| Abstract: | The stationary problem of convective diffusion in a channel with absorbent walls is considered. It is assumed that a Poiseuille flow exists. Two methods are employed in the solution, the method of separation of variables, and the method of expansion in eigenfunctions of the corresponding problem with piston profile (expansion method). It is established by comparison with independently obtained solutions for high Peclet number that for the first eigenfunctions and eigenvalues the expansion method gives satisfactory results over the entire Peclet-number range. For approximate calculation of subsequent eigenfunctions and eigenvalues a modification of the smooth asymptotic expansion method is used. The results are used to calculate matter flow density on the wall, to evaluate the length of the entrance region, and to obtain an analytical expression for the limiting Nusselt number in terms of the Peclet number.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 63–73, November–December, 1973. |
