwares. These are basically discretization method, which are used to obtain algebraic equations, although the governing equations are partial differential equation, but in computer we solve set of linear algebraic equation. So, I will take the finite volume method starting with for a here we will restrict to two dimensional cases, although the extension to three dimensional is straightforward. We will start with heat conduction, I can also call is a computational heat conduction. So, I will start with the finite volume discretization of the heat conduction problem, explicit and implicit method of solution of the linear algebraic equations. Whenever you want to develop a program or a software, there are certain implementation details, which are required. So, this will be discussed with the help of some figures and animations. I will also discuss the solution algorithm, there are some special topics on heat transfer, such as multi-solidity and non-linear heat conduction. These are some of the special topics for heat conduction, some example problems. From conduction, we move on to heat convection and one of the example problem is hydrodynamically fully developed, thermally developing flow. So, it is an advection diffusion equation. This will be also starting with the finite volume method, then I will discuss the different convection schemes, solution algorithm and finally some example problem. So, after completing the conduction and convection part, when you go to the fluid dynamics or the coupled fluid dynamics heat transfer problem, it is a combination of the conduction and convection, which are diffusion and convection. So, only thing which is left to be discussed is the pressure, how to handle the pressure term, which is the most challenging part of the CFD. So, this will be discussed again with finite volume method and there is a pressure velocity coupling, which is needed to solve CFD problem. This will be discussed for staggered as well as collocated grid. Staggered grid was used initially, but later on the developments collocated grid are popular nowadays. Here also it will be discussed for explicit and implicit method, solution algorithm will be discussed and finally and with some example problem. These are some of the reference books. However, these are we are not giving any textbook, because we do not following any textbook strictly, but these are some of the books which you can refer. First is the Anil, Anderson and Fletcher. Second is an edited book by Murli Dhar and Sundarajan. Third is a book written by professor of our department, professor Darte. And the last is one of the most classical book in CFD written by Patanthi. So, the methodology of the instruction is it consists of two parts, lectures in the first half and may be one hour in the second half and the mode of teaching will be using both board and power point slides. Complete course material would be put up on the web immediately after the course and regarding a lab part we had started working on because handling lab for CFD is one of the bigger issue as compared to other courses. The way we had planned is that we are developing programs using open source software. And the idea is when you will come for the coordinator workshop we will hand over the programs as well as the open source software. What we are planning is there is an open source software which is similar to Matlab which is called a Psylab. So, we will hand you over the software open source software as well as the programs which will be used in the laboratory sessions for the CFD course. And the software research that it has is inbuilt graphics. So, the program will and even if you want to do some small some if you do few lines of programming it is quite easy. So, that way we have planned to develop programs which will provided to the participants and they are expected to solve various CFD problems for various because in a CFD as it is an open-ended applications you can vary the governing parameter. So, the problems will be given where in the program you have to change some number and see the results. You are also expected to plot and analyze the results. And the long term objective is that you should be able to develop your own programs. It is very clear what the expectations are. Whatever will be taught in the course is something that we will expect you know and be able to do on your own when you go back to your college. That is what really is written out here. So, I do not need to really read out what the expectations are. So, the only one thing that I would like to add in addition to what is written out here is that we are very seriously thinking that we will give you guys at the end of the course an assignment which you are expected to work on for maybe a week or so wherein you will be required to develop a program to solve a certain problem. And we will be expecting that you will submit it back to us. And only when the successful completion of that assignment is finished, really speaking the course is complete for you. That is the idea. The reason is because CFD is one course which is I think Professor Sharma will agree completely. It is a truly hands on course. You cannot read books and understand it. You have to sit on the computer and you have to go through as we say getting your hands dirty. That is writing your own program, learning how to debug and so on. So, the only way you will really have a reasonable confidence in yourself as well as to go and teach this class eventually is by writing something on your own and making sure that you know exactly how to do it. I would like to highlight that by teaching this course, earlier I taught this course in one of the NITs. I had realized that and the background of most of the participants in this course are one of the bigger one of the problem is that although this course can be taught mathematically intensive but I had come up with a procedure by which even if your mathematical background is not that strong you can still get a more physical feel which I called as a novel physics based finite volume method. The idea is shown by this three by a block diagram. We start always with a control volume and in a course on fluid physics or heat transfer we derive partial differential equations. Now in most of the CFD books what they do is that they start with those differential equations. So, when we start teaching CFD starting with equations that to not algebraic but differential equations many time I had found that the students with or the college teachers with not very strong mathematical background get scared. So, they follow Gauss divergence theorem and the convert the differential equation to the algebraic equation. So, the traditional finite volume method is shown through green arrows. So, first derivation of partial differential equation which is done in the fluid matrices transfer then algebraic equation done in a CFD course. What finite volume method I will be teaching is that I will start with the same control volume with which you feel quite comfortable in the first lecture of maybe heat transfer of fluid mechanics course. So, from the same control volume the same algebraic equation can be derived. So, this is what will be the methodology of the finite volume method which will be taught. See this is the approach that Professor Sharma will follow in the finite volume discretization part which will be about I will say 60 percent of the course. So, the first 40 percent is what I will be dealing with and the remaining 60 percent is what he will be dealing with with this finite volume procedure. What I will point out to you that the first 40 percent I will actually try to on purpose focus on the traditional side just so that you get both feels. So, to say that you know how you go from the green arrow as well is something that I would like to point out and then later on in the second half is what Professor Sharma will handle in a different manner as far as the discretization procedure is concerned. So, hopefully what we expect is that at the end of the class you will have been exposed to both methods approaches of the traditional more sort of applied mathematics side versus more of an engineering approach of going through a physical process. That is a very important point I forgot to mention. So, you will get both the flavors you will get a feel at the end of the course the mathematical as well as physical feel of the discretization. So, with this we had come to the end and we thanks all of you for your attention if you have any question we will be happy to answer. In this course in we have certain topic which is which are called as implementation details where we talk in detail about how we will not show you the programming language, but without programming language at least flow chart will be clear to you. If I am right already they are teaching Syla. So, the course is thoroughly on Syla even if you have not attended that course I am sure those course are in the best are available you can run through that and make yourself comfortable with Syla. I think what we will try to do is to not only explain the flow chart, but possibly even try to give you a pseudo code for the program. Correct. Finally, just a matter of putting it in the Syla syntax. Is this a pseudo code? Pseudo code is just a step by step procedure which they have to simply code it in a particular syntax whatever language. So, for example, I am very sure that some of these people are used to C++ or C or Fortran perhaps. So, that pseudo code is something like a generalized algorithm which you can just look at and then put it in any syntax. Yeah, pseudo code will also be provided. And secondly, we will give you for lab session the program which are already written in Syla. So, you will get some feel of the syntaxes also. But actually homework assignment as you had mentioned will come up after the course if you do that for work for one week and if you have any questions you can get back to us. Any other questions? Yeah. We are not introducing you to a CFD software. So, open four is a CFD software. Let us say commercial software such as Fluent or Star CD or CFD. They are also CFD software. Our purpose is not to introduce a CFD software. It is a programming environment which is an open source is what you want to introduce. And by that open keep in mind that the kind of programs that we will discuss here as well as we will expect you to write are not extremely complicated. So, as to solve some heavy real life situation. We want to make sure that the ABCs of CFD are covered correctly. So, that when you go back to your colleges and go through these material again and again, hopefully then when you use a CFD software possibly later you will be able to use it more in terms of that is the idea. Thanks for your attention. Okay, thank you. Thank you. Thanks a lot.