Unsteady Convective Diffusion of Solute in a Micropolar Fluid Flow through a Cylindrical Tube
Pradeep Ganapathi Siddheshwar, SHRIPAD MARKANDE · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 1999
The problem of unsteady convective diffusion of miscible solute in a fully developed micropolar fluid flow in a cylindrical tube is solved for the cases of no chemical reaction at the bounding walls of the tube and when there is heterogeneous chemical reaction. The convection and dispersion coefficients of all time validity are obtained when there is no chemical reaction. The exchange coefficient arises in the heterogeneous chemical reaction case. The time dependent expression for the exchange coefficient is obtained explicitly and is found to be independent of the velocity distribution of the flow; however it does depend on the initial solute distribution. Because of the complexity of the interphase mass transfer problem only an asymptotic long time analysis is made of the convection and dispersion coefficients. The expression for the mean concentration distribution of the solute is also evaluated in both non-reactive and reactive cases. The problem succeeds in demonstrating the generality of the Eringen micro-continuum model by spanning the results of a few continuum fluid models as limiting cases of the present study.