The present study investigates the flow and heat transfer characteristics of blood carrying gold nanoparticles in a porous channel with moving/stationary walls in the presence of thermal radiation. Blood is considered as Newtonian fluid which is the base fluid and gold (Au) as nanoparticles. The governing equations are transformed into system of ordinary differential equations by using similarity transformations. The analytical solutions are obtained for the flow variables by employing homotopy analysis method (HAM). The analytical solutions are compared with the numerical solutions which are obtained by shooting technique along with Runge-Kutta scheme. It was noticed that there is a good agreement between analytical and numerical results. The influence of various parameters on velocity, temperature and heat transfer rate of gold-blood nanofluid has been discussed in detail. The temperature of the nanofluid increases with increasing the nanoparticle volume fraction. The heat transfer rate at the top wall increases with increasing nanoparticle volume fraction while it decreases for a given increase in radiation parameter.

In this paper, a finite element method is proposed to investigate multiple solutions of the Navier-Stokes equations for an unsteady, laminar, incompressible flow in a porous expanding channel. Dual or triple solutions for the fixed values of the wall suction Reynolds number R and the expansion ratio α are obtained numerically. The computed multiple solutions for the symmetric flow are validated by comparing them with approximate analytic solutions obtained by the similarity transformation and homotopy analysis method. Unlike previous works, our method deals with the Navier-Stokes equations directly and thus has no similarity and other restrictions as in previous works. Finally we use the method to study multiple solutions for three cases of the asymmetric flow (which has not been studied before using the similarity-type techniques).