Finite element solution of nonlinear convective flow of Oldroyd-B fluid with Cattaneo-Christov heat flux model over nonlinear stretching sheet with heat generation or absorption

Wubshet Ibrahim ^a,*, Gosa Gadisa ^b

a. Department of Mathematics, Ambo University, Ambo, Ethiopia    
         b. Department of Mathematics, Wollega University, Nekemte, Ethiopia

Abstract: In this study, a two-dimensional boundary layer flow of steady incompressible nonlinear convective flow of Oldroyd-B fluid over a nonlinearly stretching sheet with Cattaneo-Christov heat flux model and heat generation or absorption is examined. The governing equations of the boundary layer flow which are highly nonlinear partial differential equations are converted to the ordinary differential equations using similarity transformations and then the Galerkin finite element method (GFEM) is used to solve the proposed problem. The effect of local Deborah numbers β₁ and β₂, local buoyancy parameter λ, Prandtl number Pr, Deborah number γ, and heat generation/absorption parameter δ on the temperature and the velocity as well as heat transfer rate and shear stress are discussed both in graphical and tabular forms. The result shows the enlargement in the local buoyancy parameter λ will improve the velocity field and the heat transfer rate of the boundary layer flow. Moreover, our present work evinced both local skin friction coefficient and heat transfer rate step up if we add the values of non-linear stretching sheet parameter and local heat generation/absorption parameter has quite the opposite effect. The numerically computed values of local skin friction coefficient and local Nusselt number are validated with available literature and evinced excellent agreement.

Keywords: Galerkin finite element method (GFEM); Oldroyd-B fluid; Cattaneo-Christov heat flux model; Nonlinear convective flow; Nonlinear stretching sheet