INTRODUCTION TO HEAT AND MASS TRANSFER




At the high level when we think of heat or mass transfer we need to think about the flux equation there's this general equation that applies time and again to everything we're going to be doing and that is this rule that tells us that flux is equivalent to some kind of coefficient which we'll just abbreviate times some driving force and so without looking at any numbers or any greek letters this is all it's telling us is that we've got some flux is equal to this coefficient times a driving force and i was beginning to depict these terms what we're going to know is that flux is equivalent to a quantity per area per time and then this coefficient is generally something that's in a form of like a k or some some literally just a constant or coefficient that depends on some other factors and then this driving force is usually some kind of difference between two things or a differential and so when we take this kind of template breadboard and look at the heat transfer equation that we may have learned in

high school chemistry or physics class usually what you'll see people write is this stuff where you've got you to know q dot is equivalent to k times a times delta t or something like this and as you introduce differentials into these equations we look at the dt kind of temperature gradient and so this flux if we look at this equation here is really just dividing both sides of this equation by area so flux here corresponds to this q dot over a term I'm sorry my, uh computer's acting up a little bit but you get the point so flux is equal to this coefficient times this driving force and specifically this heat flux is equivalent to this coefficient of heat transfer times a difference in temperature some kind of temperature gradient and what we also remember from the fundamental laws of thermo is that heat is transferred from hot objects to cold objects so we know the directionality of this heat transfer

so very important to remember that heat moves from hot to cold objects and we can say something very similar to things regarding mass transfer and when we look at mass transfer we'll say that mass moves from high to low concentrations so if I took a ball pit of many

different colored balls just like we used to have a chuck e cheese and we had all these red balls stuck in the corner that's an area of high concentration and what do I expect to happen over time is we have mass transfer occurring in my ball pit as I expect to see a bunch of my red balls eventually diffuse through the ball pit and then they'll be widely distributed everywhere just the same thing can be said with heat or this energy it's that energy doesn't like to be jammed up in this one spot it wants to kind of diffuse through systems and if we ask ourselves the big question here why is because it's how we maximize entropy how do we give something the most degrees of freedom it can possibly have in our closed system and so um this is the very important conceptual overview of everything we're going to be discussing in heat and mass transfer classes as engineers and scientists now the next

the thing we're going to be looking at is the units that we're going to be using or the dimensions that are going to be in all of our equations and so when we talk about a rate of heat transfer like how many joules per second of something are moving through an object we usually define the term watts so w I'll just write it out watts one watt is equal to one joule per second so it's a rate of energy how much energy have I just transferred in this given period is equal to one watt and so commonly when we're talking about a heat flux which I'll put a little hat on top of our cube just so we know that q q hat which is really equivalent to this q dot

over the area this heat flux is equal to q dot which q dot is just going to have units of watts per area so if we look at the dimensions on this equation we'll have watts per and we can go with like meter squared area will be equal to some coefficient of heat transfer and my computer sucks today anyway um some kind of coefficient of heat transfer which I'll just leave it to ask for now and we'll keep these dimensions the same and we can actually do a dimensional analysis determine what, uh k is so it's going to be equal to some coefficient

times a difference in temperature this difference in temperature will have units of something like degrees Celsius or degrees Kelvin for instance and I'll go with degrees c just so that I am sticking to not having too many k's present so this thing here will have units of

times you know degrees c so you'd have like 0 and 100 degrees celsius would be this difference in temperature that is causing a movement of energy in your system and so if we wanted to do a dimensional analysis and say like okay tell me what are the units of uh k in this equation it's literally just rearranging it k your coefficient of heat transfer is going to have units of watts per meter squared per degree celsius and so these can have a lot of different dimensions to them depending on what units you're doing within your specific problem statement and so when we look at something like mass transfer i'm going to try to keep this video short too by the way but when we look at units of mass mass transfer well what do we measure mass in we measure mass usually in stuff like kilograms or kilomoles so we've got kilograms and we're carrying about some rates so this would be a kilogram of something moved per second for instance would be equivalent to what is our heat flux or i'm sorry our mass flux and then we're going to be dividing this whole thing by the an area so we'd say you know how many kilograms per second are moving through this material in one square meter of space for instance and so this would be the left side of our general flux equation

and on the right side we're going to have again some kind of coefficient of mass transfer which i'll again just say let's call it k sub m k sub m times and then a driving force for this mass transfer and this driving force is going to have units of concentration differences so how many you know kilograms per given volume are we going to have of something that is resulting in this mass exchange and so if we begin to think about well what is units of concentration as we were saying this is usually equivalent to you know we can think of stuff in terms of like moles per uh something so i'd say like kilomoles per cubic meter and then if we do some kind of dimensional analysis on this and for the sake of uh simplicity i will keep things in units of kilograms per cubic meter so it's amount of stuff for a given volume and if we were to now do a dimensional analysis on what is k sub m k sub m would be equivalent to the following so we would have kilograms per second per square meter and we would multiply this by the reciprocal we would have kilograms per cubic meter so the dimensions on the following here would be meters per second which is actually equivalent to velocity which is very interesting but anyway so these are the dimensions we're going to be working with in our mass and heat transfer equations and these are the core concepts that we should just get right from the start and then to give an example problem of something that you know i think all of us can relate to if we think about the following in which we are sweating I think it's an excellent example of something that shows how connected rates of heat and mass transfer are to one another and uh to set up some kind of example problem that can be food for thought let's say that the human body has an area of two square meters so you've got two square meters of exposed skin and when we are sweating what's happening to this sweat so if I was to take a section of skin exposed skin and we've got this sweat right here on the surface i'll just label this skin and sweat and we think about what is the objective of sweating it's to cool us down right so the objective here is to cool down the body as soon as possible because you're really hot and what is happening here is when we think about the two things that are happening with the sweat is number one we are changing the thermal properties of our skin by having this fluid on its surface it's making this fluid much more conductive and or it's making this surface a lot more conductive which is allowing a lot more heat to go from your body to the outside world assuming that you know if you had t sub b and t sub a where t sub b was greater than t sub a which is generally the case because your body temperature is 98.6 outside temperature is probably 70 degrees c or i'm sorry 70 degrees f you're going to have temperature flowing you're going to have heat flowing in the direction from your body to the outside world so this would be q sub dot right there and so the two equations here to think about would be in terms of this heat transfer that is occurring at this moment in time we can say that q dot will be equivalent to some kind of coefficient of heat transfer which i'll just call k and then this would be q dot per area by the way just we stick to what we were talking about earlier.