Investigation of Thin Film Flow on a Stretching Cylinder in Unsteady Motion with variable Heat Source/Sink

In this study, we explore the effects of momentum and heat transfer in a thin liquid film over a cylinder that is stretched and undergoes unsteady motion, with the impact of a magnetic field and a non-uniform heat source/sink. Through the use of similarity transformations, the complex system of PDEs (Partial differential equations) is transformed into the ODEs (Ordinary differential equations). This process involves manipulating the equations in such a way that they can be simplified into a set of ODEs, which are typically easier to solve and analyze. By applying these transformations, the system becomes more manageable and can be studied more effectively. Using the bvp4c function in MATLAB which was provided a powerful tool for solving boundary value problems (BVPs) efficiently, particularly when dealing with systems of ODEs. This function utilizes a robust algorithm to numerically solve the ODE system while considering the specified boundary conditions. Graphs are frequently utilized to visually illustrate the effects of different parameters on temperature and velocity profiles in the presence of a variable heat source/sink and an external magnetic field. When the magnetic parameter increases, we observe that the decrease in the velocity profile and film thickness of the fluid and also Heat source\sink parameters lead to fluid temperature enrichment.