Good Day
I am new to heat transfer technique please give me some suggestion on solving energy balance equation. PLEASE SUGGEST SOME NUMERICAL METHOD TO SOLVE THIS EQUATION
a*∂Tp/∂t=∂/∂x(b*∂Tp/∂x)+∂/∂z(c*∂T/p∂z)+b
which is discretized as
a(Tp−Tp0/Δt)=c(Tu−Tp/ΔXuΔX)+d(TD−Tp/ΔXdΔX)+e(Tw−Tp/ΔZwΔZ)+f(TE−Tp/ΔZEΔZ)+b
b=Sc+SpTp
Where Tp is the temperature of solar panel
a,c,d,e,f are the constant value.
I am not getting how to proceed with this equation. Please suggest some hints at solutions.
For example, you can use Crank–Nicolson method or Leapfrog method.....
Hello Sayed,
The second equations is, in practice, a linear system. In other words, you start with the solution at t=0 (initial condition) and solve one linear system per time step (which is, Ax=b where x contains all the temperatures at the new time step and b contains all temperatures at the present time step).
If you are a beginner on this kind of approach, there are simpler ways to do this (although not necessarily the best ones), which will allow you to produce results while grabbing a hold of how the method works. You are now using the Implicit Scheme to solve the problem in time. Consider checking the Explicit scheme (there are several other options, but these two are found in any finite-difference book).
A really good reference is the book Finite-Difference Methods in Heat Transfer, by M.N.Ozisik.
Regards,
Dear Sayed Ameenuddin Irfan
As @César said, the explicit finite difference approach is the simplest one to solve the problem. This method is simply introduced in any fundamental heat transfer text book (like J.P. Holman, Heat Transfer or F.P. Incropera, D.W. Dewitt, Fundamentals of Heat and Mass Transfer, or ...)
Cheers
Thank you all for this wonderful solution. I will solve it as you suggested.
You can solve it by finite difference method or keller box method
you can solve this problem using explicit methods given in the book of G.D. Smith
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