MHD flow of a nanofluid in an expanding or contracting porous pipe with chemical reaction and heat source/sink

In the present investigation, an analytical analysis has been carried out to study the influence of chemical reaction on MHD flow of a nanofluid in an expanding or contracting porous pipe in the presence of heat source/sink. The pipe wall expands or contracts uniformly at a time dependent rate. Similarity transformations have been invoked to reduce the governing flow equations into coupled nonlinear ordinary differential equations. An analytical approach, namely the homotopy analysis method (HAM) is employed to obtain the analytical solutions of the ordinary differential equations. The convergence of the obtained series solutions is analyzed. The effects of various physical parameters such as wall expansion ratio, Brownian motion parameter, thermophoresis parameter, Lewis number, chemical reaction parameter and heat source/sink parameter on flow variables have been discussed. Further, for the case of hydrodynamic viscous fluid, we find a good agreement between the HAM solutions and solutions already reported in the literature.