​

Abstract :

We propose new approach for the solution of system of semilinear elliptic equationsarising in thermally developing pressure driven flow of nanofluid in a parallel plate problem. A model(Buongiorno model) incorporating the effects of Brownian motion and thermophoresis is adopted. The system of semilinear elliptic equation is derived from the local energy balance equation for above flow problem. A new higher order accurate method is proposed. The proposed method is based on spectral Galerkin- Legendre approach for discretizing spatial derivative and finite difference approach for axial derivatives. Optimal a priori error bounds are derived in the 𝐿 2norm for the semidiscrete formulation. Finally, the effects of parameters such as Lewis number, Schmidt number, Brownian diffusion, and thermophoresis on the heat transfer are studied for both low and high peclet number. The results show that the local Nusselt number is decreased when the Lewis number is increased. 

Keywords: Buongiorno model; Spectral Galerkin- Legendre method; Semilinear elliptic equation; Brownian motion; Error analysis.