A numerical study of free convection heat and mass transfer in a Rivlin–Ericksen viscoelastic flow past an impulsively started vertical plate with variable temperature and concentration

Abstract In this paper an analysis of the effect of viscoelasticity on the natural free convective unsteady laminar heat transfer fluid flowing past an impulsively started vertical plate with variable surface temperature and mass concentration. The Rivlin–Ericksen model is employed to simulate the rheological liquids encountered in cooling of electronic devices, polymer solutions, hydrocarbons and chemical engineering processes. The transport equations employed in the flow are governed by a coupled non-linear system of partial differential equations and include the five parameters. viz. G r (the thermal Grashof number), G m (the solutal Grashof number), Γ (viscoelastic parameter), P r (the fluid Prandtl number) and S c (the Schmidt number). The transformed two-point boundary value problem is solved numerically using the Gauss-Seidel process of the finite element method subjected to appropriate boundary conditions. Numerical results are obtained to study the influence of viscoelasticity parameter ( Γ ), surface temperature power law exponent ( m ) and surface concentration power law ( n ) on the velocity, temperature, concentration fields, the local skin-friction ( τ x ), the Nusselt number ( Nu x ) and the Sherwood number ( Sh x ). The results indicate that the velocity, temperature and concentration fields decrease with increase in viscoelastic parameter. Likewise, the skin friction coefficient, the local Nusselt number and Sherwood number increase with the increase in viscoelastic parameter for X ⩽ 0.48 .