Mathematical modeling of magnetized nanofluid flow over extending and contracting pipe with heat source and chemical reaction: Error estimation and stability analysis

The aim of the current study is to examine the magnetohydrodynamic (MHD) flow over the permeable pipe containing the nanoparticles with a heat transport mechanism. The leading equations of flow are obtained in terms of partial differential equations (PDEs). The suitable transformation is applied to alter PDEs to ordinary differential equations (ODEs) and solved numerically via the RK4 method. The novelty of the current work is to investigate the MHD nanofluid overextending and shrinking pipe enclosing the chemical reaction with a heat reservoir. The outcomes of different factors are depicted through graphs and tables on the flow phenomena. It is observed that for both situations of wall extension or contraction with injection, the temperature is the increasing function of the thermophoresis and Brownian motion factors. It is explored that the heat is upraised when the heat generation is augmented but decays for heat absorption. The point to be noted here is that the Hartmann number and Prandtl number enhance the heat curves in the presence of a heat source. It is also observed that when the thermophoresis factor is increased the nanoparticles concentration is also enhanced via heat source/sink. The error estimation is computed for different order approximations. For the confirmation of the mathematical modeling, the current study is validated with the previous.