 I am just taking couple of questions here and there. Over to NIT 3G, any questions please. Sir, in the case of nanofins, that will enhance the heat transfer. In that case, surface thickness is less than the laminar sublayer thickness. Why it is enhanced in the heat transfer? Okay, the question here is the nanoparticles, if I put the nanoparticles in the fluid, the heat transfer coefficient increases and the viscous sublayer gets affected. I do not think these, the answer is these two are two disjoint things. In fact, I do not remember exactly, I think Mr. Sandeep Pawan, one Mr. Sandeep Pawan had asked me this question on nanoparticles. I have uploaded one of our papers which we have worked on nanoparticles. So for details, you please read that paper. Coming to the answer for your question, the answer is what is that we are doing? When I put nanoparticles, that is typically I take alumina, that is aluminum oxide particles or cupric oxide, that is COO particles or silicon, what is that? Carbon nanotubes. So any of these particles, if I embed in water, usually nanofluids are typically liquids, they do not work well for gases. So when I put this in liquids, what will happen? I am having a combination of thermal conductivity of liquid is 0.6, let us say for water and thermal conductivity of copper is 400. So my thermal conductivity will be higher, for water will be higher. It is like a homogeneous fluid, it is a multi phase flow, that is I have two phases, one is solid and the another one is liquid phase, but it now acts like an imaginary homogeneous fluid whose thermal conductivity is high. We have also done measurements with the nanoparticle, nanofluid that is water embedded with nanoparticles. When we do this, we have found that Nusselt number slightly increases, that is by 5 to 10 percent. Even for a minute, if I assume that the Nusselt number does not increase, what is that which makes the heat transfer coefficient go up? H d by k f equal to my whatever I had got earlier, that is 0.023 r e to the power of 0.8 p r to the power of 0.3. Now k of my nanofluid has gone up because of which my heat transfer coefficient goes up. It does not go up significantly, it goes up only by 10 to 15 percent. So that is what people have found and people are working heavily and even today in all the journal papers tens of papers are coming out. So that is the answer for your question. Sir, if you are coating with nanoparticle, power of the surface, what is the effect? No, no that is not, we are, we never, the question is if we coat with the nanoparticles, usually we do not coat with the nanoparticles. Usually we put the surface roughness, if you put the nanoparticles, if you coat with the nanoparticles, you would have not broken the laminar sublayer. If you are not broken the laminar sublayer, there is no increase in the heat transfer coefficient. So there is no effect of coating the nanoparticles and I just want to take a minute and just tell something about one of the questions asked by earlier one of the professors. So here one of my student Mr. Sameer has generated this transparency. So that is how does induction stow work? So and why does the question was why does we need to put only stainless steel vessels on my induction stow? So very fancy advertisements we see for this, the black thing, I also did not know the answer for this until one of the professors asked us this question. So when Sameer looked at Wikipedia, from Wikipedia only I think Wikipedia or some other website he has got this. So what he says is essentially the induction stow works on eddy currents. So in transformers, in generators and all eddy current is to be avoided. That is why we use copper there. If we use copper eddy currents generated are less. But if here opposite to that that is we are supposed to use the electrical stow and sorry we are supposed to use the stainless steel vessel. So when I put the stainless steel vessel the circuit gets closed. Just let us run through this how it works. High frequency magnetic field is produced by the coil and field penetrates the ferromagnetic material and sets up the eddy current generating heat. So if I put copper or brass or something then the eddy currents electromagnetic field is not set up. So this electromagnetic field itself will be absent then there is no question of eddy current generation then there is no question of heat generation. So that is why we have to use only the stainless steel material. And magnetic properties of steel vessel concentrate the induced current in a thin layer near the surface which makes the heating effect stronger. I think this is obvious nothing outside the vessel is affected because there is no outside the vessel there is no eddy current there is the circuit is that is there is no electromagnetic field. So electromagnetic field is only within the electrical stow and the stainless steel material. And as soon as the vessel is removed heat generation is stopped because electromagnetic field has been cut off and there is no eddy current generated. That is the reason why aluminum and copper cannot be used and moreover I do not think as the magnetic field penetrates too far and does not encounter any resistance. In fact they are not ferromagnetic materials so so my electromagnetic field itself will not be generated if I put the copper and aluminum. So that is the reason that is how induction stow works. Still things are not clear put things in the moodle we will take it further from here. So this is the basic thing which Sameer has generated from his study. Let us get started with radiation. So let us move on to very interesting phenomena of radiation phenomena of heat transfer or mode of heat transfer which is radiation. We intend to today's plan is something like this we will cover radiation 1 and radiation 2 hopefully today. And in the second half somewhere between 230 to 330 we will take to how to take you through how to plan experiment and how to conduct some simple experiment we do not need lot of money to conduct experiments that is what we are going to demonstrate in the afternoon session. And another thing is that scale analysis which I have left out as an assignment I will be taking that in the second half and I will solve it for Prandtl numbers greater than 1. And after that we will be taking up tutorial and already the problems are uploaded. So those are the things which is the this is the plan for complete day tomorrow let us get started with radiation. The first important important thing we need to realize in case of radiation is that radiation does not require medium. But for conduction and convection there was radiation there was medium required. For example I said in space convection is not there why because there is no molecule there is no medium and there can be no conduction also there. So the point is if you conduction I said conduction in the space means conduction within the space shuttle will be there that is space shuttle material it will be there but conduction outside the air which is the in the space there is no air in the space there is no conduction because there is no molecule there. So that is why it is called as rarefied and of course the fluid dynamics itself there it is called rarefied gas dynamics. The question here the point here is that for conduction and convection to materialize you need a medium but for radiation you do not need a medium. So why do we study radiation what are all the applications of radiation plenty of applications we can think of in fact everywhere radiation only is there solar application is full of radiation only from sun we are receiving heat from him and we are feeling the thermal heat what I mean is thermally we are getting heated up because of radiation thermal radiation when I say radiation here I mean thermal radiation not x-ray radiations or neutron radiations why so I will tell you little later on. So it is thermal radiation that is there is a temperature being generated that is we get we feel heated up when we are exposed to sun this is essentially because radiation and of course it does not mean that between sun and earth there is no medium there is medium but it is not so much participating it is not so much participating here what I mean is participating I will come to that little later for now let us say that radiation enjoys or relishes or works perfectly well when there is no medium but when there is a medium what will happen the medium also will act as a deterrent or act as an interference for the radiation to take place between one surface to another surface. Let us say we have two surfaces and between the two surfaces one surface is hotter and the other surface is cooler and there is a medium which is involved between these two surfaces let us say if this medium is participating that means that also interacts it also interferes in radiation let us say that means it is also capable of absorbing some thermal energy which is coming out from the hot plate to the cold plate then the amount of the heat transfer which is received by the cold plate from the hot plate gets impeded because of this participating medium the point is if it is vacuum the heat transfer is perfect that is the radiation heat transfer is perfect if there is a participating medium there is a deterrence for heat transfer. So these two differences that is I am saying that radiation in non participating medium participating medium and another one is participating medium. So vacuum is perfectly non participating because there is no interference that is there is no absorption or transmission or reflection what is taking place within the vacuum but if it is filled with some participating medium let us say my full room is filled with some suit some suit it is filled with suit there is a fire burning in my room and in the room completely it is filled with suit this suit is having some absorptivity and transmissivity because of which my interaction of the heat or the interaction of the heat between the two walls of the enclosure get affected that is radiative heat transfer within the walls that is this is my enclosure and this is filled with suit let us say the heat transfer from this wall to this wall gets affected because of the absorptivity and the transmissivity of this medium that is the suit this is what is called as participating medium but if it is perfectly filled with vacuum then it is then there is no participating medium and the heat transfer between this wall and this wall would be perfect by radiation and I am saying all of this in terms of radiation. So now with this so in our course we are going to be worried about only non participating medium that means every time we say that our medium is going to be vacuum we are not taking any participating medium into account participating medium is little involved so at this juncture we are not taking participating medium at all we are taking only the non participating medium. So now with this assumption being kept in mind that is we are going to take only the perfect radiation perfect radiation scenario what are the applications the applications are up plenty so let us say we have to understand let us say we have to understand for example for hardening or tempering what we what people do for all automobile products that is what we have seen here in nearby IIT we had visited a furnace where in which they have they keep all materials that all automobile material for hardening within this furnace. Now to reach certain temperature of the body for a for this body which is kept inside to reach to a certain temperature I need to maintain certain temperatures of the walls of the furnace. So what should be the temperature if I have to understand that I have to know the interaction of the heat transfer from the wall of the enclosure to the body temperature of the body which is that is automobile body which is kept in the furnace and how much time it take to reach steady state having reached that is all walls reaching steady state after reaching steady state if I put this automobile body inside my furnace how much time this body takes to reach steady state if I have to understand that I need to know the fundamentals of radiation. Now another example I can quote is that now let us say there is an example here I mean there is a figure here. Now let us say here there is a person and this example actually we I usually take it you see for non participating medium I was wondering to get which example I have kept it here and I forgot see this is a fire is there and a person is there sitting here. So now the person standing near the fire fire temperature is if you take a typical fire let us say you just would burn the wood and you are just campfire you have put up it can be of the order of 900 degree Celsius if the temperature is 900 degree temperature of the fire is 900 degree Celsius and human body human body's temperature is around 30 33 or 34 35 that is 7.5 degree Celsius is the human body temperature but the ambient typically is between 20 to 25 here in this example I have taken it is a cold cold day that is why I have put the campfire. So that is 5 degree Celsius so what is happening from the fire the radiation is taking place and I am feeling the heat but does the air in between get heated up no it does not get heated up because the air in between is generally not so participating. So it is non participating medium so that is why the air in between does not get heated up as much as I get heated up so but then the way I stand also it depends that is if I am facing my front to the fire I will feel more heat as opposed to if I am standing side way so we will understand this concept through view factor that is how much one body is weaving the other body also decides the amount of the heat transfer by radiation so that is that would be dealt by view factor concept that is that is what here we are telling. So what was I trying to say yeah why are we studying radiation so here let us say now if I have a fire you have you have seen lot of examples see I do not know whether if you recollect or not in Jaipur if you remember two years back yeah two years back exactly one and half years back in Jaipur what had happened is that there were a lot of containers there were a lot of containers which were filled with hydrocarbon fuel one besides the other one of the container caught fire one of the container which was filled with diesel or petrol caught fire and it burned for almost 10 days so they could just not stop the burning of this why because it is why because it is very difficult to control the fire the point here I want to make is if in that sort of situation what is the safe distance and a fire fighter can stay himself so that he does not get affected he does not he remains safe that fire safety distance what is called as FSD fire safety distance if I have to predict I need to know what is the emissive power that is what is the heat radiated what is the heat transfer rate from the fire to the human body and at what rate the human body that skin temperature goes up so typically they say it is 4.5 kilowatts per meter square 4.5 kilowatts per meter square 4.7 kilowatts per meter square if I am at a distance of whatever it is whatever distance I am if I am exposed to 4.7 kilowatts per meter square per 30 seconds if I am exposed to 30 seconds my skin will start burning so I cannot stay if in front of a fire whose heat flux is more than 4. or around 4.7 kilowatts per meter square for more than 30 seconds that is why if a fire fighter is there a fire fighter will be convectively cooling a fire fighter who is closer to the fire that is he is putting a jet of water a fire fighter he is putting a jet of water on to a another fire fighter who is closer to the fire why because he is convectively cooling while he is getting radiatively heated up okay so the point is if I have to understand or compute this fire safety distance I need to know how much is the fire how much is the emissive power I am not defined emissive power I will just say how much is the heat flux generated by this fire so and it is getting incident on to my body. So these are all the various concepts which are important or applications which are important for studying or the motivating as to study the radiation and of course solar radiation all of you are very comfortable I see lot of questions on model in solar on solar cookers and things like that so for solar radiation if I have to understand I need to know the fundamentals of radiation because for solar radiation will be seeing that emissivity has to be very less and absorptivity has to be very high so what is emissivity what is absorptivity I have not told so for those guys who are working in solar they will understand what I am trying to say so the point is there are various applications and there is no medium required for the radiation to take place and what are the objectives of this radiation so how does this radiation get occurred and what is the specific nature of the radiation and how does it interact with the matter is what we are going to study. So now if I have to understand that radiation there is something like radiation let us just do a thought experiment let us just take a container which is perfectly evacuated how do I evacuate this take a vacuum pump and remove all the air which is filled in it so then you get you cannot get perfect vacuum few millibar is going to stay some millibar is going to stay within the container assuming that it is vacuum now I take a hot body and keep it inside this evacuated chamber what will have happened eventually what will happen sorry I have put I have put a cold body into this and complete of my wall is sitting at a higher temperature sorry what am I saying is the surface temperature is greater than the surrounding sorry I have the first thing let me repeat I have an enclosure I have evacuated this enclosure so this enclosure is perfect vacuum now I have put a hot body into this evacuated chamber so when I have put this evacuated chamber ultimately this body gets cooled ultimately this body gets cooled what does that mean there is some mode of heat transfer which is taking place between this body and the surrounding wall so reverse also if you do if the surrounding wall temperature is high and if I put a cold body ultimately the cold body's temperature will go up and this surrounding wall temperature will come down so that is that is this only demonstrates that demonstrates that there is radiative heat transfer even in the absence of conduction and convection there is no medium so there is no question of convection or conduction in spite of that there is heat transfer taking place so that heat transfer we are attributing it as radiative heat transfer now how does it take place it takes place through electromagnetic waves so who is carrying this radiation is electromagnetic waves so radiation propagates through electromagnetic waves and this was told by Maxwell Maxwell said that there are accelerated charges which give rise to electric or magnetic field and these moving fields are nothing but electromagnetic waves or electromagnetic radiation and when I say wave I need to characterize it by either a wavelength or frequency so that wavelength is given by speed of the light upon the frequency because these electromagnetic waves move at a speed of light in vacuum in vacuum if it is moving in a medium in a medium it will move at a speed which is given by c equal to c naught upon n where c naught is the velocity of speed velocity of light in vacuum that is 3 into 10 to the power of 8 meters per second so 3 into 10 to the power of 8 meters per second is the velocity of light in vacuum that gets decreased so if it is moving in water let us say what is the refractive this n is what refractive index what is the refractive index of water 1.33 so that much is the decrease in the speed of light in water so this is the wavelength is given by speed of light in perfect vacuum or in the medium whichever it is moving upon the frequency next thing so for I just listed the refractive index is refractive index of air and most of the gases is 1 and glass is 1.5 and water is 1.33 this itself decides whether my fluid is participating or non participating we get a feel you see air and most gases it is 1 that itself means that it is non participating on the other hand for glass and water it is participating because the refractive index is high so the way the speed with which my electromagnetic waves are moving is now decreased so that itself says whether my medium is participating or non participating medium air and most of the gases can be assumed as non participating medium and of course here lambda and c depend on the medium through which the wave travels but nu is depends on this source that is independent of the medium that I think it is very easy to because electromagnetic waves frequency is dependent on the source this is what we have studied in physics but the wave length with which it moves or the speed with which it moves is decided by the medium through which it moves. Now what is the propagation what is the electromagnetic radiation so what is the electromagnetic radiation it says that the electromagnetic radiation takes place through propagation of discrete package of energy called photons or quantum so actually it is a combination of wave theory and quantum theory it is a combination of these two I think we all have studied this when we studied optics in plus two that is where I studied at least so each photon of frequency nu is considered to have an energy of equal to h nu what is nu c by lambda so h is the Planck's constant 6.625 into 10 to the power of minus 34 joule second so energy of the photon is inversely proportional to each wavelength so shorter wavelength produces larger photon energy and that is why x rays are highly destructive we will see we have not yet said that x rays have larger shorter wavelength we have not said that we will see that in the next transparency so this is the electromagnetic spectrum so if you are not able to see this I think you are able to see this if you are not able to see this let me help you out what is that we are saying is the first line is the wavelength this is saying wavelength that is this is 1000 meters 100 meters 10 meters 1 meter 10 to the power of minus 1 that is 0.1 meter 10 to the power of minus 2 and 10 to the power of minus 3 meter that means 1 mm 10 to the power of minus 3 means 1 mm 1 mm means a full stop around full stop and 10 to the power of 200 meters means it is almost like a football ground so who is having football ground wavelength radio waves radio waves have a wavelength of football ground no wonder that is why we use them for transmission of radio waves that is radio waves have larger wavelength now the period that is full stop and an amoeba amoeba is of the size of 10 to the power of minus 5 meters that is 0.01 mm so and bacteria all of them for this size wavelength that is for this size wavelength what are the waves micro waves infrared waves and visible waves that is visible light visible waves means visible light whatever we see if they are violet green and all that is visible light that visible light micro waves and the infrared waves have very small wavelength how small as small as full stop to as small as amoeba that is 10 to the power of minus 3 to 10 to the power of minus 7 meters okay now smaller than this are x-rays that is they have a wavelength of 10 to the power of minus 9 meter that is why we said that smaller wavelength ones will be having the larger energy x-rays that is why they have larger energy that is why we are saying that we should not be getting exposed to x-rays quite often for kids actually x-rays are not at all allowed because it is having high energy it may destroy any of our biological tissues that is the reason why we are not supposed to get exposed to x-rays even the x-rays what we get exposed are soft x-rays there are hard x-rays what is the difference between soft and hard the energy of hard x-rays is high because its wavelength is much smaller than that of soft x-ray and subsequent to that is gamma rays so that is nuclear radiation gamma rays and all will come into picture in case of nuclear radiation that is where you see here for all nuclear applications this shows the application for all nuclear applications and x-ray radioactivity you see here x-rays and gamma rays and we also emit thermal radiation human body also emits thermal radiation any body which is having a certain finite temperature emits thermal radiation so that is thermal radiation infrared radiation all of that are contributed by people electric bulb all of them contribute to the thermal radiation of course so there are microwaves radio waves I have explained so this is the this is how we can understand what is the spectrum what is this called electromagnetic spectrum that is spectrum means how is this wavelength changing and corresponding to that how is the frequency changing and how is the energy changing this is each wave as a particular wavelength that is what is being demonstrated and we need to realize although I am not going to tell you the answer why we will understand the answer why when we study Planck's distribution for now we need to appreciate that infrared waves visible light contribute for the a certain amount of ultraviolet light contributes for the thermal radiation no other waves contribute for thermal radiation why we will understand when we study Planck's distribution so the same thing is told in the next transparency that is each of this visible light colors we see have a particular wavelength and wavelength band of 0.3 to 3 micrometer you will see and if you see here what is happening is red is having larger wavelength than green I think we know why do we use green light for stopping in signal and red light sorry red light for stopping for signal and for moving we see green light why red is having larger wavelength so a person who is much farther also can see it compared to green whose wavelength is lesser so that is and green is there everywhere actually so you do not have to make a special effort to see green and going need not it occurs naturally anyway he is going he has to be stopped to make a stoppage you need to put an effort to put an effort that has to be shown much earlier that is why larger wavelength you see for everything there is a reason even signal light choice is having a reason so that is what comes out from this wavelength concept or the electromagnetic spectrum. So in the heat transfer what is that we are saying is that the heat transfer we are interested in energy emitted by bodies due to temperature only that is the reason why we attribute always thermal radiation thermal radiation we are not saying nuclear radiation we are saying thermal radiation so whenever I use the word radiation I only mean thermal radiation in fact to be precise we should say the chapter heading has not just radiation it should be thermal radiation ok so why because the radiation occurring by virtue of temperature that is what is thermal radiation next same thing it is shown very nicely here if you are not able to see that figure I am sure you will be able to this is gamma rays x rays ultra violet rays visible infrared microwaves the thermal radiation is contributed by visible and infrared so this is wavelength and this is wave number and this is frequency what is wave number what is wave number one upon wavelength is the wave number so it is typically represented as 70 meter to the power of minus 1 it is just that people use wave number because they do not want to write 10 to the power of minus 5 and all so that is the reason they put it as wave number that is what I think so you have wavelength, wave number and frequency. Now all bodies emit radiation radiation at absolute zero temperature absolute zero temperature is what what is absolute zero temperature minus 273.15 degree Celsius that is the absolute temperature till today no one has gone a temperature lower than that so minus 273.15 degree Celsius till that that is at that is zero Kelvin zero Kelvin at zero Kelvin only there will be no radiation anything above zero Kelvin one Kelvin two Kelvin anything above that is going to radiate but all bodies which are there in nature are going to have a finite temperature every one is going to have above zero Kelvin that means what there everyone is going to radiate so thermal radiation is the rate at which energy is emitted by matter as a result of its finite temperature so all furniture plants walls people seats yourself myself everyone is radiating so the mechanism of emission is energy released as a result of oscillations of many electrons that constitute matter so this is you can think of oscillation or you can think of as a wave if the electron is oscillating then what does it work the oscillation we have studied in plus two oscillation is represented as a sine wave so that is how the we imagine that this oscillation moves as an electromagnetic wave okay that is radiation actually is a volumetric phenomena but it becomes quite difficult to handle it as volumetric phenomena so we are worried about radiation on the surfaces so we imagine that the radiation is being contributed by the outermost layer that is the exposed surface outermost layer of the surface this figure is more explanatory we will not worry about the radiation within the thickness of the material we will consider that the radiation is occurring only the top layer of the surface that is what we are saying although it is a volumetric phenomena we will consider it as a surface phenomena I think it is a reasonably good assumption now after this what we understand is that the radiation is unlike conduction and convection radiation is little complicated unlike conduction and convection radiation is complicated why do I say radiation is complicated in conduction we never took directionality into account did we take we always made a statement that thermal conductivity is homogeneous it is isotropic that is it is independent of direction but in radiation it is not in radiation in which direction the radiation is taking place it makes a difference it makes a difference so two important things additional things which come into picture in case of radiation are those are one is wavelength one is wavelength and another one is direction for wavelength we say spectral we say spectral the word we use is spectral distribution wavelength things change with wavelength and direction that is emission changes with wavelength that is spectral distribution and directionality this is what makes our radiation little difficult or adds to the complication otherwise it is more or less same so what we are saying in this transparency is that emitted radiation is continuous non-uniform distribution of monochromatic single wavelength component that means what we are saying if I think in vibration we do this very much see in vibration if you have a periodic signal that is if you have a signal consisting of multiple wavelengths what do you do you handle them as multiple periodic signals that is you say a naught sin omega 1t plus a1 sin omega 2t plus a3 sin omega 3t like that so here also we are going to handle multiple radiation multiple wavelength radiations as several radiations of each having a particular wavelength that is what is each one is having a single wavelength that is what is spectral distribution that is this is that is this is the spectral distribution so what is this radiation we are not quantified radiation yet however if it is radiation if I imagine that some quantity this radiation is going to be a function of wavelength now and at the same time the radiation is dependent on the direction also you can see here radiation is dependent on the direction so radiation is dependent on spectral spectrality that is the wavelength and directionality not to mention the radiation is dependent on the temperature also we will come to the other things little later but for now the most important thing is to understand the spectral distribution and the directional distribution now I am giving the mike to professor Arun he is going to teach us radiation intensity through very good examples good morning so I think professor Prabhu has introduced what radiation is about and what are the issues or I would not say complexities what are the things that make radiation a little bit more non-intuitive in terms of you can understand conduction convection relatively easy but radiation on the other hand you need to think a little bit and cannot just read a book like a story and understand because of the fact that radiation involves this directionality as well as the spectral distribution now for understanding these terms there are there are a few terms which will come again and again in radiation repeatedly these will be there that is why we are going to introduce these terms very slowly and we will try to give as many examples as possible so that we understand these concepts very nicely and if there are any questions I would request you to please note down all these questions and put it to us little later so what is we use this term radiation intensity now I want to tell you that we are going to do three or four terms simultaneously I will first define those three or four terms simultaneously and then I will go to actual definitions of each of these so first what do we mean by intensity we will come to that when a surface is giving out energy by virtue of its finite temperature which is greater than absolute zero we refer to that quantity or that phenomena as emission so emission all of us have used this word emissive power what I am saying is this is emission so emission is something where we deal with energy leaving a surface by virtue of its finite temperature so emission means if any body by virtue of temperature greater than absolute zero so let us take if you are in a classroom or you are in a room where there is a projector there is a source of light tube lights are there camera is there so on and so forth all of these are at different temperatures you are at a different temperature you are roughly at 98.4 Fahrenheit so by virtue of this finite temperature T in absolute scale Kelvin every object is going to emit energy so this is related to emit energy how is it going to emit by in the form of electromagnetic waves and what is the amount of energy that it is going to emit we have seen it is that some sigma t to the power 4 with some epsilon in front of it we do not we do not want to deal with all those things at that point but all of us can relate to emission so if I am having a surface this is at a finite temperature T let me call it T s just for convenience because we will have some other T also and by virtue of its temperature T s the amount of energy that is emitted by it that is leaving the surface in the form of electromagnetic radiation so if I have a cup of coffee which is at 60 degree centigrade and it is placed in a vacuum even then you will see that after some time the coffee is going to get cool why that is because of the effect of radiation so there is no medium there by virtue of its finite temperature if the surrounding medium is at a lower temperature than the source of energy that is T s then you are going to have a reduction in temperature because so this is emission this is very easy to understand now you are in the room let us think of the room in a class it is lot easier to explain because I can see the faces of the students we know whether they are understanding or no here it is a little bit difficult but imagine I am there and talking you are in the classroom by virtue of a finite temperature the light above you or light in front of you is going to emit some amount of energy now let us say this light is oriented like this so this is the light this is at temperature T this is also going to give energy in all direction I do not care about direction at this point what is the best example for this directionality you think of a bulb you always take this as a symbol for a bulb what is a bulb look like a bulb looks like a sphere take off this part the bulb looks like a sphere and you are travelling by train in dark in remote corners or even in outside big cities if you are going and you are travelling at night one or two lights you will see here and there and that will be like a source of a source of light for a large distance large would mean depending on the wattage of the light it would either you know you will feel the effect of the light for about 10 feet or for about 2 feet depending on the water if it is a 0 watt bulb but what I am trying to say is that the intense I should not use the word intensity because I am talking of intensity what I am saying is the inner the light presence of the light is felt around like as if it is a sphere as if it is enclosing a sphere. So, as if it is enclosing a sphere you will see the effect of the light all around you all around the source. So, if I want to write this if I want to show it diagrammatically let us. So, this is the point this is the light it will be seen in badly drawn but it will be seen like this all around and it is not going to have any specific direction preference why should it know that I have to go up more or go down more there is no direction preference. So, a source of energy will emit in all possible directions now in in radiative heat transfer that we deal with here. So, what is what is this surface this surface is a sphere all of us agree that this is a sphere this sphere is of radius some are up to which the light is felt if I am very close to it we know that we start to feel a little bit hot you can try this at home lighter lighter lamp oil lamp put your hand very close to it you are going to feel hot take it away from there you are going to feel a little bit less hot further if you are sitting on the ceiling of the room you are not going to even feel that heat from the wick ok. So, what I am saying is that the light is going to the energy is going to come out in the form of a sphere and the I should not use intensity that is why I am looking for a different word the hotness or how much light or how bright the light is is felt more when you are closer and as you go out it is going to decrease with temperature it is easy to understand with light it is slightly bit more difficult because I have to look for the word like brightness etcetera. So, now in our course what we are going to do is. So, any point source generates a sphere of influence around it we are going to deal primarily with hemisphere. So, that is the first thing. So, hemispherical quantity what it means is that now all of us have squeezed a squeezed an orange how do you squeeze an orange you cut the orange first diametrically. So, it has representation typically is like this when we draw also it will be drawn like this in school books also for orange this will be the citrus fruits will be drawn like this what is this please try to imagine now we are stretching our imagination this represents half of the orange what do you call that fruit that you eat you you skin it out and eat the pulp this represent the top half represents half of that. So, we are dealing with only hemispherical. So, I do not care what is happening below I am dealing only with top part in real life is it the case most cases if it is a point source like a bulb or like the sun it is not, but engineering applications where I am talking of a furnace wall where I am talking of a heated plate which is radiating energy it is all going to be only in either the top surface or bottom surface or the side surface if you are talking of a furnace wall energy is not going to go out by radiation on the outside. Yeah probably yes because the temperature on the outside will be a little bit warmer than the room temperature, but inside of the furnace if the wall is 600 degree centigrade radiation is going to be primarily in this part that is why we are dealing with hemispherical quantities that is the first thing. Now, hemisphere classic example is a fruit any spherical fruit guava orange or whatever you are you are used to eating that fruit is a very very good example to deal with when we are talking with talking about radiation. What are the things this if I take this hemisphere all this is given in most textbooks it is just that we find it difficult to read that is all. Now, I take a small region here all of us can visualize this I hope. So, if I cut the orange like this I get half a peel. So, this is that half fruity peel now I do not want half the fruity peel I want only a small portion of this. So, that small portion is different from a small portion here. So, let me call it 1 and 2 1 and 2 I will draw a better diagram actually this. So, if this is my hemisphere if I take a element if I do not take a strip we can we can all imagine one other very nice example is latitude and longitude on the globe. How are longitudes going longitudes are going from the bottom of the earth to the north pole and they the space between two longitudinal lines represent what you see in an orange peel correct. So, if you are sitting at the center of the earth if you want to look at say a country like India which is just above the equator you have to look like this meaning your field of vision is not horizontal it is just raised a little bit. If I want to look at say green land which is in the northern part then I will have to look much steeper. So, that much steepness of looking is representing some kind of an angle from the center of the earth. So, that is what that is the concept that we are going to use. So, radiation is very direction specific in real life. So, that is why if you understand this you understand all of us understand this from sun practically we are experiencing this. Equator countries are hotter much hotter than polar regions or northern or southern hemisphere close to the poles why because the rays of the sun are not falling directly on it it is falling at an angle when things are falling at an angle it is different. So, if I am sitting at the center of the earth and I am trying to look up if this is a area D A in India I have to look up in a particular area way. If this is an area D A same area I am looking at same infinitesimal area in Sweden I have to look very steeply I have to just bend my head almost till 90 degrees. If I am doing only with the northern hemisphere because we are dealing with hemisphere same thing if you want to look in the south we will deal that way. Let us not confuse ourselves the point I am trying to make is this area 1 this area 2 though they are the same D A the location physical location of these two matters a lot and the angle at which these are with respect to the center I am sitting here this is me lot of ego I have that is why I am putting I here. I am sitting there and I am observing this this is a little bit different as opposed to this as opposed to going to the left side if I want to see Japan if I want to see USA it is going to be in a different direction the point I am trying to emphasize is the directionality. Now, I hope you can understand that a light bulb though it will emit what we are seeing is uniform in real life radiation may not be like that depending on the surface characteristic radiation will be direction specific. So, that is why our spherical geometry r theta 5 become very very important. So, emission we said is related to energy leaving the surface now why did we come up with all this is the surface at T s I have another surface the tube light in your room there will be multiple tube lights in your hall where you are sitting one of them will be directly above you another would be very far from you another would be just above the projector all of them are going to contribute to the energy transfer from them. Let us say all the three tube lights are at temperature T they will have the same amount of energy leaving them which is ok, but what is received by you sitting on the first bench or wherever you are sitting is going to be different because of the relative orientation of each of you with respect to that tube light am I right. So, what I am saying is these quantities which are coming in is called as irradiation these are three terms which we will use in conjunction emission we saw is energy leaving the surface by virtue of a finite temperature in energy emission is given by symbol e irradiation refers to energy coming in to the surface from all other surfaces which are interacting with it this goes by symbol g I hope irradiation is understood terminology now one more thing is that all energy that is coming in from other surfaces it is where will it go in real life some of it will get absorbed some will get transmitted absorbed means it will go in sensible heating light when you flash when you when you have a torch and you flash the light through a plane glass window glass many times you will see opaque glass with the where the surfaces where the glass is made milky if you stand on the other side of the glass the amount of light you receive is less but if you have a transparent glass where you can see everything on the other side the amount of light that you see is more. So, that is a transparency opacity which are all material characteristics. So, transmit there will be some amount of energy transmitted there will be some amount of energy reflected and there will be some amount of energy absorbed absorption will cause a increase or increase in the stored energy will cause a rise in the temperature. So, what I am saying is always a surface is going to reflect some amount of energy. So, this quantity is more for convenience we are defining we call this as a radiosity. Radiosity represents the sum of emitted plus the reflected. So, emission is because of its finite temperature radiosity refers to emission plus something more which is a reflected component of energy that is coming in from all directions. So, this rho times g which I am going to write is called this is given by symbol j radiosity. Radiosity is because of the surfaces finite temperature which is related to emission and reflected component of all incident radiation. Now, is that a uniform thing I do not know let us not worry about it, but from a definition point of view radiosity refers to E plus rho g where rho is the fraction which is called as reflectivity which represents the fraction of energy being reflected by the surface with respect to what is incident on the surface. What is incident total energy incident is g if I have one tube light and you are standing you are you have a you are standing right below it energy coming in is g whatever is leaving it is coming in you are reflecting some component rho times g. Now, I move little away from it the g that is coming on to you will be a slightly different number rho will probably be the same because it depends on you. So, the reflected component of the energy would have decreased because g has decreased. Now, this rho can be uniform non uniform all those things we do not worry at the definition state, but we have to remember these three things emission, irradiation, radiosity fall even though I will be repetitive these are so important emission refers to again energy leaving by virtue of its finite temperature irradiation refers to energy coming in from all other surfaces which depends not on this surfaces temperature, but it depends on their individual temperatures T 1, T 2, T 3. Last quantity radiosity which is the emitted component emitted part which is because of this surface is finite temperature and the reflected component of all incident radiation that is the energy leaving the surface energy emitted plus reflected is the net energy leaving the surface. So, this is radiosity. So, these three things again and again we will revisit. Now, let us go to this so called intensity I have gone little bit ahead because this intensity is a little bit more confusing than what these things are these things if you understood we are we are going to use this word intensity to explain these three concepts. Let us read radiation intensity is a radiation emitted by a surface propagates in all direction radiation incident on the surface may come in from different direction I have told you the story. So, it is a light bulb it will go in all directions it can come in from all direction multiple tube lights in a room always when you are confused with definitions when you are confused with the concept please think of easy example radiation is actually easy that way to understand because you have it is there everywhere you do not have to imagine a flow you are standing right below a bulb commensensically you place a hand on top of a gas stove which is burning it is going to be hot you move away it is going to be cold. So, all this we have experienced we even teach our children do not do this do not go near the fire why precisely because of radiation. So, response to the of the surface to radiation depends on the direction obviously we saw that far away closer how it is oriented are you directly below or away etcetera directional effects this is leading to this concept of intensity. So, when I am dealing with direction then I have to use this thing as intensity why because what is intensity intensity in a layman's term what do we understand by intense the course is very intense what does it mean lot of information is packed light course this is a very light course it is not it is not so intense classical music is very intense meaning what you have to understand things deeply whereas, full music it is not you do not have to think so much it is it just flows it flows with the psych of the people. So, the intensity refers to some kind of how to tell it is an abstract thing, but if I say light if I am if I am shining a torch the light is so bright you know you are driving all of many of you who drive will realize it is opposing traffic vehicle comes with a high beam of light you get blinded, but if the light is on low beam cars have high beam low beam scooters have high beam low beam high beam is essentially very bright basically it you get completely blinded. So, you say it is so bright this light is manageable. So, this brightness etcetera are what we associate with intensity now in radiation what we are saying is directional aspects are there we will associate this term intensity I will come to the solid angle in a minute. So, all of us are aware of plane angle plane angle this is a example taken slice of a two dimensional surface arc of a circle subtends an angle d alpha at the center this is called as plane angle. Now, let us go to what is called as solid angle area infinitesimal area d a of a sphere subtends an angle d omega solid angle d omega at the center of the sphere quite complicated you might think it is not go back to the center of the earth where I am sitting I am looking at India like this I am having the same area I have to look differently if I have to look at green land I have to look differently though the area may be same the directionality matters go back to the sun sun is fixed earth is fixed, but the amount of energy coming into green land is much lesser than what comes to Malaysia. So, that is roughly what you understand by intensity the source does not know anything sources it does not know I am giving energy to green land or South Africa it is the same it is not knowing, but the relative positions etcetera will dictate the intensity. So, solid angle refers to this area sorry this angle central angle another example I give is ice cream cone ice cream cone larger the cone larger the cone larger is the central angle subtended smaller the cone smaller is the central angle that central angle that you are subtending is called as the solid angle clear. Now, let us go to the formal definition emission of radiation from a differential area d a 1 this is the area I am at the center of the earth I am looking at an area d a 1 into a solid angle d omega subtended by area d a n at the point on d a 1 lot of words let us understand word by word this area is me d a 1 is me. So, amount emission of radiation from a differential area why differential because we like to deal with differential small elements in where in which direction is it a big ice cream cone or a small ice cream cone it is an ice cream cone which subtends an angle d omega at the center. So, that is what this ice cream cone can be oriented if I have the same area I can have it facing India I can have it facing green land anything. So, that relative position of this d a n though d a n is the same I am taking 1 inch by 1 inch in India versus 1 inch by 1 inch in green land area is the same, but the relative positions are dictated by what angles theta here and phi here that if you understand I think the difficulty is over solid angle essentially takes takes care of this plane angle does not take care of this it just takes care of the central angle associated with the r here in radiation we have to deal with theta and phi though d a n might be the same these things matter with respect to the intensity. So, this d a n subtends an angle d phi in the x y plane and subtends an angle theta in the the third dimension what is this phi called phi is which is phi is what angle azimuthal this is the zenith angle I always zenith yeah. So, this is the zenith angle. So, d omega solid angle refers to the area d a n divided by r square. Now, let us go to these definitions. So, differential a pizza that we have told differential area d a 1 d a n is a normal to theta phi direction as in the figure this is shown here that 1 meter by 1 meter area in India is going to subtend this angle the 1 meter by 1 meter area is going to subtend the same angle, but it will be at a different relative theta phi direction that is what if you understand we are in good shape. So, at this point I just want to break.