Mathematical Modelling of the Impact of Mass Concentration on Viscoelastic Fluid Flow through a Non-Porous Channel

In this article, we theoretically derived a system of partial differential models representing mass concentration and momentum of viscoelastic fluid flowing through a non-porous channel in dimensional form and were further reduced to a system of ordinary differential equations using the oscillatory perturbation equations. The perturbed ordinary differential equations were solved analytically using the direct method, and the numerical simulation was performed using Wolfram Mathematica, version 12, where the physical parameters such as Schmidt number, solutal Grashof number, retardation time, and the ratio of relaxation to retardation time parameters, oscillatory frequency parameter, and mass concentration parameter were varied at a fixed period of ten units. The investigation reveals that the viscoelastic fluid velocity decreases for an increase in Schmidt number and mass concentration reaction parameter, and the velocity increases for a change in Solutal Grashof number, retardation time parameter, and the relaxation to retardation ratio parameter. In addition, the volumetric flow rate decreases for the increasing values of the Schmidt number and mass concentration reaction parameter; however, the flow rate increases for an increased value of the relaxation to retardation ratio. This study is important in understanding and proposing solutions to viscoelastic fluid flow challenges through a non-porous channel.