An Application of the Finite Element Method for Heat and Mass Transfer of Boundary Layer Flow Using Variable Thermal Conductivity and Mass Diffusivity

Abstract

Since mass diffusivity and thermal conductivity cannot be considered constants in practical analysis, an existing heat and mass transfer model of unsteady mixed convection flow over a stretching sheet is modified by incorporating the effects of nonlinear mixed convection variable thermal conductivity and mass diffusivity and solved its dimensionless form by applying the finite element method which is the main novelty of this work. Nonlinear governing equations are created because of changing thermal conductivity and mass diffusivity. Nonlinear solutions can be achieved by employing the Galerkin finite element approach. Temperature and concentration-based thermal conductivity and mass diffusivity are considered. The model is expressed as a set of partial differential equations, and furthermore, it is reduced to a system of dimensionless ordinary differential equations. These obtained equations are solved with the finite element method with linear interpolating polynomials and numerical integration. In addition, a Matlab solver bvp4c is also considered for comparison purposes or validation of the computed results. The graphs depict the effect of various parameters on the velocity, temperature, and concentration curves. The results show that thermal and diffusive wave propagation is significantly affected by thermal conductivity and mass diffusivity changes. Results show that flow velocity escalates by rising values of thermal and solutal Grashof numbers.