 Today, we will begin the first introductory lecture on our course convective heat and mass transfer. In this lecture, I will cover and recall your knowledge of modes of heat and mass transfer, recall some important definitions, give you some examples of convective heat and mass transfer and then mention syllabus and references. As you all know, whenever there is a temperature difference, heat transfer Q joules per second or watts takes place spontaneously by three modes. The first of it is the conduction mode and it takes place in solids, liquids and gases. It is essentially a molecular phenomenon. The second mode is radiation. It requires existence of a transparent medium including vacuum. It is an electromagnetic phenomenon. Convection on the other hand takes place in liquids and gases. In this, the transfer of energy is both by bulk motion as well as by conduction. Likewise, whenever concentration difference exists, mass transfer m dot kilograms per second takes place spontaneously by firstly diffusion which takes place in solid, liquid and gas. It is a phenomenon very akin to heat conduction. It is also a molecular phenomenon. Likewise, convective mass transfer takes place only in liquid and gases in which there is a transfer of mass by bulk motion and diffusion. There is no radiation like counterpart in mass transfer. Very briefly, the scope of this course is as follows. The course contained is designed for masters and PhD students who wish to pursue careers in research and development. Our concern is with convective phenomena. To the extent that fluid motion is involved, the neighbors of convective heat transfer are fluid mechanics, thermodynamics and undergraduate heat transfer. I shall be assuming that you have familiarity with these three courses. For example, you have already determined heat in mass transfer coefficients from experimental correlations such as the set number is equal to constant multiplied by Reynolds number to the power of m multiplied by Prandtl number to the power of n and C m n are specific to a particular situation in which you are considering the heat transfer. The aim of this course is to determine the heat and mass transfer coefficients from theory of mass momentum energy transfer in moving fluids. Many a times, we shall obtain results in closed form that will look like experimental correlations. On many other occasions, you will find that we can only give results in tabulated forms which can then be correlated in this experimental like form. The most important quantity in convective heat transfer is the heat flux at the wall as shown here. For example, consider a solid surface past which a fluid is flowing then due to action of viscosity close to the wall the fluid will develop a velocity profile with zero velocity at the wall. This is called the no slip condition meaning thereby the fluid does not slip at the surface but is brought absolutely to rest at the surface. If there was a heat transfer then the most commonly developed temperature profile will be as shown in this where there would be some reference temperature far away from the wall and the wall temperature would be greater than fluid temperature. So, the heat transfer would take place that way. Heat transfer however would also take place in another way in the sense although T w here is also greater than T rev we shall encounter situations in which the fluid temperature close to the wall is greater than that of the wall in which case the heat transfer would take place to the wall although the wall temperature is bigger than the free stream temperature. So, I have shown here both the cases of positive heat transfer as well as negative heat transfer. We define heat transfer flux suffix q w across interface area A as q suffix w equal to the total heat transfer q w in joules per second divided by area and therefore has units of watts per meter square. Because the fluid is brought to rest at the wall the heat transfer is actually by conduction and therefore we represent it as by Fourier slope heat conduction minus k f dT dy at y equal to 0 where k f is the conductivity of the fluid. So, in this case dT dy is negative and therefore the heat flux is positive. In this case however dT dy is positive and therefore the heat transfer is negative or into the surface. We define heat transfer coefficient in the following ways h is equal to q w divided by T w minus T rev and since q w is equal to minus k f dT dy at y equal to 0 h can also be defined in this manner. Experimentalists typically use this definition because q w and T w are easy to measure. In theory however we shall be using this definition theoretical results are compared with experiments. It is very important to remember the difference here between the two. Usually we expect agreement of the order of plus minus 10 percent in single phase heat transfer. Here I have shown the velocity profile most commonly occurring temperature profile for positive heat flux, but we could also get situations in which T w is less than T reference, but still the heat transfer is positive that is because the temperature profile here has a negative gradient at the wall and T w is less than T rev. So, in general then h can be both positive or negative because in this case q w is positive, T w is greater than T rev and therefore h would be positive that is shown here, but in this case T w is less than T rev q w is positive and therefore h would be less than 0. I emphasize this because in most of your undergraduate courses you have not encountered situations in which h can be negative, but as one moves towards research one must be prepared and alert to the fact that h could also be negative. T rev is an important quantity because it is defined in different flow situations differently, but for the time being we will say that T rev is known or is knowable somehow k f as I said is the conductivity of the fluid. So, in order to define h completely we need to know q w, T w and T rev. When defining heat transfer we refer only to the interface state and the reference state, but in mass transfer we need to consider three states the reference state which is far away from the interface into which mass transfer is taking place. The interface state w and a third state deep inside what is called the transferred substance phase. Imagine for example that water in a plate is evaporating into the atmosphere. Then we would need to know what are the conditions deep inside the water at the surface of the water and far away from the water in the ambient air in order to be able to calculate the rate of evaporation of water from the pond. The mass transfer flux and here I use the symbol n suffix w is again a mass transfer rate m dot per unit area and therefore has units of kilograms per meter square second and it will be defined as n w equal to g multiplied by b where b is a ratio is a dimensionless quantity comprising any quantity phi at the reference state minus phi at the interface state divided by the phi at the interface state minus phi in the transfer substance phase. Since b is dimensionless notice that the g and n w have the same units kilograms per meter square second whereas in heat transfer the heat flux and heat transfer coefficients have different units. Phi for the time being note that it is a conserved property what it is we will see as we go along. In general there are three types of mass transfer. The first is mass transfer without heat transfer and chemical reaction which means the water deep inside in the pond at the surface and in the considered phase far away from the pond surface all have same temperature and therefore there is no possibility of any heat transfer. Nonetheless mass transfer would take place should the relative humidity in the ambient air is less than 100 percent then mass transfer would still take place. Mass transfer with heat transfer but without chemical reaction. Now imagine that the ambient is hotter than the interface temperature and it is still hotter than the temperature deep inside the pond. Obviously there would be heat transfer into the water but there would be mass transfer accompanied by heat transfer. Of course evaporation is a inert process there are no chemical reactions taking place in any of the phases and therefore we call it as mass transfer with heat transfer but without chemical reaction. Finally the mass transfer with heat transfer and chemical reaction. A very good example of this is of course the combustion of fuels solid liquid or gas in which for example when a coal particle burns mass transfer takes place from the particle into the surrounding air. Heat is transferred from surrounding air to the coal particle continuously to keep its surface temperature high and there is a chemical reaction at the surface of the coal particle as well as there is a reaction of the released gases in the ambient air. So in each case of course conserved part property fine must be appropriately defined and we shall be considering these aspects as we go along. It is very important to recall the main task of an engineer. The engineer is concerned with design and performance evaluation of practical heat transfer equipments. Design means sizing for a given heat transfer rate Q w. How much area should I provide so that the surface never attains a temperature T w and always remains less than some safe metallurgical temperature determined from metallurgical considerations. So safety is also a very important aspect. Finally the economy. The capital cost and the compactness of the heat transfer surface is related to surface area A required to transfer heat Q w. But the running cost is related to pressure drop because the fluids are being moved past the surface and therefore area A must be chosen or so structured that the pressure drop is as small as possible and the pumping power is small. So reducing the running cost. Thermodynamics determines the delta P as well as the velocity profile and the profile in turn determines the gradients of temperature and phi profiles at the wall which enables you to calculate H. Note that thermodynamics cannot help design simply because thermodynamics deals with the change of state and not with the rate of change of state and therefore if you want to design any practical equipment what you need to know is the rate of heat transfer per unit area per unit time and that can only be determined with the knowledge of H or G as the case may be whether one is considering heat transfer or one is considering mass transfer. Thermodynamics however can help in performance evaluation and we shall see the importance of thermodynamics in its relation to heat convective heat transfer in the examples that follow. Here I consider the very simple example of a hot metal sphere which is suddenly dropped into cold water and the water is held in a perfectly insulated vessel. Obviously as the time progresses the metal sphere will cool down and the water will heat up. Ultimately both of them will attain the same temperature. Let us call this temperature T final T F. Thermodynamics will readily tell you what this final temperature will be because the heat lost by the sphere would equal the heat gained by the water and if you know the mass and specific heat of the sphere and water you could readily determine the final temperature T F. Thermodynamics however cannot answer the question what will be the cooling rate of the sphere? In other words what will be the rate of change of temperature with time of the sphere nor can it readily determine what will be or rather how long it will take to reach T F the final temperature. If you want to determine the time required for the sphere to reach the final temperature you would need to now heat transfer coefficient between the surface of the sphere and the water that surrounds it. In this case of course the heat transfer would be by natural convection because we assume that the water is stagnant and motion in it is induced simply by the density gradient set up by the temperature differences. We take another example of a sizing a condenser. So consider a condenser in which a low pressure steam is coming in on the shell side whereas the cold water or the cooling water is passed into the tubes inside the condenser. The cooling water will enter at a low temperature T in and would come out at the temperature T out and the steam would condense and the condenser would be collected at the bottom of the condenser. So in a steam condenser knowing the mass flow rate of steam and the condenser pressure thermodynamics can determine the mass flow rate of cooling water required when the allowable temperature difference T out minus T in is specified. The difference T out minus T in is specified simply because often temperature of water coming out of the condenser is let off into a pond or a creek and in order to save the marine life. For example, one would specify that T out should not exceed 32 to 33 degree centigrade because it is hotter than that than the it is harmful to marine life. So thermodynamics will tell you what the mass flow rate of water will should be for a given mass flow rate of steam. However, what thermodynamics cannot tell you is how many tubes will be required or in other words what would be the surface area required at the interface between the tube and the steam. For example, its diameter length number of tubes etcetera the actual pressure drops are less than the allowable pressure drops on both the cell and the tube side that can only be determined by knowledge of edge on the steam side and on the water side in the tubes. Pressure drops must then be determined from fluid mechanics knowing the fluid flow rates on either side. Here is another example of gas turbine blade cooling. Now of course thermodynamics tells us that the temperature leaving the combustion chamber of a gas turbine must be as high as possible so as to achieve high thermal efficiency of the turbine. Today temperatures of the order of 1500 to 1900 k are expected in practical gas turbines. These hot gases however flow over turbine blades and the designer must ensure that the blade temperature anywhere in the blade will be always less than a safe temperature defined by metallurgical limit in order to prevent melting. But also because some temperature gradients are inevitable inside the turbine blade the gradients must not be high so as to cause warping or twisting of the blade that will destroy its hydrodynamic performance. Therefore, designer has to provide extremely complicated cooling systems in this figure. The cooling air from the compressor is brought in from within the blade and made to pass through serpentine passages or blade passages as shown near the leading edge and also pin fin passages near the trailing edge which is extremely thin and the pin fins provide the strength to the trailing edge. Of course the amount of air that you draw from the compressor to bring about cooling of the blade must be small because you have pressurized the air and it is no point losing some of that air for the cooling purposes because when it comes out of cooling the amount of air passing over the blade for generating the power would be reduced and therefore the amount of thrust produced by the engine is also reduced. Therefore, a designer has to make several compromises. He must obtain high heat transfer coefficients inside the blade so that its temperature is low and he must make sure that the amount of cooling air required to do this is also very very small. So, the question then arises how should internal passages be shaped? What I have shown here is a very typical arrangement inside a blade. For example, in order to increase heat transfer coefficient the rib roughness is employed. These are the ribs you will see some are at right angles to the floor, some are at angle to the floor. It also employs bends. Fluid is made deliberately to go through bends because bends obtain good heat transfer and there is also jet impingement as you can see here near the leading edge. From this passage there is a perforated wall so that the air actually impinges on the leading edge of the blade and cools the blade. Likewise at the trailing edge there are pin fins as I said to provide strength to the trailing edge as well as impingement heat transfer in order to make sure that there is no concentration of stress due to temperature gradients in this region of the blade. These techniques improve the heat transfer coefficient. Roughness, bends, jet impingement, etc. Let us take another example from a thermal power plant. Here is a thermal power plant with its condenser. The power plant is taking cool water from the pond and releasing back hot water into the pond again but the pond is exposed to ambient solar radiation as well as wind velocity and therefore there is an evaporation loss of water and therefore the pond needs to be topped up with water brought from elsewhere and it is very important to determine the topping up water requirement for such a pond. To determine such requirement one would need to know the mass transfer coefficient between the water surface and the ambient. The driving force B in this case would depend on water vapor mass fractions in the ambient at the surface and deep inside the pond as well as temperatures in the ambient surface and deep inside the pond. So, we have a situation of simultaneous heat and mass transfer but without chemical reaction because both the air and water do not participate in any chemical reaction in this evaporation process. I now take another example from the thermal power plant that of a pulverized fuel furnace. In pulverized fuel furnaces of the type shown or the boiler session, coal particles typically less than 250 microns are injected along with air in the form of jets from the burners which are located somewhere near the bottom of the furnace. If I take a cross section AA at this point it would look something like this and the burners are situated in the corners of the cross section and the coal particle and air are injected in this manner so as to provide good mixing inside the furnace. The particles burn inside air and release heat. The heat is then transferred to water tubes which are lined along the walls of the furnace and the heat transferred to the water tubes is by convection as well as by radiation because the gas inside the furnace is a transparent medium. The gases then flow over superheated tubes and then flow through the economizer and air preheater to electrocrotic precipitator. What is of interest in such a situation is of course the heat and mass transfer or the heat transfer by radiation and convection to the water tubes but more importantly the particle burn rate. What is the rate at which these particles are going to burn so as to make sure that the height of the furnace is sufficient and all particles are completely burnt before the flue gases go out through their exit. Nowadays secondary air is also added somewhere above the where the nozzles are or the burners are in order to lower the temperature of the hot gases and thereby reduce NOx emissions. All these environmental considerations would require along with the power production considerations would require simultaneous heat and mass transfer with chemical reaction at the coal particle surface as well as in the released gases. So we have a situation of simultaneous heat and mass transfer with chemical reaction in a pulverized fuel furnace. In fact, the entire field of convection is called upon in a pulverized fuel furnace because boiling takes place in the water tube which is a heat transfer with phase change, radiation takes place, convection takes place, mass transfer takes place because there is burning involved and chemical reaction involved. So we have the most complex situation of convection in a pulverized fuel furnace. So let me run through very briefly the syllabus. The numbers in the brackets indicate roughly the number of lectures I will take on each of these topics. The first topic would be definitions and the flow classification. The second lecture would consider the flow classification. Then I shall derive the equations of mass momentum energy which are also called the transport equations. I will then consider a very special class of flows called laminar boundary layers and in two dimensions because in a classroom one can only consider two dimensional problems. I would then consider ducted flows because they are most commonly occur in heat exchangers. Firstly, I would develop laminar duct flow and heat transfer solutions. I would then turn to turbulent flows because they are the most commonly occurring in almost all our heat transfer equipments. Then I will develop like in laminar case solutions to 2D velocity and temperature boundary layers as well as to ducted flows. Then I will spend a couple of lectures on what is called turbulence modeling which requires drawing up of energy budgets in flows. Here by energy I mean kinetic energy of turbulence. So the first set of lectures would be concerned with fluid flow and heat transfer and then I would turn to mass transfer. I would be spending 6 lectures on formulating the total mass transfer problem. Mass transfer without heat transfer and chemical reaction, mass transfer with heat transfer but without chemical reaction and mass transfer with heat transfer and with chemical reaction. I will develop that problem as a whole and I will be developing sub models which would enable us to determine the value of the mass transfer coefficient from knowing the value of the heat transfer coefficient in the corresponding situations. These sub models essentially depend on postulate of analogy between heat transfer and mass transfer but it is very important to understand the nuances that are involved in this formulation of sub models. Out of this I will pick one model called the Reynolds flow model and show how well it applies to practical problems involving mass transfer. By way of references I have listed here 6 references but there are many, many others. To my liking the first reference K is in Crawford convective heated mass transfer. This McGraw-Hill Asian edition is available and published in 1993 is probably the closest to what I shall be doing in my lectures. In this book the mass transfer aspect is largely based on a very exhaustive book called Introduction to Convective Mass Transfer by D. B. Spaulding. It was written in 1963 but K's in Crawford have brought in the modern notations and has made the entire formulations much more easy to access and grasp. A very useful book largely used by chemical engineers is called The Transport Phenomena by Bert Stuart and Lightfoot. It is an excellent treatise on fundamentals of fluid flow, heat and mass transfer. It derives equations in three dimensions which are very valuable and also has very small problems, solved problems in the book which are also very illustrative. But of the most definitive work on boundary layers from the engineering standpoint is the work of Schlichting published the sixth edition of which was published in 1968. The title of the book is Boundary Layer Theory. A much more modern book largely used for undergraduate and introductory postgraduate courses covering all aspects of heat and mass transfer at this level is by Incroop Hara and Jewett. The fourth edition of it is by John Wiley and Sons. It is very much available. It was published in 1996. And finally for those of you who wish to take this subject forward and understand where its present status lies, the book by Sebesi and Krustix is published by Springer and is called Modeling and Computation of Boundary Layer Flows. Now this book really contains material which I shall only allude to because I will not be dealing here with numerical methods of solving here convective heat transfer problem, but largely be concerned with simpler analytical methods for solving. But more complex situations do require modeling, extensive use of computers and the book by Sebesi and Krustix gives you a very good update on the latest developments in this field. In the next lecture, I shall consider the flow classifications of interest in convective heat transfer and in particularly those that I shall be considering in this course. Thank you.