Heat and Mass Transfer in Unsteady Third-Grade Fluid with Variable Suction Using Finite Element Method

Abstract

The heat and mass transfer in an unsteady boundary layer flow of an incompressible, laminar, natural convective third-grade fluid is studied. The flow is taken over a semi-infinite vertical porous plate with the temperature-dependent fluid properties by taking into account the effect of viscous dissipation and variable suction. The partial differential equations governing the problem are reduced into the nonlinear, coupled, nondimensional ordinary differential equations with the help of suitable similarity transformations. The Galerkin Finite Element Method is implemented to solve this acquired system. The effects of various significant parameters such as Grashof number, Prandtl number, Eckert number, Solutal Grashof number and Schmidt number on dimensionless velocity, temperature and concentration profiles are presented graphically. The Nusselt number is found to be depressed whereas the Sherwood number is observed to be enhanced with the increasing values of Grashof number and Prandtl number. The study has important applications in chemical process industries such as filtration in food industry, production of drinking water and recovering salts from solutions.