Convective-diffusive transport with a wall reaction in Couette flows

Convective-diffusive mass transport coupled with a wall reaction in a planar Couette flow has been investigated. The system is isothermal and it features a first-order chemical reaction at the (upper) moving wall (or interface) combined with axial convective transport and lateral diffusion. The mathematical model defines a two-point boundary value problem in the lateral direction and an initial value problem in the axial direction. The solution to the model is obtained following an operator-theoretic approach whose Sturm-Liouville problem has been solved analytically in terms of Airy functions. The solution is illustrated with calculations for a wide range of parameter values and the effect of the reaction on the Sherwood number has also been investigated.