×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Modeling pv module using FDM (implicit scheme)

Modeling pv module using FDM (implicit scheme)

Modeling pv module using FDM (implicit scheme)

(OP)
Greetings. I am currently trying to model a photovoltaic module, mounted on a roof, using an implicit scheme of FDM (finite difference method). My primary concern is the boundary conditions. To be more precise, assuming a one dimensional heat flow, the heat diffusion equation is ∂T/∂t=(k/ρCp)∂2T/∂x2.

Internal nodes
Applying the implicit scheme to the heat diffusion equation leads us to the following equation, valid for internal nodes:
(-kdt/ρCpdx2)Ti-1p+1+(1+2kdt/ρCpdx2)Tip+1+(-kdt/ρCpdx2)Ti+1p+1=Tip



Boundary conditions
Upper surface (i=0)
Qsol-Qconv-Qrad=Qcond→-k(T1p+1-T0p+1)/dx=Qsolp+1-Qconvp+1-Qradp+1→-k(T1p+1-T0p+1)/dx=Qsolp+1-hc(T0p+1-Tairp+1)-εσ(Τ0p+14-Tairp+14)

Lower surface (i=n-1)
Qcond=Qconv+Qrad→-k(Tn-1p+1-Tn-2p+1)/dx=Qconvp+1-Qradp+1→-k(Tn-1p+1-Tn-2p+1)/dx=hc(Tn-1p+1-Tairp+1)-εσ(Τn-1p+14-Tairp+14)

where:
Qsol: insolation
Qconv: convective heat losses
Qrad: radiative heat losses

k: thermal conductivity
Cp: specific heat capacity
ρ: density
ε: emissivity
σ: Stefan-Boltzmann constant
T: temperature

Subscripts:
Spatial i=0,1,...,n-1
Temporal p=0,1,...,m-1

My questions are:
Am i right so far? If i am, what happens when unknown temperatures to the power of four are inserted into the system of equations? Do i assume an overall/combined coefficient h=hconv+hrad to linearize the radiation factor (Qrad+Qconv)=h(Tsurface-Tair)? I really need help on this one.

Thank you in advance and i apologise for any unclarities.

RE: Modeling pv module using FDM (implicit scheme)

Simply the math and the model. By far the greatest heat loss will usually be convective, unless you have attached some thermal jacketing. I'd leave out the conduction and radiation losses for now. See how well that matches actual performance then decide about adding them back in, if and when you need to.

RE: Modeling pv module using FDM (implicit scheme)

If you have radiation in the boundary condition then you'd need to iterate until convergence was achieved. In such schemes it's normal to use the first step of Newton's method to reduce the quartic down and improve convergence. Look at this site https://www.math.ohiou.edu/courses/math3600/lectur... as an example

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources