Note that in the below code we use the scipy.special functions k0, k1, i0 and i1 which are faster and more accurate implementations of the more general kn and iv functions for calculating the modified Bessel functions of the first and second kinds.
import numpy as np
from scipy.special import k0, k1, i0, i1
# Component temperature, ambient temperature (K)
T0, Te = 400, 300
# Fin width, internal radius, external radius (m)
w, r0, r1 = 0.1 * 1.e-3, 0.005, 0.01
# Heat transfer coefficient (W.m-2.K-1), thermal conductivity (W.m-1.K-1)
hc, kappa = 10, 200
beta = np.sqrt(hc / kappa / w)
u0, u1 = beta * r0, beta * r1
# Cooling efficiency
eta = 2*r0/beta * (k1(u0) * i1(u1) - i1(u0) * k1(u1)) /\
(r1**2 - r0**2) / (k0(u0) * i1(u1) + i0(u0) * k1(u1))
print('eta = {:5.3f}'.format(eta))
fin_area = 2 * np.pi * (r1**2 - r0**2)
# Heat dissipation (W)
Qdot = eta * hc * fin_area * (T0 - Te)
print('Qdot = {:.2f} W'.format(Qdot))
Output:
eta = 0.994
Qdot = 0.47 W