I am trying to make a model of non-stationary heating on a plate, where I must use an explicit numerical method to solve the model. I decided the plate will be made of steel (0,5% C) and I found that the thermal diffusivity coefficients $k/\rho c_p$ are:
$$\alpha_{steel} = 14.74 \times 10^{-6} \:\mathrm{m^2/s}$$ $$\alpha_{air} = 1.9 \times 10^{-5} \:\mathrm{m^2/s}$$
I also have to implement a heat source but I don't know what coefficient I should use for that.
As it's a 2D problem, my solving code looks like this:
def heat_source(x, y, matrica):
if (x >= 0.8 and x <= 1.2) and (y >= 0.8 and y <= 1.2):
if matrica[10,10]<300.:
return 280 + randn(1)*20
else:
return 0.
else:
return 0.0
dmx = (M0[iY,iX+1] + M0[iY,iX-1] - 2.0 * M0[iY,iX])/dx**2.0 # conduction in x-direction
dmy = (M0[iY+1,iX] + M0[iY-1,iX] - 2.0 * M0[iY,iX])/dy**2.0 # conduction in y-direction
M_new[iY,iX] = M0[iY, iX] + k_diffusion*dt*(dmx+dmy) + dt*k_heating*heat_source(X[iX], Y[iY], M0) - dt*k_cooling*(M0[iY,iX]-T_ok)
My questions are:
- Am I using the right coefficients? If yes, what coefficient should I use for the heat source?
- What's the difference between non-stationary and stationary source?