 So, we need to really radiate. So, this is radiation 1 for camera team, this is radiation 1. So, now only I guess I have modulated to you to your needs. So, we all know that for radiation, we do not need any medium. This is quite different from what we have been thinking for conduction and convection and this radiation occurs instantaneously. Why do I say instantaneously? Why do I say instantaneously? It travels at the speed of light. Radiation is occurring because of electromagnetic waves and these electromagnetic waves are moving at the speed of light. Only that speed gets little bit stunted provided my medium starts participating. So, that thunting is dependent on the refractive index of my material. In fact all properties, I realized only a off-late, all properties emissivity, absorptivity, refractivity, transmissivity, everyone is dependent on refractive index, dependent on refractive index. If I have to come from electromagnetic wave theory and I will just simply touch and go, I will not be trying to model anything and show you that emissivity of this surface is a function of refractive index. I am not intending to do that because I have not done that so far. So, maybe before workshop I can demonstrate one. I was just seeing modest. So, I saw that it is all about refractive index. So, thermal radiation, the point is thermal radiation does not require any matter quite unlike conduction and convection. So, why do we study radiation? For that matter what all the examples you give for studying conduction I guess we can give plenty of examples. Convection I guess we can give. Why do we study radiation? What are the typical examples you quote in the class for studying radiation? Solar. What is the issue in furnaces? What are the issues in furnaces? When I say furnace, what are the issues in furnaces we are looking for? Not heat loss. How do I create a furnace? How do I, why do I need a furnace first of all? If you see it typically yes, right that is one of the examples, but furnaces we said I mean furnaces here. So, in furnace why do I use furnaces? For heat treatment of all our automobile part almost all our equipment whatever is there it undergoes heat treatment. So, for heat treatment my furnace either has to be electrical heater or oil fired furnaces. I think generally they are all oil fired furnaces not electrical heaters because everywhere you cannot get electrical electricity is always a problem. Now, the question is a furnace is typically a room of this size. It can be much bigger than this actually. We have I have seen at least furnaces just across Ghatkopur jethis just 10, 15 minutes from here. Furnace is much double than this where they keep almost you can drive in a car and keep it inside. I mean it is that big. So, the point is they keep all sorts of materials for fixed amount of time, but then before they keep you have to reach the steady state. Each of these walls have to be maintained either constant heat flux or constant wall temperature whichever it takes. Typically if it is a electrically heated it will be constant heat flux. So, you have to have you have to have an idea how much power you need to supply to each wall and also someone was saying losses are going to go away if it is electrical heat. Electrical heater is reasonably easy to design but electrical furnace is easy to design. But if it is oil fired furnace let us say it depends now which oil typically we use diesel because it is cheaper diesel fired furnace but then diesel is not such a good fuel to burn. We all know diesel diesel is not such a good fuel to burn. So, when you burn diesel now when you burn diesel there are burners you have to put burners at various locations. Now I need to optimize the location of the burner design and burner design is specific to the fuel I use. If it is a gaseous fuel if it is methane or propane or butane it is one design. If it is as I said oil fired furnace I have to have an injector mechanism and then I have to burn it. So, there are several issues when I am designing a furnace and now the question is when I said burner why I took the example of burner because the heat transfer mode from my burner flame to my furnace wall is what radiation alone. In a gas stove every day we cook our mothers and boys and we also cook. What is the mode of the heat transfer between the flame and the plate or the vessel very true, very true. Why convection? Why radiation is not there? What is that? Image, no it is not like that. No it is not that way, it is not that way, it is not that way. What is the color of the flame? I always quote this because I have learnt it in a very hard way. So, sakeeth is already laughing because maybe you have heard it N number of times but that is okay. So, blue flame, if it is blue what is the emissivity of a blue flame? I will ask you like this. If I put my hand near the blue flame that is my gas stove, do I feel any heat? Do I sweat when I stand in front of gas stove and cook? That is my question, no. You do not sweat as much as you sweat when you cook in front of wooden cooking stove. Why? What is the color of the flame in wood burning cooking stove? Yellowish red. Why? Because the emissivity of the flame of yellowish or slash reddish flame is very high. How high it depends on the character of the fuel which you burn? Character of the fuel which you burn, size of the fuel container whatever you have. So, why it is emitting? Who is emitting there in the yellowish flame? Yellowish is complete combustion or blueish is complete combustion? Blueish is complete combustion. So, there is no suit. There is no black particles. When you burn, now our steel utensils do not become blackish when by flame, when it is gas stove. But when my grandmother used to cook on wooden stoves, wooden based mud stoves, mud cooking stoves, all my utensils used to be, steel utensils used to be blackish. She used to do only on mud based pots, earthen pots she used to use because they were getting blackish. The point is they become, the yellowish flame is incomplete combustion. Because it is incomplete combustion, you have suit particles. Those suit particles are emitting that reddishness. So, that is why it is reddish, that is why it is reddish slash yellowish. So the point was what I was trying to say is that the color also suggests the emissivity and what was I trying to say? What was I trying to say is that in a furnace it depends. If I am using an yellowish flame, if it is a diesel based burning, it is not going to be blue. It is going to be yellowish because there is suit. But if I am using methane based burner then it is blueish flame. What was I trying to say is what is the mode of the heat transfer? The mode of the heat transfer in a gas stove between the flame and the plate is purely convection. Emissivity of my flame may be is of the order of 0.03 of my blueish flame. So you can conveniently neglect radiation. As for a classroom, if you are doing research and doing nitpicking, you will have to worry about that portion also. But otherwise it is purely mode of heat transfer is convection. But if it were to be yellowish flame, that is if I am using wooden cooking stove or in a furnace where it is diesel based burner, then it is going to be yellowish and there is a combination of convection and so we have to be very careful. I mean the point is identifying the mode of heat transfer itself becomes tricky in case of radiation and most of the times as I keep saying in the class, we study conduction convection radiation separately for the sake of simplicity only because we cannot take all together in one go. But in real life, there is nothing like pure conduction, pure radiation. Some components will be there everywhere. How much is dependent on case by case basis. But otherwise you have everything everywhere. So that is, see I was just trying to give the examples. Of course solar radiation I do not want to touch because you are all very good at it. So solar radiation I am sure many of you are working on solar radiation also. So I will not touch upon that. So now. There also temperatures are quite high. In flame also, in blue flame also, temperatures are as high as around 700 to 750 degrees Celsius. But we are not able to feel the heat as. Why because it is not emitting. It has to emit to radiate. My temperature is high. Let me explain this in a very simple fashion. Emissive power is equal to e into sigma epsilon t to the power of 4. Anybody which emits sigma epsilon t to the power of 4. Your point is my t is going to be 750 degrees Celsius. How come you are saying there is no radiation? Is that right? That is what you are saying. So my point is epsilon is 0.03. So its component will be very less. My heat transfer coefficient on the other hand in a gas stove in a heat transfer will be very high. It will be of the order of thousands. It will be of the order of thousands. So convective component will be quite high compared to radiation. Who is pulling it down because of my epsilon? Because of my epsilon of whom? Epsilon of my flame. I hope I have reached you. But furnace also we have the same from a suit formation. If my flame is yellowish. If my flame is yellowish only I get this suit. Then there is emissivity. If there is suit means what? There is emissivity. Then radiation becomes that. Is that okay? Is that convincing? Yes. Blue flame is just like a hot gas. Very well put. You can take it. That is why I am saying it is convection. It is like a hot gas coming and heating my cold plate. That is very well put. So now coming back. So radiation does not require any medium. So we always quote this example. This also I have copy pasted from chungal. So if I sit in front of fire. If I sit in front of fire. Although my the temperature of the fluid between me and the fire is less the radiation takes place and I feel the heat. But at the same time in radiation I need to be worried whether I am facing the fire front or sidewards. Okay. Because you know everything. So I can go farther and come back. That is what is that concept. How do I factor in this concept? Whether I am facing the fire or facing sidewards. How do I factor in this concept? View factor. That is view factor. How much I am weaving? How much the source and sinker in which way they are weaving each other? That is the view factor. Okay. View factor sidewards should be lower than the view factor. Otherwise. Okay. Okay. So now if I take this is just a thought experiment which suggests that I have taken a body whose temperature is quite high compared to the surrounding temperature. And my enclosure is at a surrounding temperature. And there is no medium inside. And eventually this body attains the temperature of surrounding. This demonstrates that there is a heat transfer even in the absence of medium. So this is just to suggest that there is radiation even in the absence of medium. Okay. So now as I said little earlier the radiation takes place through electromagnetic waves. And electromagnetic radiation energy is passing through waves. And this wave is passing at a speed of light and in vacuum. If it is in vacuum it is going to velocity of the speed of light is sorry speed of light in vacuum is 2.998 into 20 to the power of 8 meters per second. And n if it is any given medium c is going to get decreased by as much as the refractive index. So c0 by n typical refractive indices are for air and most of the gases it is near 1. For glass it is we have done this in plus 2. I do not know whether you recollect we have measured in plus 2 refractive index of water as 1.33. I remember adjusting the angle to get 1.33. So that is how I never used to get the alignment of prisms properly. I was a hopeless experimentalist at that time. So but my teacher used to insist that I need to get 1.33. So I had to do that. So glass 1.5. So now what does this say? The main observation is that the lambda and c you can imagine a wave and it is going to have a wavelength. What is the wavelength between 2 peaks or 2 troughs is the wavelength. And c we can all that is I said c. So this wavelength and this speed with which the light or the electron not the light electromagnetic wave or light passes through that medium they are dependent on the source. Sorry they are dependent on the medium through which my electromagnetic wave passes. But the frequency is dependent on the source. This we have studied in physics. So now frequency to wavelength is given by lambda equal to c by nu. And then see this is history we have studied there also. I mean in plus 2 also we handle I mean now only I realize while reading thermal radiation optics. If I can understand optics well I can understand thermal radiation. Why because electromagnetic wave is moving like a light wave. And we have studied when in plus 2 our teachers for teaching us light wave can be quantified or can be understood as a wave and also as packets of energy that those packets of energy are called as photons. And we married or we applied these to any of these to wherever it was convenient to explain any of the experimental observation. This is what we recollect recollect from our plus 2 that is what we are applying here also. So each of the photon with a frequency is moving with a frequency nu is going to have an energy equal to h nu that is what Planck gave us equal to h nu nu is equal to c by lambda h c by lambda and the Planck's constant is 6.625 into 10 to the power of minus 34 joule second. So now energy of the photon as you can see that it is inversely proportional to wavelength that means shorter wavelength waves. We will get to know this little later the gamma rays and x rays are highly destructive because they are going to be carrying larger energy but this figure I like always because this is what gives us the feel of various waves. I do not know from where I downloaded this was I downloaded 10 years back when I was in IIT Govati. So but I still love this because I cannot get any figure better than this why I love this figure because the first what is that first line representing wavelength. The second is giving the size of a wavelength with a picture which uses the size which gives me the feel of a size. For example now you see now let us for a minute let us go to the next line common name of the wave these are radio waves micro waves infrared visible ultraviolet. Actually our domain is going to be only infrared visible and a little bit of ultraviolet soft x rays hard x rays gamma rays. Now how do I feel this wavelength? How do I feel this wavelength? What is the wavelength of infrared or micro waves? Let us come from radio waves. What is the wavelength of a radio wave? It is as big as a football ground. So now you can feel. Now same there are radio waves as big as football ground and also a house typical house or this room. Now let us come to micro waves they can be from tennis ball or a baseball to a simple full stop what I put on my paper. Now my infrared waves start from full stop size to smaller than that as small as amoeba that is I have to see through a microscope. See I think this is very important figure in the sense that I can reach my student not in an abstract way but with a physical feel. Otherwise wave is there, wave is there it is having a high wavelength low wavelength I am not reaching him. This is the only way I am see always we say whenever we use another thing I want to tell whenever we use because we did not intend to solve a problem whenever we say 3 meters. What is 3 meter means we have to give the physical picture of to the student. 3 meters means how many because I always think like this this I have learned from readers that is how many feet is usually a building one story building 10 to 12 feet. Let us take it as 10 because calculation becomes easy. So 3 meters means 3 by 0.3 3 into 3 roughly 9 feet so one story building. So whenever any unit is put across I should be I should be giving him the physical picture. Physical picture we have to give that is what is happening in this. See when now when I imagine infrared wave or a electromagnetic wave which is contributing thermal radiation it is its wavelength is going to be smaller than full stop and as big as what I can see in a microscope. So that is what then I need micrometer then comes the picture then comes the that means it is smaller than my hair size I keep saying hair size always why because here I can see 75 micrometer. So it is smaller than that it is smaller than that. So this picture if you put people can or students can we can carry them along with us if I put this. Now of course so the where are the sources that you can see there are various sources of each of these waves I am not going to spend time on that. So that is about the electromagnetic what is this this is called electromagnetic spectrum. So now we will realize that in the next transparency I will go to the next one and then come back this portion of ultraviolet a portion of infrared is the one which is which is going to contribute the thermal radiation what does that mean when I say these are the ones which are going to contribute the thermal radiation by virtue of temperature they are emitting energy. So that is that is what we mean by thermal radiation of course we will appreciate this when we plot the energy versus emissive power versus wavelength for different temperatures you will see that only within this wavelength band there is emissive power contributed because of because of temperature because of temperature. So that is the that is why we say thermal radiation. There are a lot of blah blah I think this we have studied in plus two violet what is the wavelength band, Vibh Geyar we have all studied so I do not have to worry about that. So that is about the electromagnetic spectrum. Srin which was asked to my aunt when she went for a school teacher's interview physics why is traffic light red to indicate stop why not green. So that is the picture of yeah yeah yeah yeah yeah yeah that is very nice very good example. She told me when I was in about 8 to 9 standard it was just stuck in my head you know such a beautiful question. I learnt it very recently Professor Anil Kumar from chemistry department we have an enthused program to enthuse all the PhD guys and M Tech guys he quoted this example why red is red and green is green for signal. Signal why is it green because it is naturally there so everywhere in the nature the most common color is green. So green is there that is the reason it is green and red very rightly said it has longer wavelength. So for larger because I need to know that better I stop myself before I reach that so that is see everything what he was trying to say everything is there we need to observe only when we observe we will ask the question why if I do not even observe I will not even ask the question why it does not come into picture so anyway we got digressed but that is a beautiful example. So now now radiation is a volumetric phenomenon but we assume that it is a surface phenomenon and we go ahead with that so I do not want to spend time on that and then the thermal radiation is going to be having it is going to be a function of it is going to have direction and it is also going to be dependent on the wavelength. We have now seen each wavelength we have differing wavelength within our band that is within that what is that ultraviolet infrared visible all each one is having a different wavelength so my radiation has to be dependent the emitted radiation has to be not only dependent on the direction but also dependent on the wavelength for wavelength we use the word spectral distribution and for direction of course directionality. So we have to worry about spectral not only spectral but also directional distribution so that is about I think I will leave it to no professor around he is the expert in this so he will do justice better than me that is our perception till now we have been here relegating spherical coordinates to students for assignment so I think it might be a now I feel that it is a good idea perhaps even to derive spherical coordinates the heat diffusion equation now I feel now I feel actually Cartesian coordinates the moment I derive Cartesian coordinates cylindrical let us give it as assignment this is my plan for main workshop I intend to solve it for spherical coordinates in the because by that time r theta phi is now little familiar so I would request even when you are teaching instead of relegating spherical coordinates for assignment the moment Cartesian Cartesian I cannot do because if I take spherical in the first instance is itself it becomes little complicated so first let us do Cartesian but on a fast track let us do spherical so I would think that doing spherical has a merit in itself because when we come for radiation it becomes that much easier.