Question

4. Neutron Diffusion in Two Different Media Consider a plane neutron source of strength S (neutrons/cm's) placed at x = 0 between beryllium and graphite as shown below. It is desired to determine the effectiveness of these metals as neutron shielding materials. Plane source a) Solve a neutron diffusion equation for the neutron flux distributions, docx <0) in beryllium Beryllium Lead and co(x > 0) in graphite. Two boundary conditions to be specified at the source location (X (0<x) 0) are as follows: Jo(0) = J.(0) + S and (-20 < x < 0) | (0) - (0). x0 b) If the source strength is, S - 10 neutrons/em's, calculate the neutron flux at x = 1.0 m and -1.0 m. The diffusion coefficients, diffusion lengths and absorption cross sections for beryllium and graphite are as follows: D -0.5 cm and Do = 0.84 cm; Lo = 22.0 cm and Lo = 59.0 cm; 2,0=1.04 x 10 cm and 2.0 = 2.4x10 cm Which material is more effective for shielding against neutrons? c) Calculate the number of neutrons absorbed in beryllium and graphite per unit area per unit time. What is the fraction absorbed in beryllium?

Answer 1

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R solution Given that ord - kad =-5 and also ke=0 Then DD²6-0 - - 5 A &= -3 On dividing by a both sides we get A = -50 Now for General solution V¢=0 saying that or å The Laplacian Enopherical Coordinator terms vd = 22 +2% 2 Proposing an exponential solution per+2% de to ao so d = 20 and finally d = f/ofB Noter of it u weful te you please like timpup and you have any doubt on the Answer pleove leave a comment