Derivation of the Energy Equation

[@JousefM]

🎓 My Science Courses - courses.jousefmurad.com/ ✍️ Latest blog posts: jousefmurad.com 📥 My Newsletter - jousef.substack.com/ Thanks for watching! Make sure to like & comment :) Time Stamps ---------------------- 0:00 - 0:30 : Intro 0:31 - 1:45 : Recap from the last videos 1:46 - 2:27 : Derivation of the Energy Equation (Intro) 2:28 - 4:00 : Compressible vs. Incompressible 4:01 - 4:51 : What does "Compressible" mean? 4:52 - 5:40 : Mach Number 5:41 - 7:22 : Change of Energy inside of the Control Volume (CV) 7:23 - 7:35 : Recap Mass Conservation 7:36 - 7:50 : Balance for the Energy Equations 7:51 - 8:50 : Change of Internal & Kinetic Energy 8:51 - 9:44 : Energy Transport - Heat Transfer 9:45 - 10:35 : Work per Time Balance 10:36 - 12:50 : Assembling the Equations - Simplification - Stokes Hypothesis & Dissipation Function 12:51 - 13:42: Perfect Gas Ansatz & Equation 13:43 - 14:57: External Aerodynamics 14:58 - 16:29 : Torque Converter 16:30 - 16:56 : Compressible Flow Around an Airfoil 16:57 - End : Outro

[@mesharyRD]

I just saw that you uploaded a video and I'm about to sleep. I just give you a like and will see the video tomorrow. Keep up that good work 👍👍

[@JousefM]

Thanks brother

[@ahmetyilmaz6370]

This video really helped me out for understanding the derivation of thermal energy equation, thank you very much. It was such a clear explanation. Thank you for sharing. Keep up the good work.

[@JousefM]

Thanks Ahmet! 🙂

[@KevinskyChen]

Outstanding video!!! Keep on bro :)

[@JousefM]

Thanks buddy! :)

[@perdanafahrizal8948]

thanks

[@JousefM]

Thank you! 🙂

[@marcosfilho5534]

Thank you! Could you do a video on the turbulence topic?

[@JousefM]

Thanks for watching buddy! Yes, will definitely come. Actually a whole course or lecture session is planned on that topic :)

[@amalbinu1874]

what is 'e' denote in the equation for internal energy at 6:00. ?

[@arshibanu1129]

Best Energy equation in You tube

[@JousefM]

Thanks mate 🙂

[@feedyourhead2661]

Why does the energy in the CV only include internal energy and kinetic energy, but you left out potential energy? @5:50

[@nellvincervantes6233]

I dont get the math on 12:13. Why the V^2/2 term (the 2nd term being vanished) is completely vanished when you perform algebra as explained at 12:15, it will be -V^2 term not -V^2/2. And also the k term why it didnt vanish since you this on your navier stokes equation at 12:15 (kx , ky , kz) and k dot V on 12:13. So if you do subtraction as stated at 12:15, k dot V - ukx - vky - wkz = 0.

[@lila9306]

Thanks for the videos, they r very helpful. Can you make a video explaining how to turn differenctial equation (NS) to a linear system equation plz

[@JousefM]

Thanks :) Yes can put it on my to-do list! If I can condense it into a short video it might come soon.

[@shivanandsinghPCEME]

Step wise step clear the concept Thank you ☺️

[@JousefM]

Thanks! 🙂

[@GG-vw1et]

I think you missing something at work per time balance, the surface area of the stress component at min 09:57

[@tahersphysicstutoring5454]

amazing video keep it up greeting from egypt

[@JousefM]

Thanks brother 👊

[@emelvkurian158]

Thank you for your videos. Can you help me out to know what all parameters should I consider, what all equations have to be used, and how to solve them for a gas changing phase to a solid(deposition)? I wouldn't request you to make a video on it. If it has piqued your interest you may create one and I will be happy about it.

[@tannerragan1893]

Great video and super helpful! Thank you so much!

[@JousefM]

Sure 🙂

[@ChOrestisPapas]

Great content

[@heeyoon6099]

Thank you very much for your lecture. By the way, I cannot understand in terms of work balance 10:04, why do you use write down P and normal stress term? I mean isn't it the same? could you give me some kinds of details why you use pressure term and normal sress term?

[@kaanakkas1404]

at 9:40 and 10:00, at the end of the equations there are additional minus(-) and plus (+).Are these typos? Thank you for the video btw. U have clear expression and this video didn't confuse me contrary other videos about this topic.

[@JousefM]

Thanks Kaan! Not a typo. :)

[@AbiRizky]

At 13:36 where you give the equation for perfect gas,. are you sure the term for stresses is correct? In the previous slide it said p(div V) and in the perfect gas slide it was pretty much material derivative of p. Or am I missing something here?

[@JousefM]

Maybe I’m a bit confused here but I don’t get your question :) did you figure it out in the meantime?

[@AbiRizky]

@@JousefM no I haven't, sorry. Alright let me rephrase. In 12:33 where you said it was the final equation, the stresses term was p(div V), which can also be written as p(du/dx + dv/dy + dw/dz) And yet at 13:36 (the perfect gas one) you wrote (dp/dt + u dp/dx + v dp/dy + w dp/dz) which is the material derivative of pressure, no? What I would like to know is why did this term change? Am I missing something? Oh and I'm sorry for the confusion, English isn't my first language

[@JousefM]

@@AbiRizky No worries. So I am trying to explain why the term changed and what you have to do to get there, hasn't been derived step-by-step. Taking the equation from 12:33 , we derive the equation that confused you by assuming caloric perfect gas and use the thermodynamical relation e=c_p*T - p/rho - simply by using the thermodynamical relation and this equation from 12:33 we can derive the "final equation". And you are somehow right, its the material derivative or substantial derivative, however with respect to the temperature. So local, temporal change of the temperature at a fixed place PLUS the convective part of each temperature direction, does that make sense somehow?

[@AbiRizky]

@@JousefM it does actually! But I suppose it was a mistake at first for not including the temporal derivative for the pressure? Because the term p(div V) at 12:33 doesn't give out anything regarding the change of pressure with respect to time?

[@phenomenal4690]

which is the video about descritization ?

[@JamesVestal-dz5qm]

Undergrads need support from the experts using calculators. I write the ideas in pen and figure out how to use the calculator as homework.

[@MrDuonghuong1991]

Could you do a video on the turbulence topic please? i have waited for long time:))

[@JousefM]

Haha everyone is asking about that! Will come, promise! Hope you did not only subscribe for turbulence because plenty of other stuff is coming as well 😄

[@saadalzubedy6537]

Hello doctor, I need your help to solve this question (Using scale analysis, obtain the energy conservation equation for a laminar, viscous, and incompressible external flow on a flat plate and under steady-state conditions) ( heat transfer convection ) thanks for your help

[@thuzaraung5987]

could you do a video on turbulence topic? thank you!

[@JousefM]

Planned and (slowly) in scripting 🙂

[@thuzaraung5987]

looking forward to it!

[@JamesVestal-dz5qm]

I have a calculator and I use it a few times per week.

[@JamesVestal-dz5qm]

I don't bring a calculator to class because ideas I can write on paper are more important. Calculators are a homework exercise.

[@sriti_hikari]

Hello friend.

[@JousefM]

Helo fren, plz liek and supskrib.

[@sriti_hikari]

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[@husamali1306]

❤️❤️👌🏻

[@JousefM]

Thanks bro 🤛 ❤️

[@JamesVestal-dz5qm]

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