in this article using the inverse laplace transform, we show analytical solutions for the generalized mass transfers with (and without) a chemical reaction. these transfers have been expressed as the couette flow with the fractional derivative of the caputo sense. also, using the hankel contour for the bromwich's integral, the solutions are given in terms of the generalized airy functions.

Analytical solutions for non-steady flow are an important aspect of mathematical modeling in all fields of computational science. An analytical solution provides an exact solution for a specific (simplified) test case, which then can be used to test and verify numerical solutions. Within soil physics, there has been a multitude of analytical solutions that model transient flow through onedimens...

Abstract The flow of reactive fluids into porous media, a phenomenon known as infiltration, is important in natural and engineered systems. While most the studies this area cover theoretical experimental analyses linear acid flow, present work concentrates on radial conditions from wellbore field finding exact analytical solutions to moving boundary problems uniform dissolution front. Closed-fo...