In this study, heat transfer is analyzed for an incompressible steady laminar micropolar fluid flow among two symmetrical stretchable disks. The associated partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) through appropriate similarity transformations and then solved numerically by applying the quasi-linearization method along with the finite difference method (FDM). This impact from certain inclusive parameters in the heat transfer and fluid flow is presented schematically. The results are tabulated and depict that the shear stress rises for the upper disk and the opposite trend for the lower disk. It is also noted that a couple stress and heat transfer rates were reduced across the disks. The slip factor enhances the tangential stress on the top disc and it reduces on the bottom disc. Twisting stress decreases where ϕ ′ η increases due to the effect of the slip factors.

One of the fundamental amino acids for mammals is l -valine, a glycogen-type amino acid. This is an essential amino acid for the production of proteins. N -salicylidene- l -valine is getting attention in recent research due to its distinct structure and elevated catalytic and cytotoxic activity. To understand more about this structure and its characteristics in topological indices, we investigate the chain of supramolecular dialkyltin N -salicylidene- l -valine complexes-2, 3, and 4. We investigate the hyper Zagreb index (HZI), the second HZI, the reduced second HZI, and the hyper-forgotten topological index of the supramolecular chain of certain complexes of N -salicylidene- l -valine. In addition, we analyze graphically and compare these topological invariants.

Differential equations have void applications in several practical situations, sciences, and non sciences as Euler Lagrange equation in classical mechanics, Radioactive decay in nuclear physics, Navier Stokes equations in fluid dynamics, Verhulst equation in biological population growth, Hodgkin Huxley model in neural action potentials, etc. The cantilever bridge problem is very important in Bridge Engineering and this can be modeled as a homogeneous obstacle problem in Mathematics. Due to this and various other applications, obstacle problems become an important part of our literature. A lot of work is dedicated to the solution of the obstacle problems. However, obstacle problems are not solved by the considered method in the literature we have visited. In this work, we have investigated the finding of the exact solution to several obstacle problems using the optimal homotopy asymptotic method (OHAM). The graphical representation of results represents the symmetry among them.