The unsteady liquid film flow of the carbon nanotubes engine oil nanofluid over a non-linear radially extending surface

The enhancement of heat transfer through carbon material is the objective of this study. The renowned class of carbon identified as single walled carbon nanotubes and multi walled carbon nanotubes, nanofluid-flow over a non-linear and unstable surface has been explored. The thermophysical properties of the two sorts of carbon nanotube have been implemented from the experimental outputs in the existent literature using engine oil as a base fluid. The viscous dissipation term has also been included in the energy equation improve the heat transfer rate. The thickness of the nanofluid thin layer is kept variable under the influence of the unstable and non-linear stretching of the disk. The elementary governing equations have been transformed into coupled non-linear differential equations. The problem solution is achieved through BVP 2.0 package of the optimal homotopy analysis method. The square residual error for the momentum and thermal boundary-layers up to the 20th order approximations have been obtained. The numerical ND-solve method has been used to validate the he optimal homotopy analysis method results. The impact of the model parameters vs. velocity field and temperature distribution have been shown through graphs and tables. The impact of the physical parameters on the temperature profile and velocity, pitch for both multi wall carbon nanotubes and single walled carbon nanotubes is gained in the range of 0 ? ? ? 4%. From the obtained results it is observed that the single walled carbon nanotubes nanofluids are more efficient to improve the heat transfer phenomena as compared to the multi wall carbon nanotubes.