  Consider neutron transport equations in 3D convex domains with in-flow
boundary. We mainly study the asymptotic limits as the Knudsen number
$\epsilon\rightarrow 0^+$. Using Hilbert expansion, we rigorously justify that
the solution of steady problem converges to that of the Laplace's equation, and
the solution of unsteady problem converges to that of the heat equation. The
proof relies on a detailed analysis on the boundary layer effect with geometric
correction. This problem can be formulated in many different settings, and the
above one is probably the most physically significant and most mathematically
challenging. We have to utilize almost all methods and techniques we developed
in a series of papers in the past decade, and bring novel ideas to treat the
new complications. The difficulty mainly comes from three sources: 3D domain,
boundary layer regularity, and time dependence. To fully solve this problem, we
introduce several techniques: (1) boundary layer with geometric correction; (2)
remainder estimates with $L^2-L^{2m}-L^{\infty}$ framework; boundary layer
decomposition.
