Animated 2D heat map

Question

I have a function u(x,y,z,t) and I wanted to plot (x,y) animated heatmap with colorbar (u_min, u_max) where t is parameter for time animation. I've analyzed the examples, but it looks complicated. The z parameter will be constant. The defined u(x,y,z,t) is the equation u(x,y,z,t).

I made this

import matplotlib.pyplot as plt
import numpy as np

def u(x, y, z, t):

   alpha = 9*10**-6
   a = 0.01
   z = a/2


   for i in range(1,k):

       sin1 = np.sin((i*np.pi*x)/a)

       sin2 = np.sin((i*np.pi*y)/a)

       sin3 = np.sin((i*np.pi*z)/a)

       e = np.exp(-((alpha**2)*(np,pi**2)*((n**2)*(m**2)*(l**2))*t/a**2)

       a_n = 80*(2/np.pi)**3*(1/n*m*l)*(1-(-1)**n)*(1-(-1)**m)*(1-(-1)**l)

       u += 20 + a_n*sin1*sin2*sin3*e

    return u

data = u

fig, ax = plt.subplots()

for j in range(len(data)):
    ax.cla()
    ax.imshow(data[j])
    ax.set_title("frame {}".format(i))
    plt.pause(0.1)

Thank you for help.