A python library that simulates two-dimensional transient heat conduction in a square plate using ADI finite difference method
The repository can be cloned and the library TwoDHeat.py can be simply imported for use
The library uses the following two python libraries
- numpy
- matplotlib
A square plate of length 2L and thermal diffusivity α with initial temperature Tin is suddenly subjected to temperature T0
The problem is a diffusion type problem and the governing equation is given by
with IC, T = Tin at t = 0, ∀ x,y and BCs, T = T0 at x = L and y = L for ∀ t > 0
After appropriate non-dimensionalisation the equation can be given as
Alternating Directional Implicit finite difference method is used to calculate the temperature
Implicit FDM formulation in x direction for the first half time step results in
where θ* denotes θ at time step t= p+½
These equations don’t incorporates boundary cases and image point technique is used for such cases
Further FDM over y direction results in
here
The object to the class has to be passed with a dictionary of parameters for the simulation
Objects's solve() function is to be called for the animation to start
from TwoDHeatTransfer import TwoDHeatTransfer as problem
parameters ={
"Length" : 1., #Length of the plate
"T0" : 300., #Surrounding Temperature
"Tin" : 100., #Initial Temperature
"alpha" : 0.5e-6, #Thermal diffusivity
"Nelements" : 20, #Number of elements along the half plate
"timestep" : 0.01, #Value of dt(dimensionless time step)
"Niteration" : 150, #Number of iterations over
}
p1 = problem(parameters) #initialise object with these parameters
p1.solve() This is one snapshot of the animation
