Complete using Python code. Numpy and Sympy preferably. The heat diffusion equat

Question

Complete using Python code. Numpy and Sympy preferably.

The heat diffusion equation can be simplified to the following for a 1-D, steady state with constant generation case: T"(x) + q/k = 0 where T(x) is the temperature distribution as a function of x and q/k is heat generation over conductivity. Define a function, solve_bvp, that will accept the following arguments in the following order: q, k, T_0 (value of T(0)), T_L (value of T(L)), L (length of the 1-D slab of material, i.e., the position at second boundary condition), and N (number of points at which to evaluate the temperature). Your function should return T (a np. array of the temperatures) and x (a np. array of x values at which the temperature is evaluated).

Explanation / Answer

The 1-D of the heat diffusion equation is basically helps us to verify and calculate the coefficient which examines the No. of changes occuring over a time.

I have developed the Phyton Code using Numpy and Sympy along with the comments for each part of the program. i have attached an Program over here.

Program:-

# The first step is to import the numpy and sympy Files
import numpy as npa
from sympy.parsing.sympy_parser import parse_expr
import lambdify, implemented_function

# Created an function named "sol_bvp" using the following arguments.

def sol_bvp(q,k,T_0,T_L,L,N):

heatFig = 1DPlot.figure()
heatFig.set_dpi(100)
heatAxis = heatFig.add_subplot(1,1,1)

# Let us assume k heatValues as 3
k = 3

# This is an important factor for visualizing the heat generation
scale = 7

# Let us give the heatValues of Length as PI
L = pi

> T_0 = 0
T_L = 7

q = 0.01

def heatUValue(b,v):
return T_L + scale*npa.exp(-k*v)*npa.sin(v)

def oneDValue(v,b):

return scale*npa.array([npa.exp(x)+npa.(q/k)])

a = []
v = []

for i in range(500):
heatValues = heatUValue(oneDArray,T_0) + oneDValue(oneDArray,T_0)[1]*q
v.append(T_0)
T_0 = T_0 + q
a.append(heatValues)

def findTemp(i):
global k
v = a[k]
k += 1
heatAxis.clear()
1DPlot.plot(oneDArray,v,color='Blue',label='The required temparature is')
1DPlot.grid(True)
1DPlot.ylim([T_L-3,3.7*scale])
1DPlot.xlim([0,L])
1DPlot.title('The final heat equation of the 1-D array is')
1DPlot.legend()
  
heatExp = animation.FuncAnimation(heatFig,findTemp,frames=360,interval=20)
1DPlot.show()

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