Dual nature study of convective heat transfer of nanofluid flow over a shrinking surface in a porous medium

The aim of present article is the thorough study of heat transfer of nanofluid over a shrinking surface in the presence of thermal radiation. Flow is generated by two-dimensional boundary layer theory. The effects of thermal radiation are seen in energy equation. By using similarity variables, governing nonlinear partial differential equations for momentum and energy are then transformed into dimensionless nonlinear ordinary differential equation along with the convective boundary condition on temperature profile. Emerging parameters are obtained after using the transformations which are later computed analytically to obtain the dual nature exact solution. The dual nature solution is obtained due to shrinking surface that also provide the effect on temperature profile. Results are observed for velocity, temperature, skin friction, Nusselt number and streamlines. The graphical explanation of these solutions is analyzed through the variations of viscosity ratio, mass suction, porous medium and shrinking surface. The suction/injection parameter revels that shrinking parameter gives two solutions in the form of upper and lower branch.