tailieunhanh - Kinetics of Materials - R. Balluff_ S. Allen_ W. Carter (Wiley_ 2005) Episode 4

Tham khảo tài liệu 'kinetics of materials - r. balluff_ s. allen_ w. carter (wiley_ 2005) episode 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 114 CHAPTER 5 SOLUTIONS TO THE DIFFUSION EQUATION An estimate of the penetration distance for the error-function solution Eq. is the distance where c x t co 8 or equivalently erf 2 2v Di 3 4 which corresponds to XKTbVDt A reasonable estimate for the penetration depth is therefore again 2y Dt. To estimate the time at which steady-state conditions are expected the required penetration distance is set equal to the largest characteristic length over which diffusion can take place in the system. If L is the characteristic linear dimension of a body steady state may be expected to apply at times T L2 min where Drain is the smallest value of the diffusivity in the body. Of course there are many physical situations where steady-state conditions will never arise such as when the boundary conditions are time dependent or the system is infinite or semi-infinite. Bibliography 1. . Morse and H. Feshbach. Methods of Theoretical Physics Vols. 1 and 2. McGraw-Hill New York 1953. 2. J. Crank. The Mathematics of Diffusion. Oxford University Press Oxford 2nd edition 1975. 3. . Carslaw and . Jaeger. Conduction of Heat in Solids. Oxford University Press Oxford 2nd edition 1959. EXERCISES A flat bilayer slab is composed of layers of material A and B each of thickness L. A component is diffusing through the bilayer in the steady state under conditions where its concentration is maintained at c Co constant at one surface and at c 0 at the other. Its diffusivity is equal to the constants DA and DB in the two layers respectively. No other components in the system diffuse significantly. Does the flux through the bilayer depend on whether the concentration is maintained at c Co at the surface of the A layer or the surface of the B layer Assume that the concentration of the diffusing component is continuous at the AỊB interface. Solution. Solve for the diffusion in each layer and match the solutions across the A B interface. Assume that c Co at the surface of the A .

TỪ KHÓA LIÊN QUAN
crossorigin="anonymous">
Đã phát hiện trình chặn quảng cáo AdBlock
Trang web này phụ thuộc vào doanh thu từ số lần hiển thị quảng cáo để tồn tại. Vui lòng tắt trình chặn quảng cáo của bạn hoặc tạm dừng tính năng chặn quảng cáo cho trang web này.