A numerical solution for the free convective, unsteady, laminar convective heat and mass transfer in a viscoelastic fluid along a semi-infinite vertical plate is presented. The Walters-B liquid model is employed to simulate medical creams and other rheological liquids encountered in biotechnology and chemical engineering. This rheological model introduces supplementary terms into the momentum conservation equation. The dimensionless unsteady, coupled and non-linear partial differential conservation equations for the boundary layer regime are solved by an efficient, accurate and unconditionally stable finite difference scheme of the Crank-Nicolson type. The velocity, temperature and concentration fields have been studied for the effect of Prandtl number (Pr), viscoelasticity parameter (G), Schmidt number (Sc), Buoyancy ration parameter (N). The local skin-friction, Nusselt number and Sherwood number are also presented and analyzed graphically. It is observed that, when the viscoelasticity parameter (G) increases, the velocity increases close to the plate surface. An increase in Schmidt number is observed to significantly decrease both velocity and concentration.

In the present study, the effects of chemical reaction on unsteady free convection flow of a viscous, electrically conducting, and incompressible fluid past a moving semi-infinite vertical cylinder with mass transfer and temperature oscillation is studied. The dimensionless governing partial differential equations are solved using an implicit finite-difference method of Crank-Nicolson type, which is stable and convergent. The transient velocity, transient temperature, and transient concentration profiles are studied for various parameters. The local as well as average skin-friction, Nusselt number, and Sherwood number are also analyzed and presented graphically. The results are compared with available computations in the literature, and are found to be in good agreement.