DTM- Padé Modeling of Natural Convective Boundary Layer Flow of a Nanofluid Past a Vertical Surface

Abstract

In this paper, we study theoretically the natural convective boundary-layer flow of a nanofluid past a vertical plate. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is developed. The similarity transformations are applied to reduce the governing partial differential equations to a set of nonlinear coupled ordinary differential equations in dimensionless form. A mathematical technique, namely the Differential Transform Method (DTM), is used to solve the nonlinear differential equations under appropriate boundary conditions, in the form of series with easily computable terms. Then, Pad approximants are applied to the solutions to increase the convergence of the given series. The combined DTM-Pad procedure is implemented directly without requiring linearization, discretization or perturbation. The solutions depend on a Lewis number (Le), a buoyancy-ratio number (Nr), a Brownian motion number (Nb), a thermophoresis number (Nt), as well as Prandtl number (Pr). Temperatures are shown to be enhanced with Nb, Nr and Nt increasing. Mass fraction function, f, is also reduced with increasing Le. The flow is accelerated with increasing Pr. The computations also indicate that the reduced Nusselt number is a decreasing function of each of Nr, Nb and Nt. Excellent correlation is also achieved between the DTM-Pad results and numerical shooting quadrature. The model has important applications in heat transfer enhancement in renewable energy systems and industrial thermal management.