Heat and Mass Transfer Introduction

Summary

Highlights

• The general flux equation: A versatile tool for heat and mass calculations! 🧮
• Sweating illustrates how our bodies use mass and heat transfer to cool down. 🏃‍♂️💦
• The video explores the relationship between heat transfer coefficients and temperature gradients. 🧐
• Understanding units is crucial for problem-solving in heat and mass transfer. 🔍
• Sweat, as a cooling method, is tied to the heat of vaporization concept - lots of energy involved! ⚡️

Key Takeaways

• Flux is the cornerstone of understanding heat and mass transfer! 🌟
• Heat typically moves from hot to cold, while mass moves from high to low concentrations. 🔥❄️
• Sweating is a perfect real-world example of heat and mass transfer working together! 💦
• Units matter! Watts, degrees, and kilograms all play a role here. 📏
• Entropy maximization: systems love having more freedom and spread that energy or mass around! 🌌

Overview

Chapters

• 00:00 - 01:30: Introduction to Flux Equation The chapter introduces the fundamental concept of the flux equation in the context of heat or mass transfer. It emphasizes the importance of a general equation that repeatedly applies to various scenarios in scientific computations. The discussion highlights how flux is defined as equivalent to a product of a coefficient and a driving force, emphasizing an understanding beyond numerical or symbolic representations.
• 01:30 - 04:30: Heat Transfer Concepts The chapter introduces heat transfer concepts, focusing on the relationship between flux, a coefficient, and a driving force. Flux is explained as a quantity per area per time, while the coefficient is described as a constant that depends on various factors. The chapter aims to depict and explain the integral terms in the context of heat transfer.
• 04:30 - 07:30: Mass Transfer Concepts The chapter discusses core concepts in mass transfer, drawing parallels with heat transfer principles often taught at high school levels in chemistry or physics. It introduces the idea of a 'driving force', typically characterized by some kind of difference or differential between two entities, which is crucial for understanding the dynamics of mass transfer processes.
• 07:30 - 10:30: Units and Dimensional Analysis The chapter titled 'Units and Dimensional Analysis' covers foundational concepts in physics and engineering, emphasizing the importance of using correct units for measurements and calculations. Key topics include the concept of flux, which is explained as the rate of flow of energy or particles across a surface area, often expressed in terms of q dot (heat transfer rate) divided by area. The equation relates heat flux to thermal conductivity (k), surface area (A), and temperature gradient (delta T). The section additionally explores how introducing differentials can better describe changes in temperature gradients, enhancing the precision of flux calculations. The focus is on understanding and applying dimensional analysis to ensure equations are dimensionally consistent and accurately represent the physical phenomena being modeled.
• 10:30 - 15:30: Sweat as an Example of Heat and Mass Transfer The chapter discusses the concept of flux in relation to heat and mass transfer, using sweat as an example. It explains that flux is the product of a coefficient and a driving force. Specifically, heat flux is described as the product of a heat transfer coefficient and a temperature gradient. It reinforces the fundamental thermodynamic principle that heat is transferred from hot objects to cooler ones.

Heat and Mass Transfer Introduction Transcription

• 00:00 - 00:30 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
• 00:30 - 01:00 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
• 01:00 - 01:30 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
• 01:30 - 02:00 you 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
• 02:00 - 02:30 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
• 02:30 - 03:00 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
• 03:00 - 03:30 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
• 03:30 - 04:00 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 why is because it's how we maximize entropy how do we
• 04:00 - 04:30 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 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
• 04:30 - 05:00 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 time period is equal to one watt and so commonly when we're talking about a heat flux
• 05:00 - 05:30 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 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 for area will be equal to some coefficient of heat transfer and my computer sucks today
• 05:30 - 06:00 anyway um some kind of coefficient of heat transfer which i'll just leave it as k 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
• 06:00 - 06:30 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
• 06:30 - 07:00 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
• 07:00 - 07:30 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
• 07:30 - 08:00 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
• 08:00 - 08:30 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
• 08:30 - 09:00 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
• 09:00 - 09:30 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
• 09:30 - 10:00 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
• 10:00 - 10:30 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
• 10:30 - 11:00 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
• 11:00 - 11:30 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
• 11:30 - 12:00 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 this is equivalent to k times this difference in temperature which would be t sub b minus t sub a and negative signs here are pretty important um so you're going to want to just make sure that you've defined
• 12:00 - 12:30 what is the direction and then assign a sign to that specific direction but yeah so that is what this would look like and if we think about well in terms of a mass transfer equation what's happening is your sweat which we can simplify in this example as just water this sweat is evaporating it's changing phase into uh it's leaving the liquid phase and entering the vapor phase which would be the air in this example so we've got a liquid
• 12:30 - 13:00 phase right here a vapor phase in the air and over time as your sweat evaporates it is evapora evaporat is going to be grabbing energy from its surroundings in the process of doing this mass transfer into a different phase and the result of that is going to be some kind of heat loss from the surroundings and so this is the reason why your sweat is so powerful is it's not just helping you cool down by increasing the coefficient of heat transfer
• 13:00 - 13:30 between your skin and the outside world but it's also going to be grabbing energy so the molecules or the little atoms of liquid that are in the liquid phase are going to be getting enough thermal energy to be excited and leave into the vapor phase so that's the other big thing that's happening here so in that regard what we can think about is the heat of vaporization and this has units of
• 13:30 - 14:00 kilojoules per kilogram so how many kilojoules of energy do you need to put into a kilogram of something to make it change phase from a liquid to a vapor and for water at 18 degrees c this is equivalent to 2458 kilojoules per kilogram which is a lot of energy per kilogram of water so if you sweated one liter of water which is one kilogram
• 14:00 - 14:30 that one liter of water is going to be taking with it 2458 kilojoules of energy from the surroundings in order to be evaporated and so this is a lot of energy that your body is having taken away from it in order to help you cool down which is also accomplishing this goal here of why do we sweat and so as a conceptual example this is what's happening and so in terms of thinking about the relationship between these two because i think when
• 14:30 - 15:00 you're presented with this stuff as an undergrad you know you're gonna be talking about heat transfer and then you're gonna be talking about mass transfer and you know there are these parallels between the two but there's also this very beautiful relationship which is you know as we have this mass transfer occurring we're also going to be affecting the rates of heat transfer because there's going to be less water to be changing this coefficient of heat transfer and there's also going to be you know as there's more heat transfer uh the rates of mass transfer also going to
• 15:00 - 15:30 be changing too so there's this dependence on both temperature and concentration differences that are the reasons why we have to rely so much on these partial differential equations to accurately model our systems so a lot of food for thought i thought i'd just present this as a introduction to heat and mass transfer and hope you guys enjoy it let me know if any questions thank you all for watching and especially during these coveted times please stay safe wash your hands wear masks and be safe and i'll talk to you next time