what will the boundary(both side insulated) nodes equations be? please I need help in any way possible

The general energy balanced equation is given in the attach image

 for all interior nodes of the glass cover discretized equation:
 For i=2, 3, 4… Nx-1            
      j=4
attach as image.

how would the finite difference equation at i=1 and i=N for glass i.e. at j=4 look like? the complete control volume diagram is attached.

Answer 1

[Abraham Boayue]

Solution tips.

[John D'Errico]

Not sure why you were flagged as potential spam, but I removed the flag. My guess is because the attachment is much larger than the sparse comment you made as text, and/or because the attachment was a .pdf.

[Abraham Boayue]

Thanks John, I appreciate that.I'm quite new to this forum and would be glad to receive any tip to prevent this from happening again. Please direct me to a page where I can learn about these rules.I sometimes struggle to find information. For instance, it took more than a week to learn how to post a clear and readable code.

[Gadosky571]

Thank you Abraham. It's like you discretized it explicitly right?

[Abraham Boayue]

Yes, explicit in time and central in space. There are minor errors, take note. You are welcome, ask me if anything's uncleared.

[John D'Errico]

The spam flag rules are not well explained that I know of, probably because they don't want spammers to know how to get around their filters. I can understand that. Honestly, I rarely see responses mis-flagged as spam, so I would not worry too much. When it happens, one of us will wander through, and remove such misplaced flags anyway. For posts that really are clearly spam, I will notify the site admin, and they will typically delete the offending account. The site has been pretty good though, with little true spam getting through, so they have things well in hand.

[Gadosky571]

everything is clear. I'm trying to do it implicitly for all the components now but if I encounter any problem I'll ask you. Thanks once again.

Answer 2

[Torsten]

Your equation is a first-order PDE with only a convection, but no conduction term in it. Thus you cannot prescribe insulated boundaries. The only applicable conditions for this kind of equation are Dirichlet and extrapolation boundary conditions.

Furthermore, to discretize the spatial derivative term dT/dx, never use centered differences schemes, but only upwind schemes.

Best wishes

Torsten.