The novelty of using the AGM and FEM for solutions of partial differential and ordinary equations along a stretchable straight cylinder

Abstract

Near the suction/injection area, a scientific definition for laminar boundary layer flow and heat transfer of an incompressible viscous flow over a stretching cylinder is given. In the study, differential equations with partial derivatives are converted into dimensionless coupled equations using numerical and analytical methods of Akbari- Ganji and Finite Elements Methods. The goal of this first stage of research and research on this topic is to use simplified forms to simplify equations using derivatives of simplified forms; the analysis of the displacement of the heat flux and the velocity gradient will be done using the changes of the Prandtl number. Based on the results obtained on this issue, it is found that the suction process increments surface firmness and quality, whereas the injection decreases surface skin friction. Also, at the points where the water and oil are attached to the surface of the cylinder, the heat has reached its maximum value, and as the distance increases along the Y axis, the temperature decreases. The highest temperature gradient is observed for water fluid. This shows that the use of water fluid around the cylinder accelerates the process of heat transfer from the surface to the outside of the boundary layer. One of the differences between the use of oil and water fluid around the cylinder according to the 2D contours is the difference in the temperature gradient of the two fluids. So that the highest temperature gradient is observed for water fluid.

Keywords

• Suction/injection
• Incompressible viscous flow
• Finite element method
• Stretching cylinder