The studies of the behavior of fluid on the nano-level has shown to be an important means of influencing the characteristic of fluid must especially in the area of thermal conductivity. Giving relevance in numerous fields such as biomedicine, manufacturing, fuel cells and soon on. This article considers flow and heat transfer of viscous fluid conveying Gold nanoparticles through expanding or contracting porous channel with injection. The nanofluid is described by the high order coupled nonlinear equations of the fourth order which is analyzed utilizing the regular perturbation method whose analytical solutions is adopted in describing the effect of various thermal-fluidic parameters such as Reynolds number and temperature power index. Where results reveals that increasing Reynolds causes an increasing velocity distribution while increasing temperature power index demonstrates decreasing temperature effect. Also comparison of obtained analytical solution against numerical solution shows satisfactory agreement. Study provides good advancement to applications such as fluid transport, power plant operations and manufacturing amongst others.